Week 2 Discussion

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C H A P T E R

1What Is Biomechanics? After completing this chapter, you will be able to:

Defi ne the terms biomechanics, statics, dynamics, kinematics, and kinetics, and explain the ways in which they are related.

Describe the scope of scientifi c inquiry addressed by biomechanists.

Distinguish between qualitative and quantitative approaches for analyzing human movement.

Explain how to formulate questions for qualitative analysis of human movement.

Use the 11 steps identifi ed in the chapter to solve formal problems.

O N L I N E L E A R N I N G C E N T E R R E S O U R C E S

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2 BASIC BIOMECHANICS

W hy do some golfers slice the ball? How can workers avoid develop-ing low back pain? What cues can a physical education teacher pro- vide to help students learn the underhand volleyball serve? Why do some elderly individuals tend to fall? We have all admired the fl uid, graceful movements of highly skilled performers in various sports. We have also observed the awkward fi rst steps of a young child, the slow progress of an injured person with a walking cast, and the hesitant, uneven gait of an elderly person using a cane. Virtually every activity class includes a student who seems to acquire new skills with utmost ease and a student who trips when executing a jump or misses the ball when attempting to catch, strike, or serve. What enables some individuals to execute complex movements so easily, while others appear to have diffi culty with relatively simple movement skills?

Although the answers to these questions may be rooted in physiologi- cal, psychological, or sociological issues, the problems identifi ed are all biomechanical in nature. This book will provide a foundation for identify- ing, analyzing, and solving problems related to the biomechanics of hu- man movement.

BIOMECHANICS: DEFINITION AND PERSPECTIVE

The term biomechanics combines the prefi x bio, meaning “life,” with the fi eld of mechanics, which is the study of the actions of forces. The interna- tional community of scientists adopted the term biomechanics during the early 1970s to describe the science involving the study of the mechanical aspects of living organisms (28). Within the fi elds of kinesiology and ex- ercise science, the living organism most commonly of interest is the hu- man body. The forces studied include both the internal forces produced by muscles and the external forces that act on the body.

Learning to walk is an ambitious task from a biomechanical perspective. Photo © PhotoAlto/PictureQuest.

•Courses in anatomy, physiology, mathematics, physics, and engineering provide background knowledge for biomechanists.

biomechanics application of mechanical principles in the study of living organisms

Anthropometric characteristics may predispose an athlete to success in one sport and yet be disadvantageous for participation in another. Photo courtesy of Royalty-Free/CORBIS.

CHAPTER 1: WHAT IS BIOMECHANICS? 3

Biomechanists use the tools of mechanics, the branch of physics in- volving analysis of the actions of forces, to study the anatomical and functional aspects of living organisms (Figure 1-1). Statics and dynam- ics are two major subbranches of mechanics. Statics is the study of sys- tems that are in a state of constant motion, that is, either at rest (with no motion) or moving with a constant velocity. Dynamics is the study of systems in which acceleration is present.

Kinematics and kinetics are further subdivisions of biomechanical study. What we are able to observe visually when watching a body in mo- tion is termed the kinematics of the movement. Kinematics involves the study of the size, sequencing, and timing of movement, without reference to the forces that cause or result from the motion. The kinematics of an ex- ercise or a sport skill execution is also known, more commonly, as form or technique. Whereas kinematics describes the appearance of motion, kinet- ics is the study of the forces associated with motion. Force can be thought of as a push or pull acting on a body. The study of human biomechanics may include questions such as whether the amount of force the muscles are producing is optimal for the intended purpose of the movement.

Although biomechanics is relatively young as a recognized fi eld of sci- entifi c inquiry, biomechanical considerations are of interest in several dif- ferent scientifi c disciplines and professional fi elds. Biomechanists may have academic backgrounds in zoology; orthopedic, cardiac, or sports medicine; biomedical or biomechanical engineering; physical therapy; or kinesiology, with the commonality being an interest in the biomechanical aspects of the structure and function of living things.

The biomechanics of human movement is one of the subdisciplines of kinesiology, the study of human movement (Figure 1-2). Although some biomechanists study topics such as ostrich locomotion, blood fl ow through constricted arteries, or micromapping of dental cavities, this book focuses primarily on the biomechanics of human movement from the perspective of the movement analyst.

As shown in Figure 1-3, biomechanics is also a scientifi c branch of sports medicine. Sports medicine is an umbrella term that encompasses both clinical and scientifi c aspects of exercise and sport. The American College of Sports Medicine is an example of an organization that pro- motes interaction between scientists and clinicians with interests in sports medicine–related topics.

Biomechanics

Mechanics

Function

Structure

FIGURE 1-1

Biomechanics uses the principles of mechanics for solving problems related to the structure and function of living organisms.

mechanics branch of physics that analyzes the actions of forces on particles and mechanical systems

statics branch of mechanics dealing with systems in a constant state of motion

dynamics branch of mechanics dealing with systems subject to acceleration

kinematics study of the description of motion, including considerations of space and time

kinetics study of the action of forces

kinesiology study of human movement

sports medicine clinical and scientifi c aspects of sports and exercise

4 BASIC BIOMECHANICS

What Problems Are Studied by Biomechanists?

As expected given the different scientifi c and professional fi elds repre- sented, biomechanists study questions or problems that are topically di- verse. For example, zoologists have examined the locomotion patterns of dozens of species of animals walking, running, trotting, and galloping at controlled speeds on a treadmill to determine why animals choose a par- ticular stride length and stride rate at a given speed. They have found that running actually consumes less energy than walking in small ani- mals up to the size of dogs, but running is more costly than walking for larger animals such as horses (35). One of the challenges of this type of research is determining how to persuade a cat, a dog, or a turkey to run on a treadmill (Figure 1-4).

Among humans, although the energy cost of running increases with running speed, sizable differences in energy cost between individuals become even larger as running speed increases (21). Although some

Kinesiology

Adapted Physical education

Biomechanics

Sport Philosophy

Motor Control

Sport Art

Athletic Training Exercise

Physiology

Sport Psychology

PedagogySport History

Sports Medicine

Physical Therapy Cardiac

Rehabilitation

Exercise Physiology

Athletic TrainingBiomechanics

Other Medical Specialties

Sport Psychology Orthopedics

Sport NutritionMotor Control

FIGURE 1-2

The subdisciplines of kinesiology.

FIGURE 1-3

The branches of sports medicine.

•In research, each new study, investigation, or experiment is usually designed to address a particular question or problem.

CHAPTER 1: WHAT IS BIOMECHANICS? 5

individuals appear to run more smoothly and comfortably than others, no particular biomechanical factors have been associated with either good or poor running economy (21). Differences in muscle fi ber type com- position appear to translate into differences in energy utilization during running (see Chapter 6) (22).

The U.S. National Aeronautics and Space Administration (NASA) spon- sors another multidisciplinary line of biomechanics research to promote understanding of the effects of microgravity on the human musculoskeletal system. Of concern is the fact that astronauts who have been out of the earth’s gravitational fi eld for just a few days have returned with muscle atrophy, cardiovascular and immune system changes, and reduced bone density, mineralization, and strength, especially in the lower extremities (11). The issue of bone loss, in particular, is currently a limiting factor for long-term space fl ights, with bone lost at a rate of about 1% per month from the lumbar spine and 1.5% per month from the hips (26). Both increased bone resorption and decreased calcium absorption appear to be respon- sible (see Chapter 4) (39).

Since those early days of space fl ight, biomechanists have designed and built a number of exercise devices for use in space to take the place of normal bone-maintaining activities on earth. Some of this research has focused on the design of treadmills for use in space that load the bones of the lower extremity with deformations and strain rates that are optimal for stimulating new bone formation (8, 30). Another approach involves combining voluntary muscle contraction with electrical stimulation of the muscles to maintain muscle mass and tone (44). So far, however, no ad- equate substitute has been found for weight bearing for the prevention of bone and muscle loss in space (11).

Maintaining suffi cient bone-mineral density is also a topic of concern here on earth. Osteoporosis is a condition in which bone mineral mass and strength are so severely compromised that daily activities can cause bone pain and fracturing (13). This condition is found in most elderly

FIGURE 1-4

Research on the biomechanics of animal gaits poses some interesting problems.

6 BASIC BIOMECHANICS

individuals, with earlier onset in women, and is becoming increasingly prevalent throughout the world with the increasing mean age of the pop- ulation. Approximately 40% of women experience one or more osteopo- rotic fractures after age 50, and after age 60, about 90% of all fractures in both men and women are osteoporosis-related (23, 34). The most common fracture site is the vertebrae, with the presence of one fracture indicating increased risk for future vertebral and hip fractures (15). This topic is explored in depth in Chapter 4.

Another problem area challenging biomechanists who study the el- derly is mobility impairment. Age is associated with decreased ability to balance, and older adults both sway more and fall more than young adults, although the reasons for these changes are not well understood. Falls, and particularly fall-related hip fractures, are extremely serious, common, and costly medical problems among the elderly. Each year, falls cause large percentages of the wrist fractures, head injuries, vertebral fractures, and lacerations, as well as over 90% of the hip fractures, occur- ring in the United States (37). Biomechanical research teams are investi- gating the biomechanical factors that enable individuals to avoid falling, the characteristics of safe landings from falls, the forces sustained by dif- ferent parts of the body during falls, and the ability of protective clothing

Exercise in space is critically important for preventing loss of bone mass among astronauts. Photo courtesy of NASA.

CHAPTER 1: WHAT IS BIOMECHANICS? 7

and fl oors to prevent falling injuries (37). Promising work in the develop- ment of intervention strategies has shown that the key to preventing falls may be the ability to limit trunk motion (14). Older adults can quickly learn strategies for limiting trunk motion through task-specifi c training combined with whole-body exercise.

Research by clinical biomechanists has resulted in improved gait among children with cerebral palsy, a condition involving high levels of muscle tension and spasticity. The gait of the cerebral palsy individual is characterized by excessive knee fl exion during stance. This problem is treated by surgical lengthening of the hamstring tendons to improve knee extension during stance. In some patients, however, the procedure also diminishes knee fl exion during the swing phase of gait, resulting in drag- ging of the foot. After research showed that patients with this problem exhibited signifi cant co-contraction of the rectus femoris with the ham- strings during the swing phase, orthopedists began treating the problem by surgically attaching the rectus femoris to the sartorius insertion. This creative, biomechanics research–based approach has enabled a major step toward gait normalization for children with cerebral palsy.

Research by biomedical engineers has also resulted in improved gait for children and adults with below-knee amputations. Ambulation with a prosthesis creates an added metabolic demand, which can be partic- ularly signifi cant for elderly amputees and for young active amputees who participate in sports requiring aerobic conditioning. In response to this problem, researchers have developed an array of lower-limb and foot prostheses that store and return mechanical energy during gait, thereby reducing the metabolic cost of locomotion (2). Studies have shown that the more compliant prostheses are better suited for active and fast walkers, whereas prostheses that provide a more stable base of support are gener- ally preferred for the elderly population (3). Microchip-controlled “Intel- ligent Prostheses” show promise for reducing the energy cost of walking at a range of speeds (7). Researchers are currently developing a new class of “bionic” prosthetic feet that are designed to better imitate normal gait (41).

Occupational biomechanics is a fi eld that focuses on the prevention of work-related injuries and the improvement of working conditions and worker performance. Researchers in this fi eld have learned that work- related low back pain can derive not only from the handling of heavy materials but from unnatural postures, sudden and unexpected mo- tions, and the characteristics of the individual worker (27). Sophisticated biomechanical models of the trunk are now being used in the design of materials-handling tasks in industry to enable minimizing potentially injurious stresses to the low back (4).

Biomechanists have also contributed to performance improvements in selected sports through the design of innovative equipment. One excel- lent example of this is the Klapskate, the speed skate equipped with a hinge near the toes that allows the skater to plantar fl ex at the ankle during push-off, resulting in up to 5% higher skating velocities than were obtainable with traditional skates (17). The Klapskate was designed by van Ingen Schenau and de Groot, based on study of the gliding push-off technique in speed skating by van Ingen Schenau and Baker, as well as work on the intermuscular coordination of vertical jumping by Bobbert and van Ingen Schenau (9). When the Klapskate was used for the fi rst time by competitors in the 1998 Winter Olympic Games, speed records were shattered in every event.

Numerous innovations in sport equipment and apparel have also re- sulted from fi ndings of experiments conducted in experimental cham- bers called wind tunnels that involved controlled simulation of the air

Occupational biomechanics involves study of safety factors in activities such as lifting.

Aerodynamic cycling equipment has contributed to new world records. Photo courtesy of Getty Images.

carpal tunnel syndrome overuse condition caused by compression of the median nerve in the carpal tunnel and involving numbness, tingling, and pain in the hand

8 BASIC BIOMECHANICS

Biomechanists Develop a Revolutionary New Figure Skate

What do 1996 U.S. fi gure skating champion Rudy Galindo and 1998 Olympic gold medal winner Tara Lipinski have in common besides fi gure skating success? They have both had double hip replacements, Galindo at age 32 and Lipinski at age 18.

Overuse injuries among fi gure skaters are on the rise at an alarming rate, with most involving the lower extremities and lower back (4, 12). With skaters performing more and more technically demanding programs including multirotation jumps, on-ice training time for elite skaters now typically includes over 100 jumps per day, six days per week, year after year.

Yet, unlike most modern sports equipment, the fi gure skate has undergone only very minor modifi cations since 1900. The soft-leather, calf-high boots of the nineteenth cen- tury are now made of stiffer leather to promote ankle stability and are not quite as high to allow a small amount of ankle motion. However, the basic design of the rigid boot with a screwed-on steel blade has not changed.

The problem with the traditional fi gure skate is that when a skater lands after a jump, the rigid boot severely restricts motion at the ankle, forcing the skater to land nearly fl at-footed and preventing motion at the ankle that could help attenuate the landing shock that gets translated upward through the musculoskeletal system. Not surprisingly, the incidence of overuse injuries in fi gure skating is mushrooming due to the increased emphasis on performing jumps, the increase in training time, and the continued use of outdated equipment.

To address this problem, biomechanist Jim Richards and graduate student Dustin Bruening, working at the University of Delaware’s Human Performance Lab, have de- signed and tested a new fi gure skating boot. Following the design of modern-day Alpine skiing and in-line skating boots, the new boot incorporates an articulation at the ankle that permits fl exion movement but restricts potentially injurious sideways movement.

The boot enables skaters to land toe-fi rst, with the rest of the foot hitting the ice more slowly. This extends the landing time, thereby spreading the impact force over a longer time and dramatically diminishing the peak force translated up through the body. As shown in the graph, the new boot attenuates the peak landing force on the order of 30%.

Although the new fi gure skating boot design was motivated by a desire to reduce the incidence of stress injuries in skating, it may also promote performance. The ability to

New fi gure skating boot with an articulation at the ankle designed by biomechanists at the University of Delaware.

CHAPTER 1: WHAT IS BIOMECHANICS? 9

resistance actually encountered during particular sports. Examples include the aerodynamic helmets, clothing, and cycle designs used in competitive cycling, and the ultrasmooth suits worn in other competi- tive speed-related events, such as swimming, track, skating, and skiing. Wind tunnel experiments have also been conducted to identify optimal body confi guration during events such as ski jumping (42).

Sport biomechanists have also directed efforts at improving the bio- mechanical, or technique, components of athletic performance. They have learned, for example, that factors contributing to superior performance in the long jump, high jump, and pole vault include high horizontal velocity going into takeoff and a shortened last step that facilitates continued eleva- tion of the total-body center of mass (6, 16). Study of baseball pitchers has determined that high-velocity pitchers display greater external rotation at the shoulder, more forward trunk tilt at ball release, higher-extension angular velocity at the lead knee, and greater angular velocity of the pel- vis and upper torso than lower-velocity pitchers (25, 40).

One rather dramatic example of performance improvement partially at- tributable to biomechanical analysis is the case of four-time Olympic dis- cus champion Al Oerter. Mechanical analysis of the discus throw requires

move through a larger range of motion at the ankle may well enable higher jump heights and concomitantly more rotations while the skater is in the air.

Skaters who adopt the new boot are fi nding that using it effectively requires a period of acclimatization. Those who have been skating in the traditional boot for many years tend to have reduced strength in the musculature surrounding the ankle. Improving ankle strength is likely to be necessary for optimal use of a boot that now allows ankle motion.

The new fi gure skating boot with an articulation at the ankle reduces peak impact forces during landing from a jump on the order of 30%. Graph courtesy of D. Bruening and J. Richards.

0.0 0.000 0.050 0.100 0.150 0.200 0.250

Time (sec)

Standard Peak Force (N) Articulated Peak Force (N)

Reduction (%)

1597.16 1140.27

28.61

0.300 0.350 0.400 0.450 0.500

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

900.0

G ro

un d

R ea

ct io

n Fo

rc e

(N )

1000.0

1100.0

1200.0

1300.0

1400.0

1500.0

1600.0

10 BASIC BIOMECHANICS

precise evaluation of the major mechanical factors affecting the fl ight of the discus. These factors include the following:

1. The speed of the discus when it is released by the thrower 2. The projection angle at which the discus is released 3. The height above the ground at which the discus is released 4. The angle of attack (the orientation of the discus relative to the pre-

vailing air current)

By using computer simulation techniques, researchers can predict the needed combination of values for these four variables that will result in a throw of maximum distance for a given athlete (18). High-speed cameras can record performances in great detail, and when the fi lm or video is analyzed, the actual projection height, velocity, and angle of attack can be compared to the computer-generated values required for optimal perfor- mance. At the age of 43, Oerter bettered his best Olympic performance by 8.2 m. Although it is diffi cult to determine the contributions of motivation and training to such an improvement, some part of Oerter’s success was a result of enhanced technique following biomechanical analysis (38). Most adjustments to skilled athletes’ techniques produce relatively modest re- sults because their performances are already characterized by above- average technique.

