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158 Robot Dynamics

a. Rigid Coupling Shaft

If there is no compliance in the coupling shaft, ω m =ω L =ω and the state equations
reduce to (see the Problems)

(6)

T
where x=[i ω] , J=J m +J L . Defining the output as the motor speed gives

The transfer function is computed to be

(7)

Using parameter values of J m =J L =0.1 kg-m , L=0.5 H,
2
b m=0.2 N-m/rad/s, and R=5 Ω yields

(8)

so that there are two real poles at s=-2.3, s=-8.7.
Using Program TRESP in Appendix B to perform a simulation (see Section
3.3) yields the step response for w shown in Figure 3.6.2.

b. Very Flexible Coupling Shaft
Coupling shaft parameters of k=2 N-m/rad and b=0.2 N-m/rad/s correspond
to a very flexible shaft. Using these values, software like PC-MATLAB can be
employed to obtain the two transfer functions

(9)

(10)

Copyright © 2004 by Marcel Dekker, Inc.