A Complete Closed-Form Solution to the Inverse Kinematics Problem for the P2Arm Manipulator Robot

In this paper, we propose a complete closed-form solution to the inverse kinematics problem for a 5-dof manipulator robot, where the existence conditions for all the possible solutions are clearly established and the "singular configurations" where infinite solutions exist are identified. We define a "desired configuration" for the final effector as the position for the center of the gripper and the direction of the gripper's main axis. This choice seems natural for robots mainly devoted to assembling tasks, even if the rotation around this main axis cannot be freely set. Under these conditions, a straight-forward method in order to obtain all the different exact solutions is also presented.