Some of the research produced by sport biomechanists has been done in conjunction with the Sports Medicine Division of the United States Olympic Committee (USOC). Typically, this work is done in direct cooper- ation with the national coach of the sport to ensure the practicality of re- sults. USOC-sponsored research has yielded much new information about the mechanical characteristics of elite performance in various sports. Be- cause of continuing advances in scientifi c analysis equipment, the role of sport biomechanists in contributing to performance improvements is likely to be increasingly important in the future.

The infl uence of biomechanics is also being felt in sports popular with both nonathletes and athletes, such as golf. Computerized video analyses of golf swings designed by biomechanists are commonly available at golf courses and equipment shops. The science of biomechanics can play a role in optimizing the distance and accuracy of all golf shots, including put- ting, through analysis of body angles, joint forces, and muscle activity pat- terns (19). A common technique recommendation is to maintain a single fi xed center of rotation to impart force to the ball (19).

Other concerns of sport biomechanists relate to minimizing sport in- juries through both identifying dangerous practices and designing safe equipment and apparel. In recreational runners, for example, research shows that the most serious risk factors for overuse injuries are training errors such as a sudden increase in running distance or intensity, excess cu- mulative mileage, and running on cambered surfaces (20). The complexity of safety-related issues increases when the sport is equipment-intensive. Evaluation of protective helmets involves ensuring not only that the im- pact characteristics offer reliable protection but also that the helmet does not overly restrict wearers’ peripheral vision.

An added complication is that equipment designed to protect one part of the body may actually contribute to the likelihood of injury in another part of the musculoskeletal system. Modern ski boots and bindings, while effec- tive in protecting the ankle and lower leg against injury, unfortunately con- tribute to severe bending moments at the knee when the skier loses balance. Recreational Alpine skiers consequently experience a higher incidence of anterior cruciate ligament tears than participants in any other sport (33). Injuries in snowboarding are also more frequent with rigid, as compared to

•The USOC began funding sports medicine research in 1981. Other countries began sponsoring research to boost the performance of elite athletes in the early 1970s.

•Impact testing of protective sport helmets is carried out scientifi cally in engineering laboratories.

CHAPTER 1: WHAT IS BIOMECHANICS? 11

pliable, boots, although more than half of all snowboarding injuries are to the upper extremity (24, 32).

Another challenging area of research for biomechanists in the realm of sport safety is investigation of the effi cacy of prophylactic knee braces (29). Approximately 60% of all sport injuries are to the knee (36). Research shows that knee braces can contribute 20–30% added resistance against lateral blows to the knee, with custom-fi tted braces providing the best protection (1). A possible concern, however, is that knee braces act to change the pattern of lower-extremity muscle activity during gait, with less work performed at the knee and more at the hip (10). Other docu- mented problems that appear to affect some athletes more than others and may be brace-specifi c include reduced sprinting speed and earlier on- set of fatigue (1). The research literature is almost evenly divided on the effi cacy of prophylactic knee braces in preventing knee ligament injuries in football players, with some studies showing decreases and others show- ing increases in injury incidence (31).

An area of biomechanics research with implications for both safety and performance is sport shoe design. Today sport shoes are designed both to prevent excessive loading and related injuries and to enhance performance. Because the ground or playing surface, the shoe, and the human body compose an interactive system, athletic shoes are specifi cally designed for particular sports, surfaces, and anatomical considerations. Aerobic dance shoes are constructed to cushion the metatarsal arch. Foot- ball shoes to be used on artifi cial turf are designed to minimize the risk of knee injury. Running shoes are available for training and racing on snow and ice. In fact, sport shoes today are so specifi cally designed for desig- nated activities that wearing an inappropriate shoe can contribute to the likelihood of injury.

These examples illustrate the diversity of topics addressed in biome- chanics research, including some examples of success and some areas of continuing challenge. Clearly, biomechanists are contributing to the knowledge base on the full gamut of human movement, from the gait of the physically challenged child to the technique of the elite athlete. Although varied, all of the research described is based on applications of mechanical principles in solving specifi c problems in living organisms. This book is designed to provide an introduction to many of those prin- ciples and to focus on some of the ways in which biomechanical principles may be applied in the analysis of human movement.

Why Study Biomechanics?

As is evident from the preceding section, biomechanical principles are ap- plied by scientists and professionals in a number of fi elds to problems related to human health and performance. Knowledge of basic biomechanical con- cepts is also essential for the competent physical education teacher, physical therapist, physician, coach, personal trainer, or exercise instructor.

An introductory course in biomechanics provides foundational under- standing of mechanical principles and their applications in analyzing movements of the human body. The knowledgeable human movement an- alyst should be able to answer the following types of questions related to biomechanics: Why is swimming not the best form of exercise for individuals with osteoporosis? What is the biomechanical principle behind variable- resistance exercise machines? What is the safest way to lift a heavy object? Is it possible to judge what movements are more/less economi- cal from visual observation? At what angle should a ball be thrown for maximum distance? From what distance and angle is it best to observe

12 BASIC BIOMECHANICS

a patient walk down a ramp or a volleyball player execute a serve? What strategies can an elderly person or a football lineman employ to maximize stability? Why are some individuals unable to fl oat?

Perusing the objectives at the beginning of each chapter of this book is a good way to highlight the scope of biomechanical topics to be covered at the introductory level. For those planning careers that involve visual observation and analysis of human movement, knowledge of these topics will be invaluable.

PROBLEM-SOLVING APPROACH

Scientifi c research is usually aimed at providing a solution for a particu- lar problem or answering a specifi c question. Even for the nonresearcher, however, the ability to solve problems is a practical necessity for function- ing in modern society. The use of specifi c problems is also an effective ap- proach for illustrating basic biomechanical concepts.

Quantitative versus Qualitative Problems

Analysis of human movement may be either quantitative or qualitative. Quantitative implies that numbers are involved, and qualitative refers to a description of quality without the use of numbers. After watching the performance of a standing long jump, an observer might qualitatively state, “That was a very good jump.” Another observer might quantitatively an- nounce that the same jump was 2.1 m in length. Other examples of qualita- tive and quantitative descriptors are displayed in Figures 1-5 and 1-6.

It is important to recognize that qualitative does not mean general. Qualitative descriptions may be general, but they may also be extremely detailed. It can be stated qualitatively and generally, for example, that a man is walking down the street. It might also be stated that the same man is walking very slowly, appears to be leaning to the left, and is bearing weight on his right leg for as short a time as possible. The second description is en- tirely qualitative but provides a more detailed picture of the movement.

Both qualitative and quantitative descriptions play important roles in the biomechanical analysis of human movement. Biomechanical re- searchers rely heavily on quantitative techniques in attempting to answer

quantitative involving the use of numbers

qualitative involving nonnumeric description of quality

FIGURE 1-5

Examples of qualitative and quantitative descriptors.

CHAPTER 1: WHAT IS BIOMECHANICS? 13

specifi c questions related to the mechanics of living organisms. Clinicians, coaches, and teachers of physical activities regularly employ qualitative observations of their patients, athletes, or students to formulate opinions or give advice.

Solving Qualitative Problems

Qualitative problems commonly arise during daily activities. Questions such as what clothes to wear, whether to major in botany or English, and whether to study or watch television are all problems in the sense that they are uncertainties that may require resolution. Thus, a large portion of our daily lives is devoted to the solution of problems.

Analyzing human movement, whether to identify a gait anomaly or to refi ne a technique, is essentially a process of problem solving. Whether the analysis is qualitative or quantitative, this involves identifying, then study- ing or analyzing, and fi nally answering a question or problem of interest.

To effectively analyze a movement, it is essential fi rst to formulate one or more questions regarding the movement. Depending on the specifi c purpose of the analysis, the questions to be framed may be general or spe- cifi c. General questions, for example, might include the following:

1. Is the movement being performed with adequate (or optimal) force? 2. Is the movement being performed through an appropriate range of

motion? 3. Is the sequencing of body movements appropriate (or optimal) for ex-

ecution of the skill? 4. Why does this elderly woman have a tendency to fall? 5. Why is this shot putter not getting more distance?

More specifi c questions might include these:

1. Is there excessive pronation taking place during the stance phase of gait?

2. Is release of the ball taking place at the instant of full elbow extension? 3. Does selective strengthening of the vastus medialis obliquus alleviate

mistracking of the patella for this person?

FIGURE 1-6

Quantitatively, the robot missed the coffee cup by 15 cm. Qualitatively, it malfunctioned.

Coaches rely heavily on qualitative observations of athletes’ performances in formulating advice about technique. Photo courtesy of Ken Karp for MMH.

14 BASIC BIOMECHANICS

Once one or more questions have been identifi ed, the next step in ana- lyzing a human movement is to collect data. The form of data most com- monly collected by teachers, therapists, and coaches is qualitative visual observation data. That is, the movement analyst carefully observes the movement being performed and makes either written or mental notes. To acquire the best observational data possible, it is useful to plan ahead as to the optimal distance(s) and perspective(s) from which to make the observations. These and other important considerations for qualitatively analyzing human movement are discussed in detail in Chapter 2.

Formal versus Informal Problems

When confronted with a stated problem taken from an area of mathemat- ics or science, many individuals believe they are not capable of fi nding a solution. Clearly, a stated math problem is different from a problem such as what to wear to a particular social gathering. In some ways, however, the informal type of problem is the more diffi cult one to solve. According to Wickelgren (43), a formal problem (such as a stated math problem) is characterized by three discrete components:

1. A set of given information 2. A particular goal, answer, or desired fi nding 3. A set of operations or processes that can be used to arrive at the an-

swer from the given information

In dealing with informal problems, however, individuals may fi nd the given information, the processes to be used, and even the goal itself to be unclear or not readily identifi able.

Solving Formal Quantitative Problems

Formal problems are effective vehicles for translating nebulous concepts into well-defi ned, specifi c principles that can be readily understood and applied in the analysis of human motion. People who believe themselves incapable of solving formal stated problems do not recognize that, to a large extent, problem-solving skills can be learned. Entire books on problem- solving approaches and techniques are available. However, most students are not exposed to coursework involving general strategies of the problem- solving process. A simple procedure for approaching and solving problems involves 11 sequential steps:

1. Read the problem carefully. It may be necessary to read the problem several times before proceeding to the next step. Only when you clearly understand the information given and the question(s) to be answered should you undertake step 2.

2. Write down the given information in list form. It is acceptable to use symbols (such as v for velocity) to represent physical quantities if the symbols are meaningful.

3. Write down what is wanted or what is to be determined, using list form if more than one quantity is to be solved for.

4. Draw a diagram representing the problem situation, clearly indicating all known quantities and representing those to be identifi ed with ques- tion marks. (Although certain types of problems may not easily be repre- sented diagrammatically, it is critically important to carry out this step whenever possible to accurately visualize the problem situation.)

5. Identify and write down the relationships or formulas that might be useful in solving the problem. (More than one formula may be useful and/or necessary.)

CHAPTER 1: WHAT IS BIOMECHANICS? 15

6. From the formulas that you wrote down in step 5, select the formula(s) containing both given variables (from step 2) and the variables that are desired unknowns (from step 3). If a formula contains only one unknown variable that is the variable to be determined, skip step 7 and proceed directly to step 8.

7. If you cannot identify a workable formula (in more diffi cult problems), certain essential information was probably not specifi cally stated but can be determined by inference and by further thought on and analy- sis of the given information. If this occurs, it may be necessary to repeat step 1 and review the pertinent information relating to the problem presented in the text.

8. Once you have identifi ed the appropriate formula(s), write the formula(s) and carefully substitute the known quantities given in the problem for the variable symbols.

9. Using the simple algebraic techniques reviewed in Appendix A, solve for the unknown variable by (a) rewriting the equation so that the unknown variable is isolated on one side of the equals sign and (b) reducing the numbers on the other side of the equation to a single quantity.

10. Do a commonsense check of the answer derived. Does it seem too small or too large? If so, recheck the calculations. Also check to ensure that all questions originally posed in the statement of the problem have been answered.

11. Clearly box in the answer and include the correct units of mea- surement.

Figure 1-7 provides a summary of this procedure for solving formal quan- titative problems. These steps should be carefully studied, referred to, and applied in working the quantitative problems included at the end of each chapter. Sample Problem 1.1 illustrates the use of this procedure.

Units of Measurement

Providing the correct units of measurement associated with the answer to a quantitative problem is important. Clearly, an answer of 2 cm is quite different from an answer of 2 km. It is also important to recognize the units of measurement associated with particular physical quantities. Or- dering 10 km of gasoline for a car when traveling in a foreign country would clearly not be appropriate.

The predominant system of measurement still used in the United States is the English system. The English system of weights and measures

inference process of forming deductions from available information

Summary of Steps for Solving Formal Problems

1. 2. 3. 4.

5. 6. 7.

8. 9.

10. 11.

Read the problem carefully. List the given information. List the desired (unknown) information for which you are to solve. Draw a diagram of the problem situation showing the known and unknown information. Write down formulas that may be of use. Identify the formula to use. If necessary, reread the problem statement to determine whether any additional needed information can be inferred. Carefully substitute the given information into the formula. Solve the equation to identify the unknown variable (the desired information). Check that the answer is both reasonable and complete. Clearly box in the answer.

FIGURE 1-7

Using the systematic process helps simplify problem solving.

English system system of weights and measures originally developed in England and used in the United States today

16 BASIC BIOMECHANICS

S A M P L E P R O B L E M 1 . 1

A baseball player hits a triple to deep center fi eld. As he is approaching third base, he notices that the incoming throw to the catcher is wild, and he decides to break for home plate. The catcher retrieves the ball 10 m from the plate and runs back toward the plate at a speed of 5 m/s. As the catcher starts run- ning, the base runner, who is traveling at a speed of 9 m/s, is 15 m from the plate. Given that time 5 distance/speed, who will reach the plate fi rst?

Solution Step 1 Read the problem carefully. Step 2 Write down the given information:

base runner’s speed 5 9 m/s catcher’s speed 5 5 m/s distance of base runner from plate 5 15 m distance of catcher from plate 5 10 m

Step 3 Write down the variable to be identifi ed: Find which player reaches home plate in the shortest time.

Step 4 Draw a diagram of the problem situation. Step 5 Write down formulas of use:

time 5 distance/speed

Step 6 Identify the formula to be used: It may be assumed that the formula provided is appropriate because no other information relevant to the solution has been presented.

Step 7 Reread the problem if all necessary information is not avail- able: It may be determined that all information appears to be available.

Step 8 Substitute the given information into the formula:

time 5 distance

speed Catcher:

time 5 10 m 5 m/s

Base runner:

time 5 15 m 9 m/s

Step 9 Solve the equations: Catcher:

time 5 10 m 5 m/s

time 5 2 s

Base runner:

time 5 15 m 9 m/s

time 5 1.67 s

Step 10 Check that the answer is both reasonable and complete. Step 11 Box in the answer:

The base runner arrives at home plate fi rst, by 0.33 s.

Base runner

15 m

10 m

Catcher

CHAPTER 1: WHAT IS BIOMECHANICS? 17

arose over the course of several centuries primarily for purposes of com- merce and land parceling. Specifi c units came largely from royal decrees. For example, a yard was originally defi ned as the distance from the end of the nose of King Henry I to the thumb of his extended arm. The English system of measurement displays little logic. There are 12 inches to the foot, 3 feet to the yard, 5280 feet to the mile, 16 ounces to the pound, and 2000 pounds to the ton.

The system of measurement that is presently used by every major country in the world except the United States is Le Système Interna- tional d’Unites (the International System of Units), which is commonly known as the S.I. or the metric system. The metric system originated as the result of a request of King Louis XVI to the French Academy of Sci- ences in the 1790s. Although the system fell briefl y from favor in France, it was readopted in 1837. In 1875, the Treaty of the Meter was signed by 17 countries agreeing to adopt the metric system.

Since that time the metric system has enjoyed worldwide popularity for several reasons. First, it entails only four base units—the meter, of length; the kilogram, of mass; the second, of time; and the degree Kelvin, of temperature. Second, the base units are precisely defi ned, reproduc- ible quantities that are independent of factors such as gravitational force. Third, all units excepting those for time relate by factors of 10, in contrast to the numerous conversion factors necessary in converting English units of measurement. Last, the system is used internationally.

For these reasons, as well as the fact that the metric system is used al- most exclusively by the scientifi c community, it is the system used in this book. For those who are not familiar with the metric system, it is useful to be able to recognize the approximate English system equivalents of met- ric quantities. Two conversion factors that are particularly valuable are 2.54 cm for every inch and approximately 4.45 N for every pound. All of the relevant units of measurement in both systems and common English- metric conversion factors are presented in Appendix C.

SUMMARY

Biomechanics is a multidisciplinary science involving the application of mechanical principles in the study of the structure and function of living organisms. Because biomechanists come from different academic back- grounds and professional fi elds, biomechanical research addresses a spec- trum of problems and questions.

Basic knowledge of biomechanics is essential for competent professional analysts of human movement, including physical education teachers, physical therapists, physicians, coaches, personal trainers, and exercise instructors. The structured approach presented in this book is designed to facilitate the identifi cation, analysis, and solution of problems or questions related to human movement.

INTRODUCTORY PROBLEMS

1. Locate and read three articles from the scientifi c literature that report the results of biomechanical investigations. (The Journal of Biome- chanics, the Journal of Applied Biomechanics, and Medicine and Sci- ence in Sports and Exercise are possible sources.) Write a one-page summary of each article, and identify whether the investigation in- volved statics or dynamics and kinetics or kinematics.

metric system system of weights and measures used internationally in scientifi c applications and adopted for daily use by every major country except the United States

2. List 8–10 websites that are related to biomechanics, and write a para- graph describing each site.

3. Write a brief discussion about how knowledge of biomechanics may be useful in your intended profession or career.

4. Choose three jobs or professions, and write a discussion about the ways in which each involves quantitative and qualitative work.

