CS325  Lab 4 - Forward Kinematics

Objectives:

• Understand the DH convention
• Be able to derive forward kinematics

1. Download linktr.m and robottr.m and save these in your robot directory.  The linktr function returns the transformation matrix for a link given the alpha, a, theta, and d values.  The robottr function returns the transformation matrix for the three-link robot that we used as an example in class.
    
2. Consider the following three-link robot:

   

   The base is a revolute joint, above this there is a second revolute joint and then there is a prismatic joint.  The height from the base to the second joint is 1 unit. 
   
   We derived the following DH parameters:

   Link	a	alpha	d	theta
   1	0	pi/2	1	variable
   2	0	pi/2	0	variable
   3	0	0	variable	pi/2

    

3. We will use the robot toolbox to create a  model of the robot.  The link command link([alpha  a theta d sigma],'standard') will create a link object with the given DH parameters.  The parameter sigma should be 0 for a revolute joint and 1 for a prismatic joint. 
   
   So for example to create the first link:
   
   L1 = link([pi/2,0,0,1,0],'standard)
   
   Create the three links and then you can create the robot:
   
   r = robot({L1 L2 L3})
   
   You can plot the robot for various values of the joint variables.  For example to plot with theta1=0, theta2=pi/2 and d3=.5:
   
   plot(r, [0 pi/2, .5])
    
4. Use robottr to calculate the position of the tool for various values of the joint variables:
   
   If the tool is at [0 0 0] in the tool coordinates multiplying the robot translation matrix and [0;0;0;1] should give you the coordinates of the tool with respect to the base coordinates.  What would be the position of the tool when theta1=0, theta2=pi/2 and d3=.5?
   
    
5. 3-5 on p 113 of your text.  Draw the diagram of the coordinate frames and verify your DH parameters by building and plotting the robot in MATLAB.
    
6. 3-7 on p 113 of your text.  Draw the diagram of the coordinate frames and verify your DH parameters by building and plotting the robot in MATLAB.
    
7. The kinematic data for Armand is given in the file armand.m.  Try out plotting Armand for various joint values to verify that this data is correct.  The home values are given in the vector qz.
    
8. Hand in written work plus ANNOTATED plots and printouts from MATLAB.  Your annotations should explain all your results.