Unless otherwise indicated, all the problems are from the course text, Craig, Introduction to Robotics. Unless otherwise indicated, each problem is worth 10 points.

1. In Homework 2, you determined the forward kinematics for the mechanism in problem 3.18, Figure 3.38. Assume that we are interested in the (x,y,z) location of the end effector (note that you will have to add a frame at the end effector -- before your forward kinematic computations only went to the frame attached to the last link at the axis of rotation). Assume that each joint angle is 30^o.
   1. What is the direction of the maximum mechanical advantage?
   2. What is the direction of the maximum velocity amplitude?
2. In Homework 2, you determined the forward kinematics for the mechanism in problem 3.20, Figure 3.40. Assume that we are interested in the (x,y,z) location of the end effector. Assume that d₁ = 0 and that the two revolute joint angles are 30^o
   1. What is the direction of the worst velocity amplitude?
   2. What is the direction of the worst mechanical advantage?
3. In Homework 3, you determined the forward kinematics for the mechanism in problem 3.21, Figure 3.41. Assume that we are interested in the (x,y,z) location of the end effector. Assume that d₁ = 2, d₂ = 1 and d₃ = 4.
   1. What is the direction of the maximum force fidelity?
   2. What is the direction of the maximum velocity fidelity?
4. Consider the following image. The purpose of this homework is to develop software that can distinguish blurry photographs of objects that may appear similar. You can write the programs using any programming language that you want.

   

   1. (0 points) Download the photographs and convert them from jpeg format to PGM (ascii) grey-scale format.
   2. (20 points) Write and submit a program to produce a histogram of grey-scale values for each photograph. Plot and submit the histograms.
   3. (10 points) Write and submit a program to implement a thresholding scheme. For pixels with values greater than the threshold value, assign a value of 255, and for pixels with values less than the threshold value, assign a value of zero. Use the histogram from the previous problem to determine a good threshold value. Plot and submit the resulting black and white images. This is the same as the sample code from class.