5. Write a summary list of the problem-solving steps identifi ed in the chapter, using your own words.

6. Write a description of one informal problem and one formal problem. 7. Step by step, show how to arrive at a solution to one of the problems

you described in Problem 6. 8. Solve for x in each of the equations below. Refer to Appendix A for

help if necessary. a. x 5 53 e. x2 5 27 1 35 h. 7 3 5 5 240 1 x b. 7 1 8 5 x/3 f. x 5 179 i. 33 5 x/2 c. 4 3 32 5 x 3 8 g. x 1 3 5 138 j. 15 2 28 5 x 3 2 d. 215/3 5 x 1 1

(Answers: a. 125; b. 45; c. 4.5; d. 26; e. 7.9; f. 8.9; g. 3.2; h. 75; i. 54; j. 26.5)

9. Two schoolchildren race across a playground for a ball. Tim starts running at a distance of 15 m from the ball, and Jan starts running at a distance of 12 m from the ball. If Tim’s average speed is 4.2 m/s and Jan’s average speed is 4.0 m/s, which child will reach the ball fi rst? Show how you arrived at your answer. (See Sample Problem 1.1.) (Answer: Jan reaches the ball fi rst.)

10. A 0.5 kg ball is kicked with a force of 40 N. What is the resulting ac- celeration of the ball? (Answer: 80 m/s2)

ADDITIONAL PROBLEMS

1. Select a specifi c movement or sport skill of interest, and read two or three articles from the scientifi c literature that report the results of biomechanical investigations related to the topic. Write a short paper that integrates the information from your sources into a scientifi cally based description of your chosen movement.

2. When attempting to balance your checkbook, you discover that your fi g- ures show a different balance in your account than was calculated by the bank. List an ordered, logical set of procedures that you may use to discover the error. You may use list, outline, or block diagram format.

3. Sarah goes to the grocery store and spends half of her money. On the way home, she stops for an ice cream cone that costs $0.78. Then she stops and spends one-fourth of her remaining money to settle a $5.50 bill at the dry cleaners. How much money did Sarah have originally? (Answer: $45.56)

4. Wendell invests $10,000 in a stock portfolio made up of Petroleum Spe- cial at $30 per share, Newshoe at $12 per share, and Beans & Sprouts at $2.50 per share. He places 60% of the money in P.S., 30% in N, and 10% in B & S. With market values changing (P.S. down $3.12, N up 80%, and B & S up $0.20), what is his portfolio worth six months later? (Answer: $11,856)

5. The hypotenuse of right triangle ABC (shown here) is 4 cm long. What are the lengths of the other two sides? (Answer: A 5 2 cm; B 5 3.5 cm)

6. In triangle DEF, side E is 4 cm long and side F is 7 cm long. If the an- gle between sides E and F is 50 degrees, how long is side D? (Answer: 5.4 cm)

18 BASIC BIOMECHANICS

60º

30º

CHAPTER 1: WHAT IS BIOMECHANICS? 19

7. An orienteer runs 300 m north and then 400 m to the southeast (at a 45° angle to north). If he has run at a constant speed, how far away is he from the starting position? (Answer: 283.4 m)

8. John is out for his daily noontime run. He runs 2 km west, then 2 km south, and then runs on a path that takes him directly back to the place he started at.

a. How far did John run? b. If he has run at an average speed of 4 m/s, how long did the entire

run take? (Answers: a. 6.83 km; b. 28.5 min) 9. John and Al are in a 15 km race. John averages 4.4 m/s during the

fi rst half of the race and then runs at a speed of 4.2 m/s until the last 200 m, which he covers at 4.5 m/s. At what average speed must Al run to beat John? (Answer: . 4.3 m/s)

10. A sailboat heads north at 3 m/s for 1 hour and then tacks back to the southeast (at 45° to north) at 2 m/s for 45 minutes.

a. How far has the boat sailed? b. How far is it from its starting location? (Answers: a. 16.2 km; b. 8.0 km)

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NAME _________________________________________________________

DATE _________________________________________________________

LABORATORY EXPERIENCES

1. Working in a group of 3–5 students, choose three human movements or motor skills with which you are all familiar. (A vertical jump is an example.) For each movement, list at least three general ques- tions and three specifi c questions that an analyst might choose to answer.

Movement/Skill 1: ____________________________________________________________________________

General Questions

1. _____________________________________________________________________________________________

_____________________________________________________________________________________________

2. _____________________________________________________________________________________________

_____________________________________________________________________________________________

3. _____________________________________________________________________________________________

_____________________________________________________________________________________________

Specifi c Questions

1. _____________________________________________________________________________________________

_____________________________________________________________________________________________

2. _____________________________________________________________________________________________

_____________________________________________________________________________________________

3. _____________________________________________________________________________________________

_____________________________________________________________________________________________

Movement/Skill 2: ____________________________________________________________________________

General Questions

1. _____________________________________________________________________________________________

_____________________________________________________________________________________________

2. _____________________________________________________________________________________________

_____________________________________________________________________________________________

3. _____________________________________________________________________________________________

_____________________________________________________________________________________________

Specifi c Questions

1. _____________________________________________________________________________________________

_____________________________________________________________________________________________

22 BASIC BIOMECHANICS

2. _____________________________________________________________________________________________

_____________________________________________________________________________________________

3. _____________________________________________________________________________________________

_____________________________________________________________________________________________

Movement/Skill 3: ____________________________________________________________________________

General Questions

1. _____________________________________________________________________________________________

_____________________________________________________________________________________________

2. _____________________________________________________________________________________________

_____________________________________________________________________________________________

3. _____________________________________________________________________________________________

_____________________________________________________________________________________________

Specifi c Questions

1. _____________________________________________________________________________________________

_____________________________________________________________________________________________

2. _____________________________________________________________________________________________

_____________________________________________________________________________________________

3. _____________________________________________________________________________________________

_____________________________________________________________________________________________

2. Working in a group of 3–5 students, choose a human movement or motor skill with which you are all familiar, and have two members of the group simultaneously perform the movement several times as the group observes. Based on your comparative observations, list any differences and similari- ties that you can detect. Which of these are of potential importance and which are more a matter of personal style?

Movement Differences Important? (Y/N)

_____________________________________________________________ ________________________________

CHAPTER 1: WHAT IS BIOMECHANICS? 23

Movement Similarities Important? (Y/N)

_____________________________________________________________ ________________________________

3. Working in a group of 3–5 students, view a previously taken video or fi lm of a human movement or motor skill performance. After viewing the movement several times, list at least three general ques- tions and three specifi c questions that an analyst might choose to answer regarding the movement.

General Questions

1. _____________________________________________________________________________________________

_____________________________________________________________________________________________

2. _____________________________________________________________________________________________

_____________________________________________________________________________________________

3. _____________________________________________________________________________________________

_____________________________________________________________________________________________

Specifi c Questions

1. _____________________________________________________________________________________________

_____________________________________________________________________________________________

2. _____________________________________________________________________________________________

_____________________________________________________________________________________________

3. _____________________________________________________________________________________________

_____________________________________________________________________________________________

4. Having completed Laboratory Experiences 1–3, discuss in your group the relative advantages and disadvantages of each of the three exercises in terms of your ability to formulate meaningful questions.

5. Have one member of your group perform several trials of walking as the group observes from front, side, and rear views. The subject may walk either on a treadmill or across the fl oor. What observa- tions can be made about the subject’s gait from each view that are not visible or apparent from the other views?

Front View Observations

________________________________________________________________________________________________

24 BASIC BIOMECHANICS

________________________________________________________________________________________________

Side View Observations

________________________________________________________________________________________________

Rear View Observations

________________________________________________________________________________________________

CHAPTER 1: WHAT IS BIOMECHANICS? 25

R E F E R E N C E S

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4. Chaffi n DB: Primary prevention of low back pain through the application of biomechanics in manual materials handling tasks, G Ital Med Lav Ergon 27:40, 2005.

5. Chang YH, Hamerski CM, and Kram R: Applied horizontal force increases impact loading in reduced-gravity running, J Biomech 34:679, 2001.

6. Dapena J and Chung CS: Vertical and radial motions of the body during the take-off phase of high jumping, Med Sci Sports Exerc 20:290, 1988.

7. Datta D, Heller B, and Howitt J: A comparative evaluation of oxygen consumption and gait pattern in amputees using Intelligent Prostheses and conventionally damped knee swing-phase control, Clin Rehabil 19:398, 2005.

8. Davis BL, Cavanagh PR, Sommer HJ 3rd, and Wu, G: Ground reaction forces during locomotion in simulated microgravity, Aviat Space Environ Med 67:235, 1996.

9. De Koning JJ, Houdijk H, de Groot G, and Bobbert MF: From biomechanical theory to application in top sports: the Klapskate story, J Biomech 33:1225, 2000.

10. DeVita P, Torry M, Glover KL, and Speroni DL: A functional knee brace al- ters joint torque and power patterns during walking and running, J Biomech 29:583, 1996.

11. Doty SB: Space fl ight and bone formation, Materwiss Werksttech 35:951, 2004. 12. Dubravcic-Simunjak S, Pecina M, Kuipers H, Moran J, and Haspl M: The inci-

dence of injuries in elite junior fi gure skaters, Am J Sports Med 31:511, 2003. 13. Frost HM: Osteoporosis: a rationale for further defi nitions? Calcif Tissue Int

62:89, 1998. 14. Grabiner MD, Donovan S, Bareither ML, Marone JR, Hamstra-Wright K,

Gatts S, and Troy KL: Trunk kinematics and fall risk of older adults: translat- ing biomechanical results to the clinic, J Electromyogr Kinesiol 18:197, 2007.

15. Greenblatt D: Treatment of postmenopausal osteoporosis, Pharmacotherapy 25:574, 2005.

16. Hay JG and Nohara H: The techniques used by elite long jumpers in prepara- tion for take-off, J Biomech 23:229, 1990.

17. Houdijk H, de Koning JJ, de Groot G, Bobbert MF, and van Ingen Schenau GJ: Push-off mechanics in speed skating with conventional skates and klap- skates, Med Sci Sprt Exerc 32:635, 2000.

18. Hubbard M, de Mestre NJ, and Scott J: Dependence of release variables in the shot put, J Biomech 34:449, 2001.

19. Hume PA, Keogh K, and Reid D: The role of biomechanics in maximizing dis- tance and accuracy of golf shots, Sports Med 35:429, 2005.

20. Johnston CA, Taunton JE, Lloyd-Smith DR, and McKenzie DC: Preventing running injuries. Practical approach for family doctors, Can Fam Physician 49:1101, 2003.

21. Kyröläinen H, Belli A, and Komi P: Biomechanical factors affecting running economy, Med Sci Sports Exer 33:1330, 2001.

22. Kyröläinen H, Kivela R, Koskinen S, McBride J, Andersen JL, Takala T, Sipila S, and Komi PV: Interrelationships between muscle structure, muscle strength, and running economy, Med Sci Sports Exerc 35:45, 2003.

23. Lips P: Epidemiology and predictors of fractures associated with osteoporosis, Am J Med 103:3S, 1997.

24. Machold W, Kwansy O, Gässler P, Kolonja A, Reddy B, Bauer E, and Lehr S: Risk of injury through snowboarding, J Trauma 48:1109, 2000.

25. Matsuo T, Escamilla RF, Fleisig GS, Barrentine SW, and Andrews JR: Com- parison of kinematic and temporal parameters between different pitch veloc- ity groups, J Appl Biomech 17:1, 2001.

26 BASIC BIOMECHANICS

26. McCarthy ID: Fluid shifts due to microgravity and their effects on bone: a review of current knowledge, Ann Biomed Eng 33:95, 2005.

27. McGill SM: Evolving ergonomics? Ergonomics 52:80, 2009. 28. Nelson RC: Biomechanics: past and present. In Cooper JM and Haven B, eds:

Proceedings of the Biomechanics Symposium, Bloomington, Ind, 1980. 29. Paluska SA and McKeag DB: Knee braces: current evidence and clinical rec-

ommendations for their use, Am Fam Physician 61:411, 2000. 30. Peterman MM, Hamel AJ, Cavanagh PR, Paizza SJ, and Shrakey NA: In vitro

modeling of human tibial strains during exercise in micro-gravity, J Biomech 34:693, 2001.

31. Pietrosimone BG, Grindstaff TL, Linens SW, Uczekaj E, Hertel J: A systematic review of prophylactic braces in the prevention of knee ligament injuries in collegiate football players, J Athl Train 43:409, 2008.

32. Pigozzi F, Santori N, Di Salvo V, Parisi A, and Di-Luigi L: Snowboard trauma- tology: an epidemiological study, Orthopedics 20:505, 1997.

33. Prodromos CC, Han Y, Rogowski J, Joyce B, Shi K: A meta-analysis of the in- cidence of anterior cruciate ligament tears as a function of gender, sport, and a knee injury-reduction regimen, Arthroscopy 23:1320, 2007.

34. Recker RR: Osteoporosis, Contemp Nutr 8:1, 1983. 35. Reilly SM, McElroy EJ, and Biknevicius AR: Posture, gait and the ecologi-

cal relevance of locomotor costs and energy-saving mechanisms in tetrapods, Zoology (Jena) 110:271, 2007.

36. Rishiraj N, Taunton JE, Lloyd-Smith R, Woollard R, Regan W, and Clement DB: The potential role of prophylactic/functional knee bracing in preventing knee ligament injury, Sports Med 39:937, 2009.

37. Robinovitch SN, Hsiao ET, Sandler R, Cortez J, Liu Q, and Paiement GD: Pre- vention of falls and fall-related fractures through biomechanics, Exer Sprt Sci Rev 28:74, 2000.

38. Ruby D: Biomechanics—how computers extend athletic performance to the body’s far limits, Popular Science p 58, Jan 1982.

39. Smith SM, Wastney ME, O’Brien KO, Morukov BV, Larina IM, Abrams SA, Davis-Street JE, Oganov V, and Shackelford LC: Bone markers, calcium me- tabolism, and calcium kinetics during extended-duration space fl ight on the mir space station, J Bone Miner Res 20:208, 2004.

40. Stodden DF, Fleisig GS, McLean SP, Lyman SL, and Andrews JR: Relation- ship of pelvis and upper torso kinematics to pitched baseball velocity, J Appl Biomech 17:164, 2001.

41. Versluys R, Beyl P, Van Damme M, Desomer A, Van Ham R, and Lefeber D: Prosthetic feet: state-of-the-art review and the importance of mimicking hu- man ankle-foot biomechanics, Disabil Rehabil Assist Technol 4:65, 2009.

42. Virmavirta M, Kivekäs J, and Komi P: Take-off aerodynamics in ski jumping, J Biomech 34:465, 2001.

43. Wickelgren WA: How to solve problems, San Francisco, 1974, WH Freeman. 44. Yoshimitsu K, Shiva N, Matsuse H, Takano Y, Matsugaki T, Inada T, Tagawa Y,

and Nagata K: Development of a training method for weightless environment using both electrical stimulation and voluntary muscle contraction, Tohoku J Exp Med 220:83, 2010.

A N N OTAT E D R E A D I N G S

Chaffi n DB, Andersson GBJ, and Martin BJ: Occupational biomechanics (3rd ed.), New York, 2006, John Wiley & Sons. Serves as a comprehensive text on the fi eld of occupational biomechanics.

Chapman AE: Biomechanical analysis of fundamental human movements, Cham- paign, IL, 2008, Human Kinetics. Analyzes common fundamental movements such as walking, running, jumping, throwing, climbing, etc.

CHAPTER 1: WHAT IS BIOMECHANICS? 27

Winter DA: Biomechanics and motor control of human movement (4th ed.), New York, 2010, John Wiley & Sons. Serves as an advanced textbook for the study of human biomechanics.

Zeitz P: The art and craft of problem solving (2nd ed.), New York, 2007, John Wiley & Sons. Provides general strategies, as well as specifi c tools and techniques for solving quantitative problems.

R E L AT E D W E B S I T E S

American College of Sports Medicine—Biomechanics Interest Group http://www.acsm.org

Provides a link to the American College of Sports Medicine Member Service Center, which links to the ACSM Interest Groups, including the Biomechanics Interest Group.

American Society of Biomechanics http://asb-biomech.org/

Home page of the American Society of Biomechanics. Provides information about the organization, conference abstracts, and a list of graduate programs in biomechanics.

The Biomch-L Newsgroup http://www.biomch-l.org/

Provides information about an e-mail discussion group for biomechanics and human/animal movement science.

Biomechanics Classes on the Web http://www.uoregon.edu/~karduna/biomechanics/

Contains links to over 100 biomechanics classes with web-based instructional components.

Biomechanics Yellow Pages http://www.sciencecentral.com/site/433521

Provides information on technology used in biomechanics-related work and in- cludes a number of downloadable video clips.

Biomechanics World Wide http://www.uni-due.de/~qpd800/WSITECOPY.html

A comprehensive site with links to other websites for a wide spectrum of topics related to biomechanics.

International Society of Biomechanics http://www.isbweb.org/

Home page of the International Society of Biomechanics (ISB). Provides infor- mation on ISB, biomechanical software and data, and pointers to other sources of biomechanics-related information.

