ECE 470: Introduction to Robotics
Homework #3

Due: Thursday, Oct. 5, 2017.

The Denavit Hartenberg Convention

This homework should provide you with plenty of practice assigning DH frames.
  • Solve problems 3-2, 3-3, 3-4, 3-6. These problems are fairly straightforward, and will give you practice assigning DH frames. For each problem, you should show a figure of the robot. On the figure, indicate the DH frames (no need to show y-axes), and any relevant DH parameters. You should also include a table of DH parameters for each robot and the forward kinematic equation.

    Note: The phrase "forward kinematic equation" refers to the matrix equation relating the joint variables to the homogeneous transformation matrix corresponding to the position and orientation of the end effector. For instance: T(theta1,theta2,d3) = [ 4x4 matrix ].

    You will find Robotica, which is introduced in Lab 3, to be quite helpful for these problems. Robotica will generate all the A and T matrices for you, but only submit the T matrix relating the base frame to the end effector frame, T[0,n]. Please display only this matrix. Consult the Robotica manual, and employ appropriate commands to simplify and display large, complicated matrices.
    You are also free to use Matlab for your computations.

  • Solve problem 3-9. For the spherical wrist, you should assign the DH frames so that all three (i.e., frames 3, 4, and 5) share a common origin at the wrist center.

  • For this problem you are to design a four-link arm (thus, four joints). 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. Assign DH frames and specify the table of DH parameters. Include a figure that clearly shows the robot and the DH frames.

  • For this problem, you will design a new convention for assigning coordinate frames to robots such that the x-axis is assigned to be the axis of actuation, instead of the z-axis as was developed in class. First, determine two constraints that would be analogous to the constraints DH1 and DH2. Then, carefully describe the construction of the corresponding DH Matrix. Finally, prove that the the two constraints you have specified imply the resulting form of this transformation matrix.