PHYSICS EXPERTS ONLY
aroojch
lecture_12_mech_393.pptxMECH 393
Lecture 12
Introduction to Acceleration Analysis
Agenda
Consider pure rotation RAFA motion for acceleration
Introduce relative acceleration Equation
Example
RAFA motion
Single link
Change in velocity VECTOR is acceleration VECTOR
Change in direction of V
Change in magnitude of V
At early time blue position
At later time red position
RAFA motion
Change in direction of V
Consider if red and blue vectors are same length
a = change in V/change in time
Vector subtraction
Closed loop vector equation
Negative vector
RAFA motion
an (Normal acceleration) is directed from point of interest toward RAFA axis
an (Normal acceleration) has a magnitude of r * w2
an = r * w2
Negative vector
Closed loop vector equation
RAFA motion
Change in magnitude of V
If red V vector longer than blue, w is increasing
V= r * w
Angular acceleration a
a = d/dt of w or
(wlater – wearlier)/time change
a
w
w
RAFA motion
Change in magnitude of V
at (tangential acceleration)
has a direction tangential, along same line of action as velocity vector
at (tangential acceleration)
has a magnitude of r * a
at = r * a
a
w
w
Relative acceleration
Consider relative velocity equation
VB = VA + VB/A
Take d/dt of whole equation term by term
Each V becomes an a
VB = VA + VB/A
aB = aA + aB/A
Restriction: points A and B are on same rigid body
Example
4 bar all revolute joints
Given w2, a2
Find a all links
a of any point any link
O2
A
B
O4
Example
Process
1. do velocity analysis to get w3 and w4 from known w2
2. consider RAFA link 2 and find aA
3. consider RAFA link 4 and evaluate aB
4.write and apply relative acceleration equation
O2
A
B
O4
Example
Process
4.write and apply relative acceleration equation
aB = aA + aB/A
Expanded version
aBn + aBt = aAn + aAt + aB/An+ aB/At
Each part has rotational motion
Each part has normal and tangential components
O2
A
B
O4
Homework
Kepler Chapter 7
7.1
7.2
7.3
7.4