K E Y T E R M S

anthropometric related to the dimensions and weights of body segments

biomechanics application of mechanical principles in the study of living organisms

carpal tunnel syndrome overuse condition caused by compression of the median nerve in the carpal tunnel and involving numbness, tingling, and pain in the hands

dynamics branch of mechanics dealing with systems subject to acceleration

English system system of weights and measures originally developed in England and used in the United States today

inference process of forming deductions from available information

kinematics study of the description of motion, including considerations of space and time

kinesiology study of human movement

28 BASIC BIOMECHANICS

kinetics study of the action of forces

mechanics branch of physics that analyzes the actions of forces on particles and mechanical systems

metric system system of weights and measures used internationally in scientifi c applications and adopted for daily use by every major country except the United States

qualitative involving nonnumeric description of quality

quantitative involving the use of numbers

sports medicine clinical and scientifi c aspects of sports and exercise

statics branch of mechanics dealing with systems in a constant state of motion

C H A P T E R

2Kinematic Concepts for Analyzing Human Motion After completing this chapter, you will be able to:

Provide examples of linear, angular, and general forms of motion.

Identify and describe the reference positions, planes, and axes associated with the human body.

Defi ne and appropriately use directional terms and joint movement terminology.

Explain how to plan and conduct an effective qualitative human movement analysis.

Identify and describe the uses of available instrumentation for measuring kine- matic quantities.

O N L I N E L E A R N I N G C E N T E R R E S O U R C E S

www.mhhe.com/hall6e Log on to our Online Learning Center (OLC) for access to these additional resources:

30 BASIC BIOMECHANICS

I s it best to observe walking gait from a side view, front view, or back view? From what distance can a coach best observe a pitcher’s throw- ing style? What are the advantages and disadvantages of analyzing a movement captured on video? To the untrained observer, there may be no differences in the forms displayed by an elite hurdler and a novice hurdler or in the functioning of a normal knee and an injured, partially rehabilitated knee. What skills are necessary and what procedures are used for effective analysis of human movement kinematics?

One of the most important steps in learning a new subject is master- ing the associated terminology. Likewise, learning a general analysis protocol that can be adapted to specifi c questions or problems within a fi eld of study is invaluable. In this chapter, human movement termi- nology is introduced, and the problem-solving approach is adapted to provide a template for qualitative solving of human movement analysis problems.

FORMS OF MOTION

Most human movement is general motion, a complex combination of lin- ear and angular motion components. Since linear and angular motion are “pure” forms of motion, it is sometimes useful to break complex move- ments down into their linear and angular components when performing an analysis.

Linear Motion

Pure linear motion involves uniform motion of the system of interest, with all system parts moving in the same direction at the same speed. Linear motion is also referred to as translatory motion, or translation. When a body experiences translation, it moves as a unit, and portions of the body do not move relative to each other. For example, a sleeping passenger on a smooth airplane fl ight is being translated through the air. If the pas- senger awakens and reaches for a magazine, however, pure translation is no longer occurring because the position of the arm relative to the body has changed.

Linear motion may also be thought of as motion along a line. If the line is straight, the motion is rectilinear; if the line is curved, the motion is curvilinear. A motorcyclist maintaining a motionless posture as the bike moves along a straight path is moving rectilinearly. If the motorcy- clist jumps the bike and the frame of the bike does not rotate, both rider and bike (with the exception of the spinning wheels) are moving curvi- linearly while airborne. Likewise, a Nordic skier coasting in a locked static position down a short hill is in rectilinear motion. If the skier jumps over a gully with all body parts moving in the same direction at the same speed along a curved path, the motion is curvilinear. When a motorcyclist or skier goes over the crest of a hill, the motion is not lin- ear, because the top of the body is moving at a greater speed than lower body parts. Figure 2-1 displays a gymnast in rectilinear, curvilinear, and rotational motion.

Angular Motion

Angular motion is rotation around a central imaginary line known as the axis of rotation, which is oriented perpendicular to the plane in which the rotation occurs. When a gymnast performs a giant circle on

general motion involving translation and rotation simultaneously

linear along a line that may be straight or curved, with all parts of the body moving in the same direction at the same speed

angular involving rotation around a central line or point

translation linear motion

rectilinear along a straight line

curvilinear along a curved line

axis of rotation imaginary line perpendicular to the plane of rotation and passing through the center of rotation

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 31

a bar, the entire body rotates, with the axis of rotation passing through the center of the bar. When a springboard diver executes a somersault in midair, the entire body is again rotating, this time around an imaginary axis of rotation that moves along with the body. Almost all volitional human movement involves rotation of a body segment around an imag- inary axis of rotation that passes through the center of the joint to which the segment attaches. When angular motion or rotation occurs, portions of the body in motion are constantly moving relative to other portions of the body.

General Motion

When translation and rotation are combined, the resulting movement is general motion. A football kicked end over end translates through the air as it simultaneously rotates around a central axis (Figure 2-2). A runner is translated along by angular movements of body segments at the hip, knee, and ankle. Human movement usually consists of general motion rather than pure linear or angular motion.

Mechanical Systems

Before determining the nature of a movement, the mechanical system of interest must be defi ned. In many circumstances, the entire human body is chosen as the system to be analyzed. In other circumstances, however, the system might be defi ned as the right arm or perhaps even a ball be- ing projected by the right arm. When an overhand throw is executed, the body as a whole displays general motion, the motion of the throwing arm is primarily angular, and the motion of the released ball is linear. The mechanical system to be analyzed is chosen by the movement analyst ac- cording to the focus of interest.

Rotation of a body segment at a joint occurs around an imaginary line known as the axis of rotation that passes through the joint center. Photo © Design Pics/PunchStock.

•Most human movement activities are categorized as general motion.

system object or group of objects chosen by the analyst for study

32 BASIC BIOMECHANICS

STANDARD REFERENCE TERMINOLOGY

Communicating specifi c information about human movement requires spe- cialized terminology that precisely identifi es body positions and directions.

Anatomical Reference Position

Anatomical reference position is an erect standing position with the feet slightly separated and the arms hanging relaxed at the sides, with the

Rectilinear motion

Curvilinear motion

Rotation

FIGURE 2-1

Examples of rectilinear, curvilinear, and rotational motion.

anatomical reference position erect standing position with all body parts, including the palms of the hands, facing forward; considered the starting position for body segment movements

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 33

palms of the hands facing forward. It is not a natural standing position, but is the body orientation conventionally used as the reference position or starting place when movement terms are defi ned.

Directional Terms

In describing the relationship of body parts or the location of an external object with respect to the body, the use of directional terms is necessary. The following are commonly used directional terms:

Superior: closer to the head (In zoology, the synonymous term is cranial.) Inferior: farther away from the head (In zoology, the synonymous term is

caudal.) Anterior: toward the front of the body (In zoology, the synonymous term

is ventral.) Posterior: toward the back of the body (In zoology, the synonymous term

is dorsal.) Medial: toward the midline of the body Lateral: away from the midline of the body Proximal: closer in proximity to the trunk (For example, the knee is proxi-

mal to the ankle.) Distal: at a distance from the trunk (For example, the wrist is distal to

the elbow.) Superfi cial: toward the surface of the body Deep: inside the body and away from the body surface

Curvilinear motion

Rotation

General motion

FIGURE 2-2

General motion is a combination of linear and angular motion.

Anatomical reference position.

34 BASIC BIOMECHANICS

All of these directional terms can be paired as antonyms—words hav- ing opposite meanings. Saying that the elbow is proximal to the wrist is as correct as saying that the wrist is distal to the elbow. Similarly, the nose is superior to the mouth and the mouth is inferior to the nose.

Anatomical Reference Planes

The three imaginary cardinal planes bisect the mass of the body in three dimensions. A plane is a two-dimensional surface with an orientation de- fi ned by the spatial coordinates of three discrete points not all contained in the same line. It may be thought of as an imaginary fl at surface. The sagittal plane, also known as the anteroposterior (AP) plane, divides the body vertically into left and right halves, with each half containing the same mass. The frontal plane, also referred to as the coronal plane, splits the body vertically into front and back halves of equal mass. The horizontal or transverse plane separates the body into top and bottom halves of equal mass. For an individual standing in anatomical reference position, the three cardinal planes all intersect at a single point known as the body’s center of mass or center of gravity (Figure 2-3). These imagi- nary reference planes exist only with respect to the human body. If a person turns at an angle to the right, the reference planes also turn at an angle to the right.

Although the entire body may move along or parallel to a cardinal plane, the movements of individual body segments may also be described as sagittal plane movements, frontal plane movements, and transverse plane movements. When this occurs, the movements being described are usually in a plane that is parallel to one of the cardinal planes. For example, movements that involve forward and backward motion are re- ferred to as sagittal plane movements. When a forward roll is executed, the entire body moves parallel to the sagittal plane. During running in place, the motion of the arms and legs is generally forward and backward, although the planes of motion pass through the shoulder and hip joints rather than the center of the body. Marching, bowling, and cycling are all largely sagittal plane movements (Figure 2-4). Frontal plane movement is lateral (side-to-side) movement; an example of total-body frontal plane movement is the cartwheel. Jumping jacks, side stepping, and side kicks in soccer require frontal plane movement at certain body joints. Examples of total-body transverse plane movement include a twist executed by a diver, trampolinist, or airborne gymnast and a dancer’s pirouette.

Although many of the movements conducted by the human body are not oriented sagittally, frontally, or transversely, or are not planar at all, the three major reference planes are still useful. Gross-body movements and specifi cally named movements that occur at joints are often described as primarily frontal, sagittal, or transverse plane movements.

Anatomical Reference Axes

When a segment of the human body moves, it rotates around an imagi- nary axis of rotation that passes through a joint to which it is attached. There are three reference axes for describing human motion, and each is oriented perpendicular to one of the three planes of motion. The medio- lateral axis, also known as the frontal-horizontal axis, is perpendicular to the sagittal plane. Rotation in the frontal plane occurs around the antero- posterior axis, or sagittal-horizontal axis (Figure 2-5). Transverse plane rotation is around the longitudinal axis, or vertical axis. It is important to recognize that each of these three axes is always associated with the same single plane—the one to which the axis is perpendicular.

•Reference planes and axes are useful in describing gross body movements and in defi ning more specifi c movement terminology.

cardinal planes three imaginary perpendicular reference planes that divide the body in half by mass

sagittal plane plane in which forward and backward movements of the body and body segments occur

frontal plane plane in which lateral movements of the body and body segments occur

transverse plane plane in which horizontal body and body segment movements occur when the body is in an erect standing position

•Although most human movements are not strictly planar, the cardinal planes provide a useful way to describe movements that are primarily planar.

mediolateral axis imaginary line around which sagittal plane rotations occur

anteroposterior axis imaginary line around which frontal plane rotations occur

longitudinal axis imaginary line around which transverse plane rotations occur

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 35

Longitudinal axis

Mediolateral axis

Anteroposterior axis

Frontal plane Sagittal plane

FIGURE 2-3

The three cardinal reference planes.

36 BASIC BIOMECHANICS

Sagittal plane

Anteroposterior axes

FIGURE 2-4

Cycling requires sagittal plane movement of the legs.

FIGURE 2-5

For a jumping jack, the major axes of rotation are anteroposterior axes passing through the shoulders and hips.

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 37

JOINT MOVEMENT TERMINOLOGY

When the human body is in anatomical reference position, all body seg- ments are considered to be positioned at zero degrees. Rotation of a body segment away from anatomical position is named according to the direc- tion of motion and is measured as the angle between the body segment’s position and anatomical position.

Sagittal Plane Movements

From anatomical position, the three primary movements occurring in the sagittal plane are fl exion, extension, and hyperextension (Figure 2-6). Flexion includes anteriorly directed sagittal plane rotations of the head, trunk, upper arm, forearm, hand, and hip, and posteriorly directed sagit- tal plane rotation of the lower leg. Extension is defi ned as the movement that returns a body segment to anatomical position from a position of fl exion, and hyperextension is the rotation beyond anatomical position in the direction opposite the direction of fl exion. If the arms or legs are internally or externally rotated from anatomical position, fl exion, exten- sion, and hyperextension at the knee and elbow may occur in a plane other than the sagittal.

Sagittal plane rotation at the ankle occurs both when the foot is moved relative to the lower leg and when the lower leg is moved relative to the foot. Motion bringing the top of the foot toward the lower leg is known as dorsifl exion, and the opposite motion, which can be visualized as “plant- ing” the ball of the foot, is termed plantar fl exion (Figure 2-7).

•Sagittal plane movements include fl exion, extension, and hyperextension, as well as dorsifl exion and plantar fl exion.

Flexion Extension Hyperextension

FIGURE 2-6

Sagittal plane movements at the shoulder.

Dorsiflexion Plantar flexion

FIGURE 2-7

Sagittal plane movements of the foot.

38 BASIC BIOMECHANICS

Abduction Adduction

Lateral flexion (right) Lateral flexion (left)

Frontal Plane Movements

The major frontal plane rotational movements are abduction and adduc- tion. Abduction (abduct meaning “to take away”) moves a body segment away from the midline of the body; adduction (add meaning “to bring back”) moves a body segment closer to the midline of the body (Figure 2-8).

Other frontal plane movements include sideways rotation of the trunk, which is termed right or left lateral fl exion (Figure 2-9). Elevation and depression of the shoulder girdle refer to movement of the shoulder girdle in superior and inferior directions, respectively (Figure 2-10). Rotation of the hand at the wrist in the frontal plane toward the radius (thumb side) is referred to as radial deviation, and ulnar deviation is hand rotation toward the ulna (little fi nger side) (Figure 2-11).

Movements of the foot that occur largely in the frontal plane are ever- sion and inversion. Outward rotation of the sole of the foot is termed ever- sion, and inward rotation of the sole of the foot is called inversion (Figure 2-12). Abduction and adduction are also used to describe outward and in- ward rotation of the entire foot. Pronation and supination are often used to describe motion occurring at the subtalar joint. Pronation at the subta- lar joint consists of a combination of eversion, abduction, and dorsifl exion, and supination involves inversion, adduction, and plantar fl exion.

FIGURE 2-8

Frontal plane movements at the hip.

•Frontal plane movements include abduction and adduction, lateral fl exion, elevation and depression, inversion and eversion, and radial and ulnar deviation.

FIGURE 2-9

Frontal plane movements of the spinal column.

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 39

Elevation Depression

FIGURE 2-10

Frontal plane movements of the shoulder girdle.

Ulnar deviation Radial deviation

FIGURE 2-11

Frontal plane movements of the hand.

Eversion Inversion

FIGURE 2-12

Frontal plane movements of the foot.

40 BASIC BIOMECHANICS

Transverse Plane Movements

Body movements in the transverse plane are rotational movements about a longitudinal axis. Left rotation and right rotation are used to describe transverse plane movements of the head, neck, and trunk. Rotation of an arm or leg as a unit in the transverse plane is called medial rotation, or internal rotation, when rotation is toward the midline of the body, and lateral rotation, or external rotation, when the rotation is away from the midline of the body (Figure 2-13).

Specifi c terms are used for rotational movements of the forearm. Out- ward and inward rotations of the forearm are respectively known as su- pination and pronation (Figure 2-14). In anatomical position the forearm is in a supinated position.

Although abduction and adduction are frontal plane movements, when the arm or thigh is fl exed to a position, movement of these segments in the transverse plane from an anterior position to a lateral position is termed horizontal abduction, or horizontal extension (Figure 2-15). Move- ment in the transverse plane from a lateral to an anterior position is called horizontal adduction, or horizontal fl exion.

Other Movements

Many movements of the body limbs take place in planes that are oriented diagonally to the three traditionally recognized cardinal planes. Because human movements are so complex, however, nominal identifi cation of ev- ery plane of human movement is impractical.

One special case of general motion involving circular movement of a body segment is designated as circumduction. Tracing an imaginary circle in the air with a fi ngertip while the rest of the hand is stationary requires circumduction at the metacarpophalangeal joint (Figure 2-16). Circumduction combines fl exion, extension, abduction, and adduction, re- sulting in a conical trajectory of the moving body segment.

Medial rotation

Medial Lateral

Lateral rotation

FIGURE 2-13

Transverse plane movements of the leg.

•Transverse plane movements include left and right rotation, medial and lateral rotation, supination and pronation, and horizontal abduction and adduction.

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 41

Pronation Supination

FIGURE 2-14

Transverse plane movements of the forearm.

Horizontal adduction

Horizontal abduction

FIGURE 2-15

Transverse plane movements at the shoulder.

42 BASIC BIOMECHANICS

SPATIAL REFERENCE SYSTEMS

Whereas the three cardinal planes and their associated axes of rotation move along with the body, it is also often useful to make use of a fi xed system of reference. When biomechanists quantitatively describe the movement of living organisms, they use a spatial reference system to standardize the measurements taken. The system most commonly used is a Cartesian coordinate system, in which units are measured in the directions of either two or three primary axes.

Movements that are primarily in a single direction, or planar, such as running, cycling, or jumping, can be analyzed using a two-dimensional Cartesian coordinate system (Figure 2-17). In two-dimensional Cartesian coordinate systems, points of interest are measured in units in the x, or horizontal, direction and in the y, or vertical, direction. When a biomecha- nist is analyzing the motion of the human body, the points of interest are usually the body’s joints, which constitute the end points of the body seg- ments. The location of each joint center can be measured with respect to the two axes and described as (x,y), where x is the number of horizontal units away from the y-axis and y is the number of vertical units away from the x-axis. These units can be measured in both positive and negative di- rections (Figure 2-18). When a movement of interest is three-dimensional, the analysis can be extended to the third dimension by adding a z-axis perpendicular to the x- and y-axes and measuring units away from the x,y plane in the z direction. With a two-dimensional coordinate system, the y-axis is normally vertical, and the x-axis horizontal. In the case of a three-dimensional coordinate system, it is usually the z-axis that is verti- cal, with the x- and y-axes representing the two horizontal directions.

QUALITATIVE ANALYSIS OF HUMAN MOVEMENT

A good command of the language associated with forms of motion, stan- dard reference terminology, and joint movement terminology is essential for being able to describe a qualitative analysis of human movement. The ability to qualitatively assess human movement also requires both knowl-

Circumduction

FIGURE 2-16

Circumduction of the index fi nger at the metacarpophalangeal joint.

