2011 Volume 5 Issue 3 Pages 416-428
This paper presents a simplified approach for the forward dynamics of the 6-PUS parallel manipulator. In the proposed method, the parallel manipