Spherical vs Non-Spherical Wrist Configurations For Robotic Drawing 

The Jaco arm encountered multiple singularities during the wall drawing task. These appear in the torque plots as abrupt changes and large variations. Although the motion is smooth for the initial three quarters of the trajectory, the IK solver struggles as the manipulator approaches its kinematic limits. Despite these challenges, the step-by-step trajectory generation with iterative inverse kinematics allows the Jaco arm to recover from singular configurations and complete the rest of the trajectory. The unique singularities of the Jaco arm caused inferior accuracy for this task compared to the UR5e. 

The UR5e completed the circular trajectory with near-perfect accuracy, maintaining the required 5 N contact force throughout the motion. The corresponding joint torque plots remain smooth, indicating that the manipulator stayed away from singular configurations and that the Jacobian-transpose force mapping remained stable throughout the motion.

The Jaco arm completed the inner and outer circle while maintaining the required constant contact force on the canvas. The joint torques remained smooth throughout the motion, showing stable inverse kinematics and no singularity issues in this configuration. A small deviation occurred at the start of the trajectory, but the robot quickly converged to the desired path and maintained steady contact for the remainder of the drawing.

The UR5e produced nearly identical results on the floor drawing task, completing the full circular trajectory while maintaining the required contact force. The torque plots remained smooth, indicating stable motion away from singularities. The same small error appeared at the beginning of the trajectory, suggesting the deviation was caused by the path solution rather than differences in the robot kinematics. Overall, both manipulators performed similarly on the horizontal surface.