A tennis serve requires arm movement in a diagonal plane.

•Qualitative analysis requires knowledge of the specifi c biomechanical purpose of the movement and the ability to detect the causes of errors.

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 43

edge of the movement characteristics desired and the ability to observe and analyze whether a given performance incorporates these characteristics. As introduced in Chapter 1, the word qualitative refers to a description of quality without the use of numbers. Visual observation is the most com- monly used approach for qualitatively analyzing the mechanics of human movement. Based on information gained from watching an athlete perform a skill, a patient walk down a ramp, or a student attempt a novel task, coaches, clinicians, and teachers make judgments and recommendations on a daily basis. To be effective, however, a qualitative analysis cannot be conducted haphazardly, but must be carefully planned and conducted by an analyst with knowledge of the biomechanics of the movement.

Prerequisite Knowledge for a Qualitative Analysis

There are two main sources of information for the analyst diagnosing a motor skill. The fi rst is the kinematics or technique exhibited by the performer, and the second is the performance outcome. Evaluating perfor- mance outcome is of limited value, since the root of optimal performance outcome is appropriate biomechanics.

To effectively analyze a motor skill, it is very helpful for the analyst to understand the specifi c purpose of the skill from a biomechanical per- spective. The general goal of a volleyball player serving a ball is to legally project the ball over the net and into the opposite court. Specifi cally, this

FIGURE 2-17

A Cartesian coordinate system showing the x and y coordinates of the hip.

(0,0) x

(x,y ) 5 (3,7)

(0,0)

x 5 1 y 5 1

x 5 2 y 5 1

x 5 1 y 5 2

x 5 2 y 5 2

y FIGURE 2-18

Coordinates can be both positive and negative in a Cartesian coordinate system.

44 BASIC BIOMECHANICS

requires a coordinated summation of forces produced by trunk rotation, shoulder extension, elbow extension, and forward translation of the total- body center of gravity, as well as contacting the ball at an appropriate height and angle. Whereas the ultimate purpose of a competitive sprint cyclist is to maximize speed while maintaining balance in order to cross the fi nish line fi rst, biomechanically this requires factors such as maxi- mizing perpendicular force production against the pedals and maintain- ing a low body profi le to minimize air resistance.

Without knowledge of relevant biomechanical principles, analysts may have diffi culty in identifying the factors that contribute to (or hinder) per- formance and may misinterpret the observations they make. More spe- cifi cally, to effectively analyze a motor skill, the analyst must be able to identify the cause of a technique error, as opposed to a symptom of the error, or a performance idiosyncrasy. Inexperienced coaches of tennis or golf may focus on getting the performer to display an appropriate follow-through after hitting the ball. Inadequate follow-through, however, is merely a symptom of the underlying performance error, which may be failure to begin the stroke or swing with suffi cient trunk rotation and backswing, or failure to swing the racquet or club with suffi cient velocity. The ability to identify the cause of a performance error is dependent on an understand- ing of the biomechanics of the motor skill.

One potential source of knowledge about the biomechanics of a motor skill is experience in performing the skill. A person who performs a skill profi ciently usually is better equipped to qualitatively analyze that skill than is a person less familiar with the skill. For example, advanced bat- ters demonstrate greater perceptual decision making during a pitch than do intermediate batters, particularly when the pitch is a curve ball (4). In most cases, a high level of familiarity with the skill or movement being performed improves the analyst’s ability to focus attention on the critical aspects of the event.

Direct experience in performing a motor skill, however, is not the only or necessarily the best way to acquire expertise in analyzing the skill. Skilled athletes often achieve success not because of the form or technique they display, but in spite of it! Furthermore, highly accomplished athletes do not always become the best coaches, and highly successful coaches may have had little or no participatory experience in the sports they coach.

The conscientious coach, teacher, or clinician typically uses several ave- nues to develop a knowledge base from which to evaluate a motor skill. One is to read available materials from textbooks, scientifi c journals, and lay (coaching) journals, despite the facts that not all movement patterns and skills have been researched and that some biomechanics literature is so esoteric that advanced training in biomechanics is required to understand it. However, when selecting reading material, it is important to distinguish between articles supported by research and those based primarily on opin- ion, as “commonsense” approaches to skill analyses may be fl awed. There are also opportunities to interact directly with individuals who have expert knowledge of particular skills at conferences and workshops.

Planning a Qualitative Analysis

Even the simplest qualitative analysis may yield inadequate or faulty information if approached haphazardly. As the complexity of the skill and/or the level of desired analytical detail increases, so does the level of required planning.

The fi rst step in any analysis is to identify the major question or ques- tions of interest. Often, these questions have already been formulated by

Many jobs require conducting qualitative analyses of human movement daily. Photo courtesy of Digital Vision/Alamy.

•Analysts should be able to distinguish the cause of a problem from symptoms of the problem or an unrelated movement idiosyncrasy.

•Experience in performing a motor skill does not necessarily translate to profi ciency in analyzing the skill.

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 45

the analyst, or they serve as the original purpose for the observation. For example, has a post–knee surgery patient’s gait returned to normal? Why is a volleyball player having diffi culty hitting cross-court? What might be causing a secretary’s wrist pain? Or simply, is a given skill being per- formed as effectively as possible? Having one or more particular ques- tions or problems in mind helps to focus the analysis. Preparing a criteria sheet or a checklist prior to performing an analysis is a useful way to help focus attention on the critical elements of the movement being evalu- ated. Of course, the ability to identify appropriate analysis questions and formulate a checklist is dependent on the analyst’s knowledge of the bio- mechanics of the movement. When an analyst is observing a skill that is less than familiar, it can be helpful to recall that many motor skills have commonalities. For example, serves in tennis and volleyball and the bad- minton overhead clear are all very similar to the overarm throw.

The analyst should next determine the optimal perspective(s) from which to view the movement. If the major movements are primarily pla- nar, as with the legs during cycling or the pitching arm during a softball pitch, a single viewing perspective such as a side view or a rear view may be suffi cient. If the movement occurs in more than one plane, as with the motions of the arms and legs during the breaststroke or the arm motion during a baseball batter’s swing, the observer may need to view the move- ment from more than one perspective to see all critical aspects of interest. For example, a rear view, a side view, and a top view of a martial artist’s kick all yield different information about the movement (Figure 2-19).

The analyst’s viewing distance from the performer should also be se- lected thoughtfully (Figure 2-20). If the analyst wishes to observe sub- talar pronation and supination in a patient walking on a treadmill, a close-up rear view of the lower legs and feet is necessary. Analyzing where a particular volleyball player moves on the court during a series of plays under rapidly changing game conditions is best accomplished from a rea- sonably distant, elevated position.

Another consideration is the number of trials or executions of the movement that should be observed in the course of formulating an analy- sis. A skilled athlete may display movement kinematics that deviate only slightly across performances, but a child learning to run may take no two steps alike. Basing an analysis on observation of a single performance is usually unwise. The greater the inconsistency in the performer’s kine- matics, the larger the number of observations that should be made.

Other factors that potentially infl uence the quality of observations of human movement are the performer’s attire and the nature of the sur- rounding environment. When biomechanic researchers study the kine- matics of a particular movement, the subjects typically wear minimal attire so that movements of body segments will not be obscured. Although there are many situations, such as instructional classes, competitive events, and team practices, for which this may not be practical, analysts should be aware that loose clothing can obscure subtle motions. Adequate lighting and a nondistracting background of contrasting color also im- prove the visibility of the observed movement.

A fi nal consideration is whether to rely on visual observation alone or to use a video camera. As the speed of the movement of interest increases, it becomes progressively less practical to rely on visual observation. Con- sequently, even the most careful observer may miss important aspects of a rapidly executed movement. Video also enables the performer to view the movement, as well as allowing repeated viewing of the movement by analyst and performer, enabling performance feedback that can enhance the learning of a motor skill. Most playback units also enable slow-motion

A tennis player’s eyes should follow the oncoming ball long enough to enable the player to contact the ball with the racquet.

•Repeated observation of a motor skill is useful in helping the analyst to distinguish consistent performance errors from random errors.

•Use of a video camera provides both advantages and disadvantages to the movement analyst.

46 BASIC BIOMECHANICS

Primarily planar skills

Multiplanar skills

FIGURE 2-19

Whereas skills that are primarily planar may require only one viewing perspective, the movement analyst should view multiplanar skills from more than one direction.

Close-up view

Medium distance

view

Distant view

FIGURE 2-20

The observation distance between analyst and performer should be selected based on the specifi c questions of interest.

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 47

viewing and single-picture advance that facilitate isolation of the critical aspects of a movement.

The analyst should be aware, however, that there is a potential draw- back to the use of video. The subject’s awareness of the presence of a cam- era sometimes results in changes in performance. Movement analysts should be aware that subjects may be distracted or unconsciously modify their techniques when a recording device is used.

Conducting a Qualitative Analysis

Despite careful planning of a qualitative analysis, new questions occa- sionally emerge during the course of collecting observations. Movement modifi cations may be taking place with each performance as learning oc- curs, especially when the performer is unskilled. Even when this is not the case, the observations made may suggest new questions of interest. For example, what is causing the inconsistencies in a golfer’s swing? What technique changes are occurring over the 30–40 m range in a 100 m sprint? A careful analysis is not strictly preprogrammed, but often involves iden- tifying new questions to answer or problems to solve. The teacher, clini- cian, or coach often is involved in a continuous process of formulating an analysis, collecting additional observations, and formulating an updated analysis (Figure 2-21).

Answering questions that have been identifi ed requires that the ana- lyst be able to focus on the critical aspects of the movement. Once a bio- mechanical error has been generally identifi ed, it is often useful for the analyst to watch the performer over several trials and to progressively zero in on the specifi c problem. Evaluating a softball pitcher’s technique might begin with observation of insuffi cient ball speed, progress to an evaluation of upper-extremity kinematics, and end with an identifi cation of insuffi cient wrist snap at ball release.

Identify question/problem

Make decisions

Interpret observations

Viewing angle

Viewing distance

Performer attire

Environmental modifications

Use of video

Auditory

From performer

From other analysts

Collect observations

Communicate with performer

End analysis

Visual

Refine question

FIGURE 2-21

The qualitative analysis process is often cyclical, with observations leading to refi nement of the original question.

48 BASIC BIOMECHANICS

The analyst should also be aware that every performance of a motor skill is affected by the characteristics of the performer. These include the performer’s age, gender, and anthropometry; the developmental and skill levels at which the performer is operating; and any special physical or personality traits that may impact performance. Providing a novice, pre- school-aged performer with cues for a skilled, mature performance may be counterproductive, since young children do not have the same motor capabilities as adults. Likewise, although training can ameliorate loss of muscular strength and joint range of motion once thought to be inevi- tably associated with aging, human movement analysts need increased knowledge of and sensitivity to the special needs of older adults who wish to develop new motor skills. Analysts should also be aware that, although gender has traditionally been regarded as a basis for performance differ- ences, research has shown that before puberty most gender-associated performance differences are probably culturally derived rather than bio- logically determined (3). Young girls are usually not expected to be as skilled or even as active as young boys. Unfortunately, in many settings, these expectations extend beyond childhood into adolescence and adult- hood. The belief that an activity is not gender appropriate has been shown to negatively affect college-aged women’s ability to learn a new motor skill (1). Analysts of female performers should not reinforce this cultural misunderstanding by lowering their expectations of girls or women based on gender. Analysts should also be sensitive to other factors that can in- fl uence performance. Has the performer experienced a recent emotional upset? Is the sun in his eyes? Is she tired? Being an effective observer requires full awareness of the surrounding environment.

To supplement visual observation, the analyst should be aware that nonvisual forms of information can also sometimes be useful during a movement analysis. For example, auditory information can provide clues about the way in which a movement was executed. Proper contact of a golf club with a ball sounds distinctly different from when a golfer “tops” the ball. Similarly, the crack of a baseball bat hitting a ball indicates that the contact was direct rather than glancing. The sound of a double contact of a volleyball player’s arms with the ball may identify an illegal hit. The sound of a patient’s gait usually reveals whether an asymmetry is present.

Another potential source of information is feedback from the performer (Sample Application 2.1). A performer who is experienced enough to recog- nize the way a particular movement feels as compared to the way a slight modifi cation of the same movement feels is a useful source of informa- tion. However, not all performers are suffi ciently kinesthetically attuned to provide meaningful subjective feedback of this nature. The performer being analyzed may also assist in other ways. Performance defi ciencies may result from errors in technique, perception, or decision making. Iden- tifi cation of perceptual and decision-making errors by the performer often requires more than visual observation of the performance. In these cases, asking meaningful questions of the performer may be useful. However, the analyst should consider subjective input from the performer in conjunc- tion with more objective observations.

Another potential way to enhance the thoroughness of an analysis is to involve more than one analyst. This reduces the likelihood of oversight. Students in the process of learning a new motor skill may also benefi t from teaming up to analyze each other’s performances under appropriate teacher direction.

Finally, analysts must remember that observation skills improve with practice. As analysts gain experience, the analysis process becomes more natural, and the analyses conducted are likely to become more effective

•Auditory information is often a valuable source in the analysis of human motor skills.

•The ability to effectively analyze human movement improves with practice.

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 49

S A M P L E A P P L I C A T I O N 2 . 1

Problem: Sally, a powerful outside hitter on a high school volleyball team, has been out for two weeks with mild shoulder bursitis but has recently received her physician’s clearance to return to practice. Joan, Sally’s coach, notices that Sally’s spikes are traveling at a slow speed and are being easily handled by the defensive players.

Planning the Analysis 1. What specifi c problems need to be solved or questions need to be an-

swered regarding the movement? Joan fi rst questions Sally to make sure that the shoulder is not painful. She then reasons that a tech- nique error is present.

2. From what angle(s) and distance(s) can problematic aspects of the move- ment best be observed? Is more than one view needed? Although a vol- leyball spike involves transverse plane rotation of the trunk, the arm movement is primarily in the sagittal plane. Joan therefore decides to begin by observing a sagittal view from the side of Sally’s hitting arm.

3. How many movement performances should be observed? Since Sally is a skilled player and her spikes are consistently being executed at reduced velocity, Joan reasons that only a few observations may be needed.

4. Is special subject attire, lighting, or background environment needed to facilitate observation? The gym where the team works out is well lit and the players wear sleeveless tops. Therefore, no special accommoda- tions for the analysis seem necessary.

5. Will a video recording of the movement be necessary or useful? A vol- leyball spike is a relatively fast movement, but there are defi nite check- points that the knowledgeable observer can watch in real time. Is the jump primarily vertical, and is it high enough for the player to contact the ball above the net? Is the hitting arm positioned with the upper arm in maximal horizontal abduction prior to arm swing to allow a full range of arm motion? Is the hitting movement initiated by trunk rota- tion followed by shoulder fl exion, then elbow extension, then snaplike wrist fl exion? Is the movement being executed in a coordinated fashion to enable imparting a large force to the ball?

Conducting the Analysis 1. Review, and sometimes reformulate, specifi c questions of focus. After

watching Sally execute two spikes, Joan observes that her arm range of motion appears to be relatively small.

2. Repeatedly view movements to gradually zero in on causes of per- formance errors. After watching Sally spike three more times, Joan suspects that Sally is not positioning her upper arm in maximal hori- zontal abduction in preparation for the hit.

3. Be aware of the infl uence of performer characteristics. Joan talks to Sally on the sideline and asks her to put her arm in the preparatory position for a hit. She asks Sally if this position is painful, and Sally responds that it is not.

4. Pay attention to nonvisual cues. (None are apparent in this situation.) 5. When appropriate, ask the performer to self-analyze. Joan tells Sally

that she suspects Sally has been protecting the shoulder by not rotating her arm back far enough in preparation for spikes. She can correct the problem. Sally’s next few spikes are executed at much faster velocity.

6. Consider involving other analysts to assist. Joan asks her assistant coach to watch Sally for the remainder of practice to determine whether the problem has been corrected.

50 BASIC BIOMECHANICS

and informative. The expert analyst is typically better able to both identify and diagnose errors than the novice. Novice analysts should take every opportunity to practice movement analysis in carefully planned and structured settings, as such practice has been shown to improve the ability to focus attention on the critical aspects of performance (2).

TOOLS FOR MEASURING KINEMATIC QUANTITIES

Biomechanics researchers have available a wide array of equipment for studying human movement kinematics. Knowledge gained through the use of this apparatus is often published in professional journals for teach- ers, clinicians, coaches, and others interested in human movement.

Video and Film

Photographers began employing cameras in the study of human and ani- mal movement during the late nineteenth century. One famous early pho- tographer was Eadweard Muybridge, a British landscape photographer and a rather colorful character who frequently published essays prais- ing his own work. Muybridge used electronically controlled still cameras aligned in sequence with an electromagnetic tripping device to capture serial shots of trotting and galloping horses, thereby resolving the con- troversy about whether all four hooves are ever airborne simultaneously (they are). More importantly, however, he amassed three volumes of pho- tographic work on human and animal motions that provided scientifi c documentation of some of the subtle differences between normal and pathological gait.

Movement analysts today have quite an array of camera types from which to choose. The type of movement and the requirements of the analysis largely determine the camera and analysis system of choice. Standard video provides 30 resolvable pictures per second, which is per- fectly adequate for many human movement applications. Scientists and clinicians performing detailed quantitative study of the kinematics of human motion typically require a more sophisticated video camera and playback unit, with higher rates of picture capture. Digital video cap- ture systems designed for human movement analysis are commercially available with frame rates of up to 2000 Hz. For both qualitative and quantitative analysis, however, a consideration often of greater impor- tance than camera speed is the clarity of the captured images. It is the camera’s shutter speed that allows user control of the exposure time, or length of time that the shutter is open when each picture in the video record is taken. The faster the movement being analyzed, the shorter the duration of the exposure time required to prevent blurring of the image captured.

