Aerospace and Mechanical Engineering

Homework 4

B. Goodwine
Spring, 1999 |
Issued: February 18, 1999 Due: February 24, 1999 |

Unless otherwise indicated, all the problems are from the
course text, Craig, *Introduction to Robotics*. Unless
otherwise indicated, each problem is worth 10 points.

- Each project group must turn in a summary of their proposed
work for Project
2. Attach this to the homework for
*only one*group member -- everyone will get the same credit. - In class, we computed the inverse kinematics for a Puma 560
using Pieper's method. This homework problem is to find
*one*of the solutions for the given data (recall that there are four solutions). For the physical parameters of the robot, let

a_{2}= 2 ft

d_{3}= 0.5 ft

d_{4}= 2 ft

a_{3}= .16666 ft

h = .33333 ft.

Let the*desired*location and orientation of the {6} frame relative to the {0} frame be - 5.18
- 5.19
- For the three link planar robot illustrated in in the
Figure,
- determine the forward kinematics from the base frame,
S, to the tool frame T
*including the orientation of the tool frame*(in class, I only did (x,y) for the two link manipulator); - compute the Jacobian;
- determine at least two singular configurations; and,
- (optional - 10 points extra ) modify the animation code presented in class to drive the mechanism from the starting configuration given in the code along a desired trajectory that takes it near one of the workspace interior singularities. Verify that large joint velocities occur near the singularity.

- determine the forward kinematics from the base frame,
S, to the tool frame T
- In Homework 2, you determined the forward kinematics for
the mechanism in problem 3.18, Figure 3.38. Assume that we
are interested in the (x,y,z) location of the
**end effector**(note that you will have to add a frame at the end effector -- before your forward kinematic computations only went to the frame attached to the last link at the axis of rotation). Assume the reference configuration is as illustrated in the figure in the book.- Compute the Jacobian for this system; and,
- determine at least one singular configuration.

- In Homework 2, you determined the forward kinematics for
the mechanism in problem 3.20, Figure 3.40. Assume that we are
interested in the (x,y,z) location of the
**end effector.**Assume the reference configuration is as illustrated in the figure in the book.- compute the Jacobian for this system; and,
- determine at least one singular configuration.

B. Goodwine (