The inverse kinematics of the PPSP helicoidal robot manipulator

The paper shows the inverse kinematics of a 6-degree-of-freedom robot manipulator presenting the PPSP configuration. This manipulator, whose arrangement of its elements provides a spiral-shaped motion, resembles the well-known screw-based mechanism which is a serially linked chain based on the Rodrigues' formula for a general screw displacement. The mentioned mechanism provides a non-flexible motion: the work piece goes from an initial configuration to a final one, through a spiral-shaped path. The corresponding screw parameters of the mechanism are calculated in terms of the positions of three non-collinear points belonging to the piece for the two ends of the fixed path. In case of changing the task conditions, it is necessary to find new screw parameters. The paper proposes a flexible manipulator with the ability of changing them as a function of the current conditions. In order to find the adequate screw configuration, it is necessary to develop the corresponding inverse kinematics in terms of the operational coordinates.