Another important consideration when analyzing human movement with video is the number of cameras required to adequately capture the aspects of interest. Because most human movement is not constrained to a single plane, it is typically necessary to use multiple cameras to en- sure that all of the movements can be viewed and recorded accurately for a detailed analysis. When practicality dictates that a single camera be used, thoughtful consideration should be given to camera positioning rela- tive to the movement of interest. Only when human motion is occurring perpendicular to the optical axis of a camera are the angles present at joints viewed without distortion.

Motion analysis software tracks joint markers in three- dimensional space.

Refl ective joint markers can be tracked by a camera for automatic digitizing of the movement.

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 51

Biomechanists typically conduct quantitative analyses of human motion by adhering small, refl ective markers over the subject’s joint centers and other points of interest on the body, with marker locations depending on the purpose of the analysis. High-speed digital video cam- eras with infrared light rings encircling the lenses then capture high- contrast images of the refl ective markers. Since human motion is rarely purely planar, researchers typically position six to eight and sometimes more cameras around the staging area in strategic locations to enable generation of three-dimensional representations of the movements of the markers. Much of today’s biomechanical analysis software is capable of providing graphical outputs displaying kinematic and kinetic quan- tities of interest within minutes after a motion has been digitally cap- tured by the cameras.

Other Movement-Monitoring Systems

An accelerometer is a transducer used for the direct measurement of acceleration. The accelerometer is attached as rigidly as possible to the body segment or other object of interest, with electrical output channeled to a recording device. Three-dimensional accelerometers that incorporate multiple linear accelerometers are commercially available for monitoring acceleration during nonlinear movements.

SUMMARY

Movements of the human body are referenced to the sagittal, frontal, and transverse planes, with their respectively associated mediolateral, anteroposterior, and longitudinal axes. Most human motion is general, with both linear and angular components. A set of specialized terminol- ogy is used to describe segment motions and joint actions of the human body.

Teachers of physical activities, clinicians, and coaches all routinely per- form qualitative analyses to assess, correct, or improve human movements. Both knowledge of the specifi c biomechanical purpose of the movement and careful preplanning are necessary for an effective qualitative analysis. A number of special tools are available to assist researchers in collecting ki- nematic observations of human movement.

INTRODUCTORY PROBLEMS

1. Using appropriate movement terminology, write a qualitative descrip- tion of the performance of a maximal vertical jump. Your description should be suffi ciently detailed that the reader can completely and ac- curately visualize the movement.

2. Select a movement that occurs primarily in one of the three major ref- erence planes. Qualitatively describe this movement in enough detail that the reader of your description can visualize the movement.

3. List fi ve movements that occur primarily in each of the three cardinal planes. The movements may be either sport skills or activities of daily living.

4. Select a familiar animal. Does the animal move in the same major ref- erence planes in which humans move? What are the major differences

Refl ective joint markers can be tracked by a camera for automatic digitizing of the movement.

A digital camera with infrared light ring is used for tracking refl ective markers on a subject.

in the movement patterns of this animal and the movement patterns of humans?

5. Select a familiar movement, and list the factors that contribute to skilled versus unskilled performance of that movement.

6. Test your observation skills by carefully observing the two photos shown on the top. List the differences that you are able to identify be- tween these two photos.

7. Choose a familiar movement, and list aspects of that movement that are best observed from close up, from 2 to 3 m away, and from reason- ably far away. Write a brief explanation of your choices.

8. Choose a familiar movement, and list aspects of the movement that are best observed from the side view, front view, rear view, and top view. Write a brief explanation of your choices.

9. Choose one of the instrumentation systems described and write a short paragraph explaining the way in which it might be used to study a question related to analysis of a human movement of inter- est to you.

ADDITIONAL PROBLEMS

1. Select a familiar movement and identify the ways in which performance of that movement is affected by strength, fl exibility, and coordination.

2. List three human movement patterns or skills that are best observed from a side view, from a front or rear view, and from a top view.

3. Select a movement that is nonplanar and write a qualitative descrip- tion of that movement suffi ciently detailed to enable the reader of your description to picture the movement.

4. Select a nonplanar movement of interest and list the protocol you would employ in analyzing that movement.

52 BASIC BIOMECHANICS

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 53

5. What special expectations, if any, should the analyst have of move- ment performances if the performer is an older adult? An elementary school–aged girl? A novice? An obese high school–aged boy?

6. What are the advantages and disadvantages of collecting observa- tional data on a sport skill during a competitive event as opposed to a practice session?

7. Select a movement with which you are familiar and list at least fi ve questions that you, as a movement analyst, might ask the performer of the movement to gain additional knowledge about a performance.

8. List the auditory characteristics of fi ve movements and explain in each case how these characteristics provide information about the nature of the movement performance.

9. List the advantages and disadvantages of using a video camera as compared to the human eye for collecting observational data.

10. Locate an article in a professional or research journal that involves kinematic description of a movement of interest to you. What instru- mentation was used by the researchers? What viewing distances and perspectives were used? How might the analysis described have been improved?

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NAME _________________________________________________________

DATE _________________________________________________________

LABORATORY EXPERIENCES

1. Observe and analyze a single performer executing two similar but different versions of a particular movement—for example, two pitching styles or two gait styles. Explain what viewing perspectives and distances you selected for collecting observational data on each movement. Write a paragraph comparing the kinematics of the two movements.

Movement selected: _____________________________________________________________________________

Viewing perspectives: ___________________________________________________________________________

Reasons for selection of viewing perspectives: _____________________________________________________

________________________________________________________________________________________________

Viewing distances: ______________________________________________________________________________

Reasons for selection of viewing distances: ________________________________________________________

________________________________________________________________________________________________

Kinematic comparison: __________________________________________________________________________

________________________________________________________________________________________________

2. Observe a single sport skill as performed by a highly skilled individual, a moderately skilled indi- vidual, and an unskilled individual. Qualitatively describe the differences observed.

Sport skill selected: _____________________________________________________________________________

Highly Skilled Performer Moderately Skilled Performer Unskilled Performer

______________________________ ______________________________ ______________________________

______________________________ ______________________________ ______________________________ 55

56 BASIC BIOMECHANICS

______________________________ ______________________________ ______________________________

3. Select a movement at which you are reasonably skilled. Plan and carry out observations of a less- skilled individual performing the movement, and provide verbal learning cues for that individual, if appropriate. Write a short description of the cues provided, with a rationale for each cue.

Movement selected: _____________________________________________________________________________

Cues Provided Rationale

_______________________________________________ _______________________________________________

4. Select a partner, and plan and carry out an observational analysis of a movement of interest. Write a composite summary analysis of the movement performance. Write a paragraph identifying in what ways the analysis process was changed by the inclusion of a partner.

Movement selected: _____________________________________________________________________________

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 57

Analysis of Performance

________________________________________________________________________________________________

How the analysis process was different when working with a partner: _______________________________

________________________________________________________________________________________________

5. Plan and carry out a video session of a slow movement of interest as performed by two different sub- jects. Write a comparative analysis of the subjects’ performances.

Subject 1 Performance Subject 2 Performance

_______________________________________________ _______________________________________________

58 BASIC BIOMECHANICS

_______________________________________________ _______________________________________________

CHAPTER 2: KINEMATIC CONCEPTS FOR ANALYZING HUMAN MOTION 59

R E F E R E N C E S

1. Belcher D, Lee AM, Solmon MA, and Harrison L Jr: The infl uence of gender- related beliefs and conceptions of ability on women learning the hockey wrist shot, Res Q Exerc Sport 74:183, 2005.

2. Jenkins JM, Garn A, and Jenkins P: Preservice teacher observations in peer coaching, J Teach Phys Educ 24:2, 2005.

3. Lorson KM and Goodway JD: Gender differences in throwing form of children ages 6–8 years during a throwing game, Res Q Exerc Sport 79:174, 2008.

4. Radlo SJ, Janelle CM, Barba DA, and Frehlich SG: Perceptial decision mak- ing for baseball pitch recognition: using P300 latency and amplitude to index attentional processing, Res Q Exerc Sport 72:22, 2001.

A N N OTAT E D R E A D I N G S

Burkett B: Sport mechanics for coaches (3rd ed.), Champaign, IL, 2010, Human Kinetics. Provides an introductory look at the mechanics of sport to help readers under- stand and incorporate technology to enhance training, identify errors in tech- nique, and improve performance.

Hudson JL: Applied biomechanics in an instructional setting, JOPERD 77:25, 2006. Describes application of biomechanics in analyzing sport skills in a practical context.

Payton C and Bartlett R (eds.): Biomechanical evaluation of movement in sport and exercise, New York, 2008, Routledge. Practical guide to using the range of biomechanics movement analysis equip- ment and software available today, including detailed explanations of the theory underlying biomechanics testing along with advice concerning choice of equipment and how to use laboratory equipment most effectively.

Reiman M and Manske R: Functional testing in human performance, Champaign, IL, 2009, Human Kinetics. Serves as a comprehensive reference on functional testing for assessment of physical activities in sport, recreation, work, and daily living.

R E L AT E D W E B S I T E S

Mikromak http://www.mikromak.com

Advertises video hardware and software for sports, medicine, and product research.

Motion Analysis Corporation http://www.motionanalysis.com

Offers an optical motion capture system utilizing refl ective markers for enter- tainment, biomechanics, character animation, and motion analysis.

Northern Digital, Inc. http://www.ndigital.com

Presents optoelectronic 3-D motion measurement systems that track light- emitting diodes for real-time analysis.

Qualisys, Inc. http://www.qualisys.com

Presents a system in which cameras track refl ective markers, enabling real- time calculations; applications described for research, clinical, industry, and animation.

Redlake Imaging http://www.redlake.com/imaging

Advertises high-speed video products for scientifi c and clinical applications. SIMI Reality Motion Systems http://www.simi.com

Describes computer-based video analysis for the human body and cellular ap- plications; includes demo of gait analysis, among others.

60 BASIC BIOMECHANICS

K E Y T E R M S

anatomical reference position erect standing position with all body parts, including the palms of the hands, facing forward; considered the starting position for body segment movements

angular involving rotation around a central line or point

anteroposterior axis imaginary line around which frontal plane rotations occur

axis of rotation imaginary line perpendicular to the plane of rotation and passing through the center of rotation

cardinal planes three imaginary perpendicular reference planes that divide the body in half by mass

curvilinear along a curved line

frontal plane plane in which lateral movements of the body and body segments occur

general motion motion involving translation and rotation simultaneously

linear along a line that may be straight or curved, with all parts of the body moving in the same direction at the same speed

longitudinal axis imaginary line around which transverse plane rotations occur

mediolateral axis imaginary line around which sagittal plane rotations occur

rectilinear along a straight line

sagittal plane plane in which forward and backward movements of the body and body segments occur

system mechanical system chosen by the analyst for study

translation linear motion

transverse plane plane in which horizontal body and body segment movements occur when the body is in an erect standing position

C H A P T E R

3Kinetic Concepts for Analyzing Human Motion After completing this chapter, you will be able to:

Defi ne and identify common units of measurement for mass, force, weight, pressure, volume, density, specifi c weight, torque, and impulse.

Identify and describe the different types of mechanical loads that act on the human body.

Identify and describe the uses of available instrumentation for measuring kinetic quantities.

Distinguish between vector and scalar quantities.

Solve quantitative problems involving vector quantities using both graphic and trigonometric procedures.

O N L I N E L E A R N I N G C E N T E R R E S O U R C E S

www.mhhe.com/hall6e Log on to our Online Learning Center (OLC) for access to these additional resources:

62 BASIC BIOMECHANICS

W hen muscles on opposite sides of a joint develop tension, what deter-mines the direction of joint motion? In which direction will a swim- mer swimming perpendicular to a river current actually travel? What determines whether a push can move a heavy piece of furniture? The answers to these questions are rooted in kinetics, the study of forces.

The human body both generates and resists forces during the course of daily activities. The forces of gravity and friction enable walking and manipulation of objects in predictable ways when internal forces are produced by muscles. Sport participation involves application of forces to balls, bats, racquets, and clubs, and absorption of forces from impacts with balls, the ground or fl oor, and opponents in contact sports. This chap- ter introduces basic kinetic concepts that form the basis for understand- ing these activities.

BASIC CONCEPTS RELATED TO KINETICS

Understanding the concepts of inertia, mass, weight, pressure, volume, density, specifi c weight, torque, and impulse provides a useful foundation for understanding the effects of forces.

Inertia

In common usage, inertia means resistance to action or to change (Fig- ure 3-1). Similarly, the mechanical defi nition is resistance to acceleration. Inertia is the tendency of a body to maintain its current state of motion, whether motionless or moving with a constant velocity. For example, a 150 kg weight bar lying motionless on the fl oor has a tendency to remain motionless. A skater gliding on a smooth surface of ice has a tendency to continue gliding in a straight line with a constant speed.

Although inertia has no units of measurement, the amount of inertia a body possesses is directly proportional to its mass. The more massive an object is, the more it tends to maintain its current state of motion and the more diffi cult it is to disrupt that state.

A skater has a tendency to continue gliding with constant speed and direction due to inertia.

inertia tendency of a body to resist a change in its state of motion

FIGURE 3-1

A static object tends to maintain its motionless state because of inertia.

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 63

Mass

Mass (m) is the quantity of matter composing a body. The common unit of mass in the metric system is the kilogram (kg), with the English unit of mass being the slug, which is much larger than a kg.

Force

A force (F) can be thought of as a push or a pull acting on a body. Each force is characterized by its magnitude, direction, and point of application to a given body. Body weight, friction, and air or water resistance are all forces that commonly act on the human body. The action of a force causes a body’s mass to accelerate:

F 5 ma

Units of force are units of mass multiplied by units of acceleration (a). In the metric system, the most common unit of force is the Newton (N), which is the amount of force required to accelerate 1 kg of mass at 1 m/s2:

1 N 5 (1 kg)(1 m/s2)

In the English system, the most common unit of force is the pound (lb). A pound of force is the amount of force necessary to accelerate a mass of 1 slug at 1 ft/s2, and 1 lb is equal to 4.45 N:

1 lb 5 (1 slug)(1 ft/s2)

Because a number of forces act simultaneously in most situations, con- structing a free body diagram is usually the fi rst step when analyzing the effects of forces on a body or system of interest. A free body is any object, body, or body part that is being focused upon for analysis. A free body diagram consists of a sketch of the system being analyzed and vector rep- resentations of the acting forces (Figure 3-2). Even though a hand must be applying force to a tennis racquet in order for the racquet to force- fully contact a ball, if the racquet is the free body of interest, the hand is

mass quantity of matter contained in an object

force push or pull; the product of mass and acceleration

free body diagram sketch that shows a defi ned system in isolation with all of the force vectors acting on the system

Force applied by player

Weight

Air resistance

Force of ball contactForce applied

by racquet

FIGURE 3-2

Two free body diagrams showing the acting forces.

64 BASIC BIOMECHANICS

represented in the free body diagram of the racquet only as a force vector. Similarly, if the tennis ball constitutes the free body being studied, the force of the racquet acting on the ball is displayed as a vector.

Since a force rarely acts in isolation, it is important to recognize that the overall effect of many forces acting on a system or free body is a func- tion of the net force, which is the vector sum of all of the acting forces. When all acting forces are balanced, or cancel each other out, the net force is zero, and the body remains in its original state of motion, either motion- less or moving with a constant velocity. When a net force is present, the body moves in the direction of the net force and with an acceleration that is proportional to the magnitude of the net force.

Center of Gravity

A body’s center of gravity, or center of mass, is the point around which the body’s weight is equally balanced, no matter how the body is positioned, (see Chapter 13). In motion analyses, the motion of the center of gravity serves as an index of total body motion. From a kinetic perspective, the location of the center of mass determines the way in which the body re- sponds to external forces.

Weight

Weight is defi ned as the amount of gravitational force exerted on a body. Algebraically, its defi nition is a modifi cation of the general defi nition of a force, with weight (wt) being equal to mass (m) multiplied by the accelera- tion of gravity (ag):

wt 5 mag

Since weight is a force, units of weight are units of force—either N or lb. As the mass of a body increases, its weight increases proportionally. The

factor of proportionality is the acceleration of gravity, which is �9.81 m/s2.

net force resultant force derived from the composition of two or more forces

center of gravity point around which a body’s weight is equally balanced, no matter how the body is positioned

weight gravitational force that the earth exerts on a body

Although a body’s mass remains unchanged on the moon, its weight is less due to smaller gravitational acceleration. Photo courtesy of NASA.

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 65

The negative sign indicates that the acceleration of gravity is directed downward, or toward the center of the earth. On the moon or another planet with a different gravitational acceleration, a body’s weight would be different, although its mass would remain the same.

Because weight is a force, it is also characterized by magnitude, direc- tion, and point of application. The direction in which weight acts is always toward the center of the earth. Because the point at which weight is as- sumed to act on a body is the body’s center of gravity, the center of gravity is the point where the weight vector is shown to act in free body diagrams.

Although body weights are often reported in kilograms, the kilogram is actually a unit of mass. To be technically correct, weights should be iden- tifi ed in Newtons and masses reported in kilograms. Sample Problem 3.1 illustrates the relationship between mass and weight.

