Dynamic Trajectory Planning and Geometric Design of a Two-DOF Translational Cable-Suspended Planar Parallel Robot Using a Parallelogram Cable Loop

Abstract

This paper presents a trajectory planning approach and an analysis of the geometric design parameters for a planar cable-suspended translational parallel robot based on a parallelogram cable loop. The cable robot produces purely translational movements in a planar workspace. Furthermore, this special architecture only requires two actuators which makes it fully actuated. From the dynamic model of the robot, general algebraic inequalities are obtained that ensure that the cables remain taut. A general elliptic trajectory is then defined and substituted into the algebraic inequalities to obtain conditions on the geometrical design parameters that ensure that the cables are always in tension. In addition, a special trajectory-specific oscillation frequency emerges and enables the end-effector to dynamically move beyond the boundaries of the static workspace, thus expanding the workspace of the mechanism. Finally, a kinematic sensitivity index is studied in order to assess the influence of the parallelogram structure on the rotational stability of the mechanism.