Assignment 4

Due: Friday, July 24, 2015

Submit in eLearning by 10pm

This assignment must be submitted in eLearning by the date and time indi-cated. No late assignments will be accepted. Submit a single ZIP folder withMatlab files, Word file or scanned PDF file of handwritten work. Label filesappropriately so they can be easily identified. Show all your work to receivecredit.

1. (15 Points) Suppose the transformation matrix R provided below rep-resents a rotation. Determine the unit vector n and the angle .

R =

0.8387 0.0000 0.54460.0000 1.0000 0.00000.5446 0.0000 0.8387

2. (15 Points) A unit cube centered about the origin is rotated by = 45

about the line passing through the point P0 = (5, 0, 0) and having a unitvector n = (0, 0, 1). Provide the homogeneous transformation matrix and3D coordinates of all eight vertices in the original and rotated locations.

3. (35 Points) Find the equation of the surface of revolution formed byrevolving the profile curve G(u) = (u, u2, 0), u [0, 1] about the liney = x. Provide a Matlab script file that generates a plot of the surface.

4. (35 Points) Write a Matlab script file that generates the joint trajec-tories of the planar robot of Example 9 of the geometric transforma-tion notes. The tool-point trajectory the robot should follow is shown inFigure 1 where each Pi = (xi, yi,i), i = 0, ..., 3 is the location of thetool-point (xi, yi) and the orientation i relative to the +X-axis. LetP0 = (0, 3/4, 0

) correspond to time t = 0, P1 = (3/4, 1, 0) to timet = 1, P2 = (5/4, 1/2,25) to time t = 2 and P3 = (1/2, 0,90) to

1

time t = 3. The robot returns to P0 at time t = 4. For this problem,submit the following:

(a) the Matlab script file(s) used to create a skeleton (stick figure) anima-tion of the robot (the script should also generate a properly labeledMatlab plot of the three joint trajectories)

(b) and a video of the robot simulated in either CREO or SolidWorks.

P0

P1

P2

P3

Figure 1: The trajectory of the robot for Problem 4. The trajectories betweenthe tool-points are linear (including in the orientation).

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