125666 FORWARD DYNAMICS OF THE 6-PUS PARALLEL MANIPULATOR BASED ON THE FORCE COUPLING AND GEOMETRY CONSTRAINT OF THE PASSIVE JOINTS(Robotics and Mechatronics)

Abstract

This paper presents a simplified approach for the forward dynamics analysis of the 6-P__-US parallel manipulator, as shown in figure.1, based on the force coupling and geometry constraint of the passive spherical joints. In the proposed method, the parallel manipulator is divided, at the passive joints, into the limbs parts and the platform part. And for both kinds of parts, the equivalent dynamic equations relating to the decomposing joints are obtained based on the transformation principles of dynamic equations between different spaces. Then, in the acceleration level, the dynamic models for both parts can be rewritten in the form of linear equations on the generalized constraint forces and the accelerations of the passive joints on the condition that the state (position and velocity) of the manipulator is specified. Thus, according to the force coupling and geometry constraints of the passive joints, the closed form solution for the generalized constraint forces can be derived readily from the linear equations system combined by the separated parts. Additionally, in the position/velocity level, the task space variables of the manipulator (the position and orientation of the platform) are chosen as the system generalized coordinates, which only results in the utilization of the inverse kinematics for the state transformation between the workspace and the passive joints space. Hence, by virtue of the constraint forces obtained from the above linear equations, the dynamic model of the parallel manipulator can be replaced by a single free rigid body (the platform) with specified external applied forces, provided by the environment through the end-effector and the limbs through the passive spherical joints, respectively. In the end, some numerical results are provided and compared to validate the correctness and effectiveness of the proposed approach.