3. For each of the shown robot arms, determine how many solutions there are for the kinematic equations. In other words, how many different sets of joint angles can be identified to place the endpoint at a specific position. We are only concerned with the position of the endpoint, not its orientation. Also, we're interested in the solution for the vast majority of the workspace; sometimes, an arm will have some special subset within the workspace where there may be additional solutions due to symmetry, etc. For this problem we want the number of solutions for a generic location within the workspace.
If there's more than one general solution, draw a sketch of the robot showing the two configurations resulting in the same end effector position, for some convenient location in the workspace.
a. Manipulator shown in Figure 3.37
b. Manipulator shown in Figure 3.40 (assume L1 > (L2 +L3)
c. Manipulator shown in Figure 3.41
