Direct kinematics of a double parallel robot arm for real time velocity control

The determination of the direct kinematics of a parallel mechanism is a difficult problem but must be solved for practical application. This paper presents the efficient formulation of the direct kinematics and the Jacobian of a double parallel robot arm for velocity control. The robot arm consists of two parallel mechanisms, and a central axis that generates positional and orientational motions independently. Given a set of lengths for the linear actuators, the direct kinematics computes the position and orientation of the end-effector, and the Jacobian transforms the velocities of the end-effector to those of the linear actuators. The developed formulation is implemented in a real-time control setting and its efficiency is demonstrated. Department of Control and Instrumentation Engr.