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152 Robot Dynamics

Applying (3.5.11) yields (verify!)

(4)

where .
In a similar fashion, one may compute .

3.6 Actuator Dynamics

We have discussed the dynamics of a rigid-robot manipulator in joint space
and Cartesian coordinates. However, the robot needs actuators to move it;
these are generally either electric or hydraulic motors. It is now required,
therefore, to add the actuator dynamics to the arm dynamics to obtain a
complete dynamical description of the arm plus actuators. A good reference
on actuators and sensors is provided by [de Silva 1989].

Dynamics of a Robot Arm with Actuators
We shall consider the case of electric actuators, assuming that the motors are
armature controlled. Hydraulic actuators are described by similar equations.
In this subsection we suppose that the armature inductance is negligible.
The equations of the n—link robot arm from Table 3.3.1 are given by
(3.6.1)

n
where q R is the arm joint variable. The dynamics or the armature-controlled
do motors that drive the links are given by the n decoupled equations
(3.6.2)

where with, q Mi, the ith rotor position angle and vec{α i}
denoting a vector with components α i. The control input is the motor voltage
vector v R n
The actuator coefficient matrices are all constants given by

Copyright © 2004 by Marcel Dekker, Inc.