Download full document - Automatic Control

4.7 ACTUATOR DYNAMICS
In most existing industrial robots, a transmission is introduced between each actuator and the
corresponding articulated body of the manipulator. Such an actuated joint for one robot arm is
illustrated in Figure 4.7.
Figure 4.7, actuated joint with transmission between the joint and the motor.
On the assumption of a rigid transmission and with no backlash the relationship between the
input forces (velocities) and the output forces (velocities) are purely proportional (9). This
gives,
θ = k θ
m r l
Eq. 4.17
where θm is the motor shaft displacement, θ the robot joint displacement and the constant kr is a
parameter which describes the gear reduction ratio. Iload is the body moment of inertia about the
rotation axis of an actuated link. τl is the load torque at the robot axis and τm is the torque
produced by the actuator at the shaft axis. In view of Eq. 4.17 one can write
4.8 INVERSE DYNAMIC MODEL
τ
τ =
l
m
kr
Eq. 4.18
The inverse dynamic model of a parallel robot can be calculated with different methods (e.g.
Lagrange or Newton-Euler).
A way to calculate the inverse dynamic model is to cut out the closed chain mechanism at
passive joints and consider firstly the dynamics of the tree-structure robot thus created. The
closure condition can then be relaxed by the application d’Alembert virtual work principle by
mean of some Jacobian matrix.
For the Delta-3 robot, the complexity of the dynamic model arises mainly due to the movement
of the forearms. This problem can be simplified if their rotational inertias are neglected. Thus
______________________________________________________________________________
Public Report ELAU GmbH, Marktheidenfeld
22