ECE 470: Introduction to Robotics
Homework #4

Due: Thursday, Oct. 12, 2017.

This homework should provide you with practice solving inverse kinematics problems.

The Assignment

  • Solve problem 3-11. This problem addresses issues related to multiple solutions of inverse kinematic problems.
  • Solve problems 3-12, 3-13 and 3-14. These are straightforward inverse kinematics problems for several different manipulators. Note, if multiple solutions exist, you must list them. You need not give explicit equations for the additional solutions, but you must enumerate them, and explain how they differ from the solution you have provided.
  • Solve problem 3-18. For this problem, you will find the complete inverse kinematic solution for a Stanford arm equipped with a spherical wrist. There are multiple solutions for this arm/wrist, but you need only find one of them. However, you must discuss the other solutions (e.g., give the number of solutions, and explain how they differ from the solution that you have found).
  • Solve problem 3-21. For this problem, be sure to include a drawing of the robot that clearly indicates its kinematic structure and your assignment of DH frames.
  • Consider the two-link planar arm (e.g., Fig. 3.6). The inverse kinematic problem is to find the two joint angles that place the end effector frame at a given x-y position. In terms of the desired x-y position of the end effector frame, describe all situations for which
    • no solutions exist
    • two solutions exist
    • exactly one solution exists
  • For this problem you are to design a four-link arm (thus, four joints) and determine its inverse kinematics solution. Your design should include at least one revolute joint and one prismatic joint. The arm should not be a simple planar mechanism (i.e., the origin of the end effector frame should not be constrained to lie in a plane), and it should not appear in the text book. You may use your design from the previous homework assignment if you like. Include a figure that clearly shows the robot and the DH frames. Show all steps in your computations.