### ME 469: Introduction to Robotics 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.

1. 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.
2. 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
a2 = 2 ft
d3 = 0.5 ft
d4 = 2 ft
a3 = .16666 ft
h = .33333 ft.
Let the desired location and orientation of the {6} frame relative to the {0} frame be
3. 5.18
4. 5.19
5. For the three link planar robot illustrated in in the Figure,
1. 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);
2. compute the Jacobian;
3. determine at least two singular configurations; and,
4. (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.
6. 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.
1. Compute the Jacobian for this system; and,
2. determine at least one singular configuration.
7. 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.
1. compute the Jacobian for this system; and,
2. determine at least one singular configuration.

Last updated: February 22, 1999.
B. Goodwine (jgoodwin@nd.edu)