S A M P L E P R O B L E M 3 . 1

1. If a scale shows that an individual has a mass of 68 kg, what is that individual’s weight?

Known m 5 68 kg

Solution Wanted: weight Formulas: wt 5 mag 1 kg 5 2.2 lb (English/metric conversion factor)

(Mass may be multiplied by the acceleration of gravity to convert to weight within either the English or the metric system.)

wt 5 mag wt 5 (68 kg)(9 .81) m/s2

wt 5 667 N

Mass in kg may be multiplied by the conversion factor 2.2 lb/kg to convert to weight in pounds:

(68 kg)(2.2 lb/kg) 5 150 lb

2. What is the mass of an object weighing 1200 N?

Known wt 5 1200 N

Solution Wanted: mass Formula: wt 5 mag

(Weight may be divided by the acceleration of gravity within a given sys- tem of measurement to convert to mass.)

wt 5 mag 1200 N 5 m(9.81 m/s2)

1200 N

9.81 m/s2 5 m

m 5 122.32 kg

66 BASIC BIOMECHANICS

Pressure

Pressure (P) is defi ned as force (F) distributed over a given area (A):

P 5 F A

Units of pressure are units of force divided by units of area. Common units of pressure in the metric system are N per square centimeter (N/cm2) and Pascals (Pa). One Pascal represents one Newton per square meter (Pa 5 N/m2). In the English system, the most common unit of pressure is pounds per square inch (psi or lb/in2).

The pressure exerted by the sole of a shoe on the fl oor beneath it is the body weight resting on the shoe divided by the surface area between the sole of the shoe and the fl oor. As illustrated in Sample Problem 3.2, the smaller amount of surface area on the bottom of a spike heel as compared to a fl at sole results in a much larger amount of pressure being exerted.

Volume

A body’s volume is the amount of space that it occupies. Because space is considered to have three dimensions (width, height, depth), a unit of volume is a unit of length multiplied by a unit of length multiplied by a unit of length. In mathematical shorthand, this is a unit of length raised to the exponential power of three, or a unit of length cubed. In the metric

pressure force per unit of area over which force acts

volume amount of three-dimensional space occupied by a body

Pairs of balls that are similar in volume but markedly different in weight, including a solid metal shot and a softball (photo 1) and a table tennis ball and golf ball (photo 2).

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 67

S A M P L E P R O B L E M 3 . 2

Is it better to be stepped on by a woman wearing a spike heel or by the same woman wearing a smooth-soled court shoe? If a woman’s weight is 556 N, the surface area of the spike heel is 4 cm2, and the surface area of the court shoe is 175 cm2, how much pressure is exerted by each shoe?

Known

wt 5 556 N As 5 4 cm

Ac 5 175 cm 2

Solution Wanted: pressure exerted by the spike heel pressure exerted by the court shoe

Formula: P 5 F/A

Deduction: It is necessary to recall that weight is a force.

For the spike heel: P 5 556 N 4 cm2

P 5 139 N/cm 2

For the court shoe: P 5 556 N

175 cm2

P 5 3.18 N/cm 2

Comparison of the amounts of pressure exerted by the two shoes:

Pspike heel Pcourt shoe

5 139 N/cm2

3.18 N/cm2 5 43.75

Therefore, 43.75 times more pressure is exerted by the spike heel than by the court shoe worn by the same woman.

p = F– A

68 BASIC BIOMECHANICS

system, common units of volume are cubic centimeters (cm3), cubic meters (m3), and liters (l):

1 l 5 1000 cm3

In the English system of measurement, common units of volume are cu- bic inches (in3) and cubic feet (ft3). Another unit of volume in the English system is the quart (qt):

1 qt 5 57.75 in3

Volume should not be confused with weight or mass. An 8 kg shot and a softball occupy approximately the same volume of space, but the weight of the shot is much greater than that of the softball.

Density

The concept of density combines the mass of a body with the body volume. Density is defi ned as mass per unit of volume. The conventional symbol for density is the Greek letter rho (�).

density (�) 5 mass/volume

Units of density are units of mass divided by units of volume. In the metric system, a common unit of density is the kilogram per cubic meter (kg/m3). In the English system of measurement, units of density are not commonly used. Instead, units of specifi c weight (weight density) are employed.

Specifi c weight is defi ned as weight per unit of volume. Because weight is proportional to mass, specifi c weight is proportional to density. Units of specifi c weight are units of weight divided by units of volume. The metric unit for specifi c weight is Newtons per cubic meter (N/m3), and the Eng- lish system uses pounds per cubic foot (lb/ft3).

Although a golf ball and a ping-pong ball occupy approximately the same volume, the golf ball has a greater density and specifi c weight than the ping-pong ball because the golf ball has more mass and more weight. Similarly, a lean person with the same body volume as an obese person has a higher total body density because muscle is denser than fat. Thus, percent body fat is inversely related to body density.

Torque

When a force is applied to an object such as a pencil lying on a desk, either translation or general motion may result. If the applied force is directed parallel to the desktop and through the center of the pencil (a centric force), the pencil will be translated in the direction of the applied force. If the force is applied parallel to the desktop but directed through a point other than the center of the pencil (an eccentric force), the pencil will un- dergo both translation and rotation (Figure 3-3).

The rotary effect created by an eccentric force is known as torque (T), or moment of force. Torque, which may be thought of as rotary force, is the angular equivalent of linear force. Algebraically, torque is the product of force (F) and the perpendicular distance (d�) from the force’s line of action to the axis of rotation:

T 5 Fd�

The greater the amount of torque acting at the axis of rotation, the greater the tendency for rotation to occur. Units of torque in both the metric and the English systems follow the algebraic defi nition. They are units of force multiplied by units of distance: Newton-meters (N-m) or foot-pounds (ft-lb).

density mass per unit of volume

specifi c weight weight per unit of volume

torque rotary effect of a force

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 69

Impulse

When a force is applied to a body, the resulting motion of the body is dependent not only on the magnitude of the applied force but also on the duration of force application. The product of force (F) and time (t) is known as impulse (J):

J 5 Ft

A large change in an object’s state of motion may result from a small force acting for a relatively long time or from a large force acting for a relatively short time. A golf ball rolling across a green gradually loses speed because of the small force of rolling friction. The speed of a baseball struck vigorously by a bat changes because of the large force exerted by the bat during the fraction of a second it is in contact with the ball. When a vertical jump is executed, the larger the impulse generated against the fl oor, the greater the jumper’s takeoff velocity and the higher the result- ing jump.

Units of physical quantities commonly used in biomechanics are shown in Table 3-1.

FIGURE 3-3

A. Centric forces produce translation. B. Eccentric forces produce translation and rotation.

impulse product of force and the time over which the force acts

TABLE 3-1

Common Units for Kinetic Quantities

QUANTITY SYMBOL FORMULA METRIC UNIT ENGLISH UNIT

Mass m kg slug

Force F F 5 ma N lb

Pressure P P 5 F/A Pa psi

Volume (solids) V m3 ft3

(liquids) V liter gallon

Density � � 5 m/V kg/m3 slugs/ft3

Specifi c weight � � 5 wt/V N/m3 lb/ft3

Torque T T 5 Fd N-m ft-lb

Impulse J J 5 Ft N � s lb � s

70 BASIC BIOMECHANICS

MECHANICAL LOADS ON THE HUMAN BODY

Muscle forces, gravitational force, and bone-breaking force such as that encountered in a skiing accident all affect the human body differently. The effect of a given force depends on its direction and duration as well as its magnitude, as described in the following section.

Compression, Tension, and Shear

Compressive force, or compression, can be thought of as a squeezing force (Figure 3-4). An effective way to press wildfl owers is to place them inside the pages of a book and to stack other books on top of that book. The weight of the books creates a compressive force on the fl owers. Similarly, the weight of the body acts as a compressive force on the bones that sup- port it. When the trunk is erect, each vertebra in the spinal column must support the weight of that portion of the body above it.

The opposite of compressive force is tensile force, or tension (Figure 3-4). Tensile force is a pulling force that creates tension in the object to which it is applied. When a child sits in a playground swing, the child’s weight creates tension in the chains supporting the swing. A heavier child creates even more tension in the supports of the swing. Muscles produce tensile force that pulls on the attached bones.

A third category of force is termed shear. Whereas compressive and tensile forces act along the longitudinal axis of a bone or other structure to which they are applied, shear force acts parallel or tangent to a surface. Shear force tends to cause one portion of the object to slide, displace, or shear with respect to another portion of the object (Figure 3-4). For example, a force acting at the knee joint in a direction parallel to the tibial plateau is a shearing force at the knee. During the landing from a ski jump the impact force includes a component of anteriorly directed shear on the tibial plateau, elevating stress on the anterior cruciate ligament (1). (Figure 3-5).

compression pressing or squeezing force directed axially through a body

tension pulling or stretching force directed axially through a body

shear force directed parallel to a surface

Original shape

Compression Tension

Shear

FIGURE 3-4

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 71

FIGURE 3-5

During the landing from a ski jump the axial impact force at the knee includes a component of anteriorly directed shear on the tibial plateau.

Mechanical Stress

Another factor affecting the outcome of the action of forces on the human body is the way in which the force is distributed. Whereas pressure rep- resents the distribution of force external to a solid body, stress represents the resulting force distribution inside a solid body when an external force acts. Stress is quantifi ed in the same way as pressure: force per unit of area over which the force acts. As shown in Figure 3-6, a given force acting on a small surface produces greater stress than the same force acting over a larger surface. When a blow is sustained by the human body, the likeli- hood of injury to body tissue is related to the magnitude and direction of the stress created by the blow. Compressive stress, tensile stress, and shear stress are terms that indicate the direction of the acting stress.

Because the lumbar vertebrae bear more of the weight of the body than the thoracic vertebrae when a person is in an upright position, the compressive stress in the lumbar region should logically be greater. However, the amount of stress present is not directly proportional to the amount of weight borne, because the load-bearing surface areas of the lumbar vertebrae are greater than those of the vertebrae higher in the spinal column (Figure 3-7). This increased surface area reduces the amount of compressive stress present.

stress distribution of force within a body, quantifi ed as force divided by the area over which the force acts

FIGURE 3-6

The amount of mechanical stress created by a force is inversely related to the size of the area over which the force is spread.

72 BASIC BIOMECHANICS

Nevertheless, the L5-S1 intervertebral disc (at the bottom of the lumbar spine) is the most common site of disc herniations, although other factors also play a role (see Chapter 9). Quantifi cation of mechanical stress is demonstrated in Sample Problem 3.3.

Torsion, Bending, and Combined Loads

A somewhat more complicated type of loading is called bending. Pure compression and tension are both axial forces—that is, they are directed along the longitudinal axis of the affected structure. When an eccentric (or nonaxial) force is applied to a structure, the structure bends, creat- ing compressive stress on one side and tensile stress on the opposite side (Figure 3-8).

Torsion occurs when a structure is caused to twist about its longitudinal axis, typically when one end of the structure is fi xed. Torsional fractures of the tibia are not uncommon in football injuries and skiing accidents in which the foot is held in a fi xed position while the rest of the body under- goes a twist.

The presence of more than one form of loading is known as combined loading. Because the human body is subjected to a myriad of simultane- ously acting forces during daily activities, this is the most common type of loading on the body.

THE EFFECTS OF LOADING

When a force acts on an object, there are two potential effects. The fi rst is acceleration and the second is deformation, or change in shape. When a diver applies force to the end of a springboard, the board both acceler- ates and deforms. The amount of deformation that occurs in response to a given force depends on the stiffness of the object acted upon.

When an external force is applied to the human body, several factors infl uence whether an injury occurs. Among these are the magnitude and

12 1

11 10

9 8 7 6 5 4

Cervical vertebrae

Thoracic vertebrae

Lumbar vertebrae

Sacrum

Coccyx

7 6 5

FIGURE 3-7

The surfaces of the vertebral bodies increase in surface area as more weight is supported.

bending asymmetric loading that produces tension on one side of a body’s longitudinal axis and compression on the other side

axial directed along the longitudinal axis of a body

torsion load-producing twisting of a body around its longitudinal axis

combined loading simultaneous action of more than one of the pure forms of loading

deformation change in shape

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 73

direction of the force, and the area over which the force is distributed. Also important, however, are the material properties of the loaded body tissues.

The relationship between the amount of force applied to a structure and the structure’s response is illustrated by a load deformation curve (Figure 3-9). With relatively small loads, deformation occurs, but the response is elastic, meaning that when the force is removed the struc- ture returns to its original size and shape. Since stiffer materials display less deformation in response to a given load, greater stiffness translates

S A M P L E P R O B L E M 3 . 3

How much compressive stress is present on the L1, L2 vertebral disc of a 625 N woman, given that approximately 45% of body weight is supported by the disc (a) when she stands in anatomical position and (b) when she stands erect holding a 222 N suitcase? (Assume that the disc is oriented horizontally and that its surface area is 20 cm2.)

Solution 1. Given: F 5 (625 N)(0.45)

A 5 20 cm2

Formula: stress 5 F/A

stress 5 1625 N2 10.452

20 cm2

stress 5 14 N/cm 2

2. Given: F 5 (625 N)(0.45) 1 222 N Formula: stress 5 F/A

stress 5 1625 N2 10.452 1 222 N

20 cm2

stress 5 25.2 N/cm 2

Shear

Neutral axis

Torsion

Bending

Tension

Compression

FIGURE 3-8

Objects loaded in bending are subject to compression on one side and tension on the other. Objects loaded in torsion develop internal shear stress, with maximal stress at the periphery and no stress at the neutral axis.

74 BASIC BIOMECHANICS

Deformation

Ultimate failure point

Yield point

Elastic region

Plastic region

Lo ad

FIGURE 3-9

When a structure is loaded, it deforms, or changes shape. The deformation is temporary within the elastic region and permanent in the plastic region. Structural integrity is lost at the ultimate failure point.

to a steeper slope of the load deformation curve in the elastic region. If the force applied causes the deformation to exceed the structure’s yield point or elastic limit, however, the response is plastic, meaning that some amount of deformation is permanent. Deformations exceeding the ulti- mate failure point produce mechanical failure of the structure, which in the human body means fracturing of bone or rupturing of soft tissues.

Repetitive versus Acute Loads

The distinction between repetitive and acute loading is also important. When a single force large enough to cause injury acts on biological tis- sues, the injury is termed acute and the causative force is termed mac- rotrauma. The force produced by a fall, a rugby tackle, or an automobile accident may be suffi cient to fracture a bone.

Injury can also result from the repeated sustenance of relatively small forces. For example, each time a foot hits the pavement during running, a force of approximately two to three times body weight is sustained. Al- though a single force of this magnitude is not likely to result in a fracture of healthy bone, numerous repetitions of such a force may cause a fracture of an otherwise healthy bone somewhere in the lower extremity. When repeated or chronic loading over a period produces an injury, the injury is called a chronic injury or a stress injury, and the causative mechanism is termed microtrauma. The relationship between the magnitude of the load sustained, the frequency of loading, and the likelihood of injury is shown in Figure 3-10.

yield point (elastic limit) point on the load deformation curve past which deformation is permanent

failure loss of mechanical continuity

repetitive loading repeated application of a subacute load that is usually of relatively low magnitude

acute loading application of a single force of suffi cient magnitude to cause injury to a biological tissue

Likelihood of injury

Lo ad

m ag

ni tu

Frequency of loading

FIGURE 3-10

The general pattern of injury likelihood as a function of load magnitude and repetition. Injury can be sustained, but is less likely, with a single large load and with a repeated small load.

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 75

TOOLS FOR MEASURING KINETIC QUANTITIES

Biomechanics researchers use equipment for studying both muscle forces and forces generated by the feet against the ground during gait and other activities. Knowledge gained through the use of these tools is often pub- lished in professional journals for teachers, clinicians, coaches, and others interested in human movement.

Electromyography

Eighteenth-century Italian scientist Galvani made two interesting dis- coveries about skeletal muscle: (a) It develops tension when electrically stimulated, and (b) it produces a detectable current or voltage when de- veloping tension, even when the stimulus is a nerve impulse. The latter discovery was of little practical value until the twentieth century, when technology became available for the detection and recording of extremely small electrical charges. The technique of recording electrical activity pro- duced by muscle, or myoelectric activity, is known today as electromyog- raphy (EMG).

Electromyography is used to study neuromuscular function, in- cluding identifi cation of which muscles develop tension throughout a movement and which movements elicit more or less tension from a par- ticular muscle or muscle group. It is also used clinically to assess nerve conduction velocities and muscle response in conjunction with the di- agnosis and tracking of pathological conditions of the neuromuscular system. Scientists also employ electromyographic techniques to study the ways in which individual motor units respond to central nervous system commands.

The process of electromyography involves the use of transducers known as electrodes that sense the level of myoelectric activity present at a particular site over time. Depending on the questions of interest, either surface electrodes or fi ne wire electrodes are used. Surface elec- trodes, consisting of small discs of conductive material, are positioned on the surface of the skin over a muscle or muscle group to pick up global myoelectric activity. When more localized pickup is desired, indwelling, fi ne-wire electrodes are injected directly into a muscle. Output from the electrodes is amplifi ed and graphically displayed or mathematically pro- cessed and stored by a computer.

Dynamography

Scientists have devised several types of platforms and portable systems for the measurement of forces and pressure on the plantar surface of the foot. These systems have been employed primarily in gait research, but have also been used to study phenomena such as starts, takeoffs, land- ings, baseball and golf swings, and balance.

Both commercially available and homemade force platforms and pressure platforms are typically built rigidly into a fl oor fl ush with the surface and are interfaced to a computer that calculates kinetic quan- tities of interest. Force platforms are usually designed to transduce ground reaction forces in vertical, lateral, and anteroposterior direc- tions with respect to the platform itself; pressure platforms provide graphical or digital maps of pressures across the plantar surfaces of the feet. The force platform is a relatively sophisticated instrument, but its limitations include the restrictions of a laboratory setting and

Myoelectric signal traces displayed on a computer monitor.

myoelectric activity electric current or voltage produced by a muscle developing tension

transducers devices that detect signals

76 BASIC BIOMECHANICS

potential diffi culties associated with the subject’s consciously targeting the platform.

Portable systems for measuring plantar forces and pressures are also available in commercial and homemade models as instrumented shoes, shoe inserts, and thin transducers that adhere to the plantar surfaces of the feet. These systems provide the advantage of data collection outside the laboratory but lack the precision of the built-in platforms.

VECTOR ALGEBRA

A vector is a quantity that has both magnitude and direction. Vectors are represented by arrow-shaped symbols. The magnitude of a vector is its size; for example, the number 12 is of greater magnitude than the number 10. A vector symbol’s orientation on paper represents direction, and its length represents magnitude. Force, weight, pressure, specifi c weight, and torque are kinetic vector quantities; displacement, velocity, and acceleration (see Chapter 10) are kinematic vector quantities. No vec- tor is fully defi ned without the identifi cation of both its magnitude and its direction. Scalar quantities possess magnitude but have no particular direction associated with them. Mass, volume, length, and speed are ex- amples of scalar quantities.

Vector Composition

When vectors are added together, the operation is called vector composi- tion. The composition of two or more vectors that have exactly the same direction results in a single vector that has a magnitude equal to the sum of the magnitudes of the vectors being added (Figure 3-11). The single vector resulting from a composition of two or more vectors is known as the resultant vector, or the resultant. If two vectors that are oriented in exactly opposite directions are composed, the resultant has the direction of the longer vector and a magnitude equal to the difference in the mag- nitudes of the two original vectors (Figure 3-12).

It is also possible to add vectors that are not oriented in the same or opposite directions. When the vectors are coplanar, that is, contained in the same plane, a procedure that may be used is the “tip-to-tail” method, in which the tail of the second vector is placed on the tip of the fi rst vector, and the resultant is then drawn with its tail on the tail of the fi rst vector

Surface electromyographic electrodes are small discs that attach directly to the skin over a muscle or muscle group of interest to transduce electrical activity in the underlying tissue.

vector physical quantity that possesses both magnitude and direction

scalar physical quantity that is completely described by its magnitude

vector composition process of determining a single vector from two or more vectors by vector addition

FIGURE 3-11

The composition of vectors with the same direction requires adding their magnitudes.

resultant single vector that results from vector composition

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 77

FIGURE 3-12

Composition of vectors with opposite directions requires subtracting their magnitudes.

FIGURE 3-13

The “tip-to-tail” method of vector composition.

and its tip on the tip of the second vector. This procedure may be used for combining any number of vectors if each successive vector is positioned with its tail on the tip of the immediately preceding vector and the resul- tant connects the tail of the fi rst vector to the tip of the previous vector (Figure 3-13).

Through the laws of vector combination, we often can calculate or bet- ter visualize the resultant effect of combined vector quantities. For exam- ple, a canoe fl oating down a river is subject to both the force of the current and the force of the wind. If the magnitudes and directions of these two forces are known, the single resultant or net force can be derived through the process of vector composition (Figure 3-14). The canoe travels in the direction of the net force.

Vector Resolution

Determining the perpendicular components of a vector quantity relative to a particular plane or structure is often useful. For example, when a ball is thrown into the air, the horizontal component of its velocity determines the distance it travels, and the vertical component of its velocity deter- mines the height it reaches (see Chapter 10). When a vector is resolved

78 BASIC BIOMECHANICS

into perpendicular components—a process known as vector resolution— the vector sum of the components always yields a resultant that is equal to the original vector (Figure 3-15). The two perpendicular components, therefore, are a different but equal representation of the original vector.

Graphic Solution of Vector Problems

When vector quantities are uniplanar (contained in a single plane), vector manipulations may be done graphically to yield approximate results. Graphic solution of vector problems requires the careful meas- urement of vector orientations and lengths to minimize error. Vector lengths, which represent the magnitudes of vector quantities, must be drawn to scale. For example, 1 cm of vector length could represent 10 N of force. A force of 30 N would then be represented by a vector 3 cm in length, and a force of 45 N would be represented by a vector of 4.5 cm length.

Trigonometric Solution of Vector Problems

A more accurate procedure for quantitatively dealing with vector prob- lems involves the application of trigonometric principles. Through the use of trigonometric relationships, the tedious process of measuring and

FIGURE 3-14

The net force is the resultant of all acting forces.

FIGURE 3-15

Vectors may be resolved into perpendicular components. The vector composition of each perpendicular pair of components yields the original vector.

vector resolution operation that replaces a single vector with two perpendicular vectors such that the vector composition of the two perpendicular vectors yields the original vector

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 79

S A M P L E P R O B L E M 3 . 4

Terry and Charlie must move a refrigerator to a new location. They both push parallel to the fl oor, Terry with a force of 350 N and Charlie with a force of 400 N, as shown in the diagram below. (a) What is the magnitude of the resultant of the forces produced by Terry and Charlie? (b) If the amount of friction force that directly opposes the direction of motion of the refrigerator is 700 N, will they be able to move the refrigerator?

Graphic Solution 1. Use the scale 1 cm 5 100 N to measure the length of the resultant.

The length of the resultant is approximately 6.75 cm, or 675 N.

2. Since 675 N � 700 N, they will not be able to move the refrigerator.

Trigonometric Solution Given: FT 5 350 N

FC 5 400 N

Wanted: magnitude of the resultant force

Charlie

+ =

Terry

350 N

400 N

30°

20°

20° 4 cm

4 cm 130°30° 3. 5 c

m 3.5

30°20°

A researcher calibrates force plates in a laboratory in preparation for a motion analysis data capture.

drawing vectors to scale can be eliminated (see Appendix B). Sample Problem 3.4 provides an example of the processes of both graphic and trigonometric solutions using vector quantities.

350 N

400 N

30º

20º

80 BASIC BIOMECHANICS

Horizontal plane free body diagram:

Formula: C2 5 A2 � B2 � 2(A)(B)cos � (the law of cosines)

R2 5 4002 � 3502 � 2(400)(350) cos 130

R 5 680 N

3. Since 680 N � 700 N, they will not be able to move the refrigerator un- less they exert more collective force while pushing at these particular angles. (If both Terry and Charlie pushed at a 90° angle to the refrig- erator, their combined force would be suffi cient to move it.)

+ =

FT R

30°

20°

FC = 400N 130°30° F T = 3

50N

30°20°

SUMMARY

Basic concepts related to kinetics include mass, the quantity of matter composing an object; inertia, the tendency of a body to maintain its cur- rent state of motion; force, a push or pull that alters or tends to alter a body’s state of motion; center of gravity, the point around which a body’s weight is balanced; weight, the gravitational force exerted on a body; pres- sure, the amount of force distributed over a given area; volume, the space occupied by a body; density, the mass or weight per unit of body volume; and torque, the rotational effect of a force.

Several types of mechanical loads act on the human body. These include compression, tension, shear, bending, and torsion. Generally, some combi- nation of these loading modes is present. The distribution of force within a body structure is known as mechanical stress. The nature and magnitude of stress determine the likelihood of injury to biological tissues.

Vector quantities have magnitude and direction; scalar quanti- ties possess magnitude only. Problems with vector quantities can be solved using either a graphic or a trigonometric approach. Of the two procedures, the use of trigonometric relationships is more accurate and less tedious.

INTRODUCTORY PROBLEMS

1. William Perry, defensive tackle and part-time running back better known as “The Refrigerator,” weighed in at 1352 N during his 1985 rookie season with the Chicago Bears. What was Perry’s mass? (An- swer: 138 kg)

2. How much force must be applied to a 0.5 kg hockey puck to give it an acceleration of 30 m/s2? (Answer: 15 N)

6. A gymnastics fl oor mat weighing 220 N has dimensions of 3 m � 4 m � 0.04 m. How much pressure is exerted by the mat against the fl oor? (Answer: 18.33 Pa)

7. What is the volume of a milk crate with sides of 25 cm, 40 cm, and 30 cm? (Answer: 30,000 cm3 or 30 l)

8. Choose three objects that are within your fi eld of view, and estimate the volume of each. List the approximate dimensions you used in for- mulating your estimates.

9. If the contents of the crate described in Problem 7 weigh 120 N, what are the average density and specifi c weight of the box and contents? (Answer: 0.0004 kg/cm3; 0.004 N/cm3)

10. Two children sit on opposite sides of a playground seesaw. Joey, who weighs 220 N, sits 1.5 m from the axis of the seesaw, and Suzy, who weighs 200 N, sits 1.7 m from the axis of the seesaw. How much torque is created at the axis by each child? In which direction will the seesaw tip? (Answer: Joey, 330 N-m; Suzy, 340 N-m; Suzy’s end)

ADDITIONAL PROBLEMS

1. What is your own body mass in kg? 2. Gravitational force on planet X is 40% of that found on the earth. If a

person weighs 667.5 N on earth, what is the person’s weight on planet X? What is the person’s mass on the earth and on planet X? (Answer: weight on planet X 5 267 N; mass 5 68 kg on either planet)

3. A football player is contacted by two tacklers simultaneously. Tack- ler A exerts a force of 400 N, and tackler B exerts a force of 375 N. If the forces are coplanar and directed perpendicular to each other, what is the magnitude and direction of the resultant force acting on the player? (Answer: 548 N at an angle of 43° to the line of ac- tion of tackler A)

3. A rugby player is contacted simultaneously by three opponents who exert forces of the mag- nitudes and directions shown in the diagram at right. Using a graphic solution, show the magni- tude and direction of the resultant force.

4. Using a graphic solution, compose the muscle force vectors to fi nd the net force acting on the scapula shown below.

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 81

5. Draw the horizontal and vertical components of the vectors shown below.

82 BASIC BIOMECHANICS

4. A 75 kg skydiver in free fall is subjected to a crosswind exerting a force of 60 N and to a vertical air resistance force of 100 N. Describe the resultant force acting on the skydiver. (Answer: 638.6 N at an angle of 5.4° to vertical)

5. Use a trigonometric solution to fi nd the magnitude of the resultant of the following coplanar forces: 60 N at 90°, 80 N at 120°, and 100 N at 270°. (Answer: 49.57 N)

6. If 37% of body weight is distributed above the superior surface of the L5 intervertebral disc and the area of the superior surface of the disc is 25 cm2, how much pressure exerted on the disc is attributable to body weight for a 930 N man? (Answer: 13.8 N/cm2)

7. In the nucleus pulposus of an intervertebral disc, the compressive load is 1.5 times the externally applied load. In the annulus fi brosus, the compressive force is 0.5 times the external load. What are the compressive loads on the nucleus pulposus and annulus fi brosus of the L5-S1 intervertebral disc of a 930 N man holding a 445 N weight bar across his shoulders, given that 37% of body weight is distributed above the disc? (Answer: 1183.7 N acts on the nucleus pulposus; 394.5 N acts on the annulus fi brosus.)

8. Estimate the volume of your own body. Construct a table that shows the approximate body dimensions you used in formulat- ing your estimate.

9. Given the mass or weight and the volume of each of the following objects, rank them in the order of their densities.

10. Two muscles develop tension simultaneously on opposite sides of a joint. Muscle A, attaching 3 cm from the axis of rotation at the joint, exerts 250 N of force. Muscle B, attaching 2.5 cm from the joint axis, exerts 260 N of force. How much torque is created at the joint by each muscle? What is the net torque created at the joint? In which direction will motion at the joint occur? (Answer: A, 7.5 N-m; B, 6.5 N-m; net torque equals 1 N-m in the direction of A)

OBJECT WEIGHT OR MASS VOLUME

A 50 kg 15.00 in3

B 90 lb 12.00 cm3

C 3 slugs 1.50 ft3

D 450 N 0.14 m3

E 45 kg 30.00 cm3

NAME _________________________________________________________

DATE _________________________________________________________

LABORATORY EXPERIENCES

1. Use a ruler to measure the dimensions of the sole of one of your shoes in centimeters. Being as ac- curate as possible, calculate an estimate of the surface area of the sole. (If a planimeter is available, use it to more accurately assess surface area by tracing around the perimeter of the sole.) Knowing your own body weight, calculate the amount of pressure exerted over the sole of one shoe. How much change in pressure would result if your body weight changed by 22 N (5 lb)?

Surface area calculation:

Surface area: ___________________________________________________________________________________

Body weight: ___________________________________________________________________________________

Pressure calculation:

Pressure: ______________________________________________________________________________________

Pressure calculation with 22 N (5 lb) change in body weight:

Pressure: ______________________________________________________________________________________

2. Place a large container fi lled three-quarters full of water on a scale and record its weight. To assess the volume of an object of interest, completely submerge the object in the container, holding it just below the surface of the water. Record the change in weight on the scale. Remove the object from the container. Carefully pour water from the container into a measuring cup until the container weighs its original weight less the change in weight recorded. The volume of water in the measuring cup is the volume of the submerged object. (Be sure to use correct units when recording your measured values.)

Weight of container of water: ____________________________________________________________________

Change in weight with object submerged: _________________________________________________________

Volume of object: _______________________________________________________________________________

84 BASIC BIOMECHANICS

3. Secure one end of a pencil by fi rmly clamping it in a vise. Grip the other end of the pencil with an adjustable wrench and slowly apply a bending load to the pencil until it begins to break. Observe the nature of the break.

On which side of the pencil did the break begin? ___________________________________________________

Is the pencil stronger in resisting compression or tension? __________________________________________

Repeat the exercise using another pencil and applying a torsional (twisting) load. What does the nature of the initial break indicate about the distribution of shear stress within the pencil?

4. Experiment with pushing open a door by applying force with one fi nger. Apply force at distances of 10 cm, 20 cm, 30 cm, and 40 cm from the hinges. Write a brief paragraph explaining at which force application distance it is easiest/hardest to open the door.

5. Stand on a bathroom scale and perform a vertical jump as a partner carefully observes the pattern of change in weight registered on the scale. Repeat the jump several times, as needed for your partner to determine the pattern. Trade positions and observe the pattern of weight change as your partner performs a jump. In consultation with your partner, sketch a graph of the change in exerted force (vertical axis) across time (horizontal axis) during the performance of a vertical jump.

What does the area under the curve represent? ____________________________________________________

Time

Ta ke

of f

La nd

in g

Fo rc

CHAPTER 3: KINETIC CONCEPTS FOR ANALYZING HUMAN MOTION 85

R E F E R E N C E S

1. Yeow CH, Lee PV, and Goh JC: Direct contribution of axial impact com- pressive load to anterior tibial load during simulated ski landing im- pact, J Biomech 43:242, 2010.

A N N OTAT E D R E A D I N G S

Caldwell GE, Hamill J, Kmen G, Whittlesey SN, and Robertson DGE: Research methods in biomechanics, Champaign, IL, 2004, Human Kinetics. Includes chapters on kinetics, forces and their measurement, inverse dy- namics, and electromyography, among others.

Kamen G and Gabriel D: Essentials of electromyography, Champaign, IL, 2010, Human Kinetics. Presents both fundamental and advanced concepts related to collection, analysis, and interpretation of electromyography data.

LeVeau BF: Biomechanics of human motion: Basics and beyond for the health professions, Thorofare, NJ, 2010, SLACK. Discusses mechanical loading on the human body in addition to other topics.

Winter DA: Biomechanics and motor control of human movement (4th ed.), Hoboken, NJ, 2009, John Wiley and Sons. Describes a wide spectrum of biomechanical movement analysis tech- niques, among other topics.

R E L AT E D W E B S I T E S

Advanced Medical Technology, Inc. http://www.amtiweb.com

Provides information on the AMTI force platforms, with reference to force and torque sensors, gait analysis, balance and posture, and other topics.

B & L Engineering http://www.bleng.com/

Describes electromyography systems and footswitches for gait analysis. Biokinetics and Associates, Ltd. http://www.biokinetics.com/

Markets products designed to prevent injury. Bortec Biomedical Ltd. http://www.bortec.ca/pages/home.htm

Describes a multichannel telemetered electromyography system. Delsys, Inc. http://www.delsys.com/

Provides a description of surface electromyography equipment. Kistler http://www.kistler.com

Describes a series of force platforms. RSscan http://www.rsscan.co.uk/users/university.php

Describes a within-shoe pressure measurement system.

K E Y T E R M S

acute loading application of a single force of suffi cient magnitude to cause injury to a biological tissue

axial directed along the longitudinal axis of a body

bending asymmetric loading that produces tension on one side of a body’s longitudinal axis and compression on the other side

86 BASIC BIOMECHANICS

center of gravity point around which a body’s weight is equally balanced, no matter how the body is positioned

combined loading simultaneous action of more than one of the pure forms of loading

compression pressing or squeezing force directed axially through a body

deformation change in shape

density mass per unit of volume

failure loss of mechanical continuity

force push or pull; the product of mass and acceleration

free body diagram sketch that shows a defi ned system in isolation with all of the force vectors acting on the system

impulse product of force and the time over which the force acts

inertia tendency of a body to resist a change in its state of motion

mass quantity of matter contained in an object

myoelectric activity electric current or voltage produced by a muscle developing tension

net force resultant force derived from the composition of two or more forces

pressure force per unit of area over which a force acts

repetitive loading repeated application of a subacute load that is usually of relatively low magnitude

resultant single vector that results from vector composition

scalar physical quantity that is completely described by its magnitude

shear force directed parallel to a surface

specifi c weight weight per unit of volume

stress distribution of force within a body, quantifi ed as force divided by the area over which the force acts

tension pulling or stretching force directed axially through a body

torque rotary effect of a force

torsion load-producing twisting of a body around its longitudinal axis

transducers devices that detect signals

vector physical quantity that possesses both magnitude and direction

vector composition process of determining a single vector from two or more vectors by vector addition

vector resolution operation that replaces a single vector with two perpendicular vectors such that the vector composition of the two perpendicular vectors yields the original vector

volume space occupied by a body

weight attractive force that the earth exerts on a body

yield point (elastic limit) point on the load deformation curve past which deformation is permanent