The kinematic structure of a 3 DOF snow plowing robot is shown below at its home configuration. Coordinate frames are attached to the individual links, as shown in the figure below. Joint 1 is a revolute joint about the zo axis. Joints 2 and 3 are also revolute joints about the horizontal axes at points B and D, respectively. Link 1 is an L-shaped rigid body connecting Joints 1 and 2. Coordinate frame A- xyz is attached to point A. Link 2 is also an L-shaped rigid body with a coordinate frame attached to point C. A large shovel is attached to the endpoint E. All joint angles are zero at the home configuration, and are measured in a right hand sense. Three unit vectors pointing in the directions of x,, y;, and z, axes of the individual coordinate frames are indicated as n, t,,b, i = 0 ~ 3 . The link dimensions are OA l, BC = l2, CD = l3,DE = 14. Answer the following questions. = = lo, AB = Find singular configurations, and indicate in which direction the endpoint cannot be moved at a non- zero velocity. Assume 13 = 0. (5 points) Z1 b Z2 b3 A t y B Link 2 C t2 y2 Z3 Joint 2 x X E Link 1 , Link 3 y3 0 Joint 3 Joint 1 03 X3 n3 Zo bo Link 0 Yo Figure 4 Schematics of a 3DOF snow plowing robot at home configuration