wheelcair calculation

Computations Of Wheelchair Powered By Dc Motor

Name:

Institution:

Calculation of the required torque of the DC one Motor and two motor.

To compute the force and torque of a wheelchair the following equations are used:

Since Force=Mass* Acceleration

Then: F= Mrϴ

Since T=Fr

Then T=Iα =Mr2ϴ

Taking into the consideration the different masses of the wheelchair

F=Mcr ϴ+ Mwr ϴfL+ Mwr ϴfR

The torque of the left wheel and the right wheel can be expressed as:

TeL= Mwr2 ϴtL+ Mcr 2()

TeR= Mwr2 ϴtR+ Mcr 2()

When Laplace transformations of these equations is done:

F=Mcr s2ϴ+ Mwrs2 ϴfL+ Mwrs2ϴfR

= swfl+ swfR

Therefore:

TeL= swtl

TeR= swtR

The left and right force can then be expressed as:

FL=swfl

FR=swfR

The angular velocity of the wheels can be expressed as:

wL=wFL+wtL

WR=WfR+WtR

(Gerven, 2006).

For a standard DC Gear head motor it is capable of accelerating a 15lb, two wheel drive wheelchair with wheel diameters of 3.825” at a rate of 3ft/sec/sec.

Converting the parameters to SI units

Mass-15lbs=6.804Kgs

Acceleration-3ft/square second=0.9144meter/square second

According to Newton’s laws

Force=Mass* Acceleration

=6.804Kgs*0.9144m/s2

=5.8N

Since the wheelchair has two motors:

The force for every motor therefore is computed as

F1=5.8/2

=2.9N

Torque is defined as a turning force that acts on an axis. The radius of the wheel is 0.0486m.

Torque=Force * Distance

=2.9*000486

=0.14094Nm (Chin, 2011)

For a wheelchair moving up a slope:

The wheelchair moves up a slope with its axis parallel to the object thus it moves in a straight line making the angular velocity to be equal to zero. The forces the motors have to overcome are computed as follows:

To compute the torque, the two forces above have to be added together and multiplied by the distance:

T= (F1+F2) r =

(Gerven,2006).

References

Chin-Chih, O. (2011). Power- Assisted Wheelchair Design based on a Lyapunov Torque Observer. International Journal of Innovative Computing Information and Control. Volume 8, 8089- 2102.

Gerven, M. (2006). Modelling and Control of an Electrically Driven Wheelchair. Enschede

Liles, H., Huang, M., Caspall, J., & Sprigle, S. (2015). Design of a Robotic System to Measure Propulsion Work of Over-Ground Wheelchair Maneuvers. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 23(6), 983-991.