ECE 470: Introduction to Robotics
Homework #6

Due: Tuesday, Dec. 5, 2017.

The Assignment

  • Solve problem 4-5.
  • Compute the derivative of the DH rotation matrix (e.g., eq. 3.13) and find a simple expression for the angular velocity induced by a revolute joint. Solve for joint i, and express the angular velocity relative to frame i-1.
  • Solve problems 4-17 and 4-18. These problems will give you practice computing Jacobian matrices.
  • Design a four-link arm (thus, four joints) and determine its Jacobian matrix. 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 ector 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 Homework Set 3 if you like. Include a figure that clearly shows the robot and the DH frames. Show the intermediate steps in your computations.
  • Solve problems 4-19 and 4-20. These problems will give you a bit of practice finding singularities.