16711 Assignment 5 –Manipulator Dynamics solved

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Assignment 5 covers manipulator dynamics. The problem in this assignment will help you
revisit the steps needed to obtain the equations of motion for more complicated robot mechanisms. It will also expose you to symbolic math programs.
After completing this assignment, you should be able to compute the equations of motion of
Figure 1: The 3-link elbow manipulator.
1. Computing Manipulator EOMs (6+2pts)
In class, we had outlined the computational procedure of getting the EOMs for the 3-link
elbow manipulator shown in Figure 1 (example 4.3 on pages 172-175 in MLS). Use Mathematica or Matlab’s Symbolic Toolbox to implement this procedure with the help of screw
kinematics and compute the equations of motion for the elbow manipulator.
1. (2pts) What are the components of the resulting manipulator inertia matrix M(θ) (provide the result for element M11)?
2. (2pts) What are the components of the resulting Coriolis matrix C(θ, ˙θ) as defined in
the equation (4.23) of the book (provide the result for element C21)?
3. (2pts) What are the components of the vector N(θ, ˙θ) (provide the result for element
4. (+2pts) Use the EOMs to implement the forward dynamics of the elbow manipulator.
Devise and demonstrate a control that drives the end-effector from the position given in
Figure 1 into a vertical position with the end-effector pointing skywards.
Please submit a file of source code with your answer. In the file, make sure you comment all
the steps of computing these matrices.