10.5: Exercises

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Exercises

1. Think about at least three mechanisms to realize a parallel jaw gripper. How does the minimum and maximum aperture of the gripper relate to the gripper width for each of these designs?

2. Think about at least three mechanisms to actuate a fourbar linkage. Which of these will keep the payload inside the gripper during power failure?

3. Derive an equation for the distance of the fingertip from the gripper base in a 4-bar linkage gripper as a function of the gripper opening width. Use appropriate parameters for all unknown parameters.

4. Write code to generate rectangles with random dimensions and orientations. Rectangles can overlap. Use a point-in-polygon test to simulate random point samples on their surface, simulating a top-down view with a depth sensor.

Implement a segmentation routine that clusters objects based on a minimum distance.
Implement a filter that rejects connected components based on size. For which kind of objects does this work well and where does this method fail?
Implement a filter that rejects connected components that do not have rectangular shape. Are you able to specify a filter that works independent of the object size?
Apply principal component analysis to compute the principal axes of the rectangle and compare with ground truth. How does the number of samples affect the accuracy of your estimate?

5. Use a function of the kind u(x − i) + rand(j) with u(x) the unit step function, rand() uniformly distributed random noise, and i, j suitable parameters to simulate a noisy depth-image a cube with width i. Use the nearest neighbor of each point to compute its normals and a suitable clustering algorithm to identify the cube. How do i and j affect the accuracy of your estimate?