Shown below is a robot arm with three revolute joints. Coordinate system 0-xyz fixed to the base link, Link 0, represents the Cartesian coordinates of the endpoint x, y, z. Joint angle O, is measured about the joint axis OA (z axis) from axis x to line OB', where point B' is the projection of point B onto the xy plane. Another coordinate system B-uvw is placed at point B in such a way that the u and waxes are parallel to the xy plane and that the y axis is parallel to the z axis. The second joint axis AB is horizontal, and joint angle 62 is measured from axis u to line BD. Joint angle 3 is measured about the joint axis CD from line BD to Link 3, i.e. line DE. Link dimensions are OA=lo, AB=l₁, BD=l₂, and DE=3. (For the purpose of explaining the kinematic structure, points C and D are shown to be different, but they are the same point, i.e. the length CD is zero.) Note also that OAB = ZABD = 90°. Answer the following questions. Xe ye E ν z F Joint 3 Link 3 03 и Joint 2 D A Ꮎ, Link 2 Ꮎ, Link 1 Joint 18 Link 0 W O y Ꮎ B' x Figure 1 Kinematic structure of a 3 d.o.f. robot a). Obtain the coordinates of the endpoint E viewed from the frame, B-uvw, that is, u, v, in the figure. b). Obtain the endpoint coordinates x, y, z, viewed from the base coordinate system O-xyz. c). For a given endpoint position, how many solutions exist to the inverse kinematics problem? Sketch all the different configurations leading to the same endpoint coordinates.