Final Exam Question

Part 1)

The toy robot arm is a four-link manipulator with four motors that control the End Effector position. The schematic D-H diagram of the robot with the constraints 0<θ1<2π radians, 0<θ2<π/2, 0<θ3<π/2 and 0<θ4<π/2 is shown below:

Please draw the workspace of this toy robot.

Part 2)Now, suppose the limits of the joint angles of our toy robot are:

-2.35<θ1<2.35 radians, 0<θ2<2.4, -2.4<θ3<2.4, and -0.7<θ4<0.7

The desired trajectory is represented by the following plot:

And the following graphs represent the values of the joint angles that need to be performed by the robot in order to achieve this trajectory.

Do you think the robot can perform this motion (is the trajectory staying within the work space)?