CPSC 452 - Chapter 4 Exercise Assignments and Hints
The exercises assigned are from J.J. Craig's text,
"Intro. to Robotics," ed. 2.
Chapter 4 Assignment Due Wednesday, Feb. 26, 1997
Exercises 4.4, 4.6, 4.17, 4.22
Hints
Exercise 4.4 - Look at the geometry and notice that
p_z of ^0_3(T) is fixed, so arbitrary positioning is impossible.
Similarly, arbitrary orienting of {3} is impossible. Thus, your inv.
kinematic solution is subject to your discretion. You can, for example,
determine joint displacements to arbitrarily position the origin of {3}
in its plane of motion. Do at least this.
Exercise 4.17 - Keep in mind that you are interested in
theta_3 only. Geometrically it should be clear that the x and y components
of ^0(P)_{4org} are attainable. Then notice that the mechanism constrains
the z component. A good place to start then is to find the bounds on
z imposed by the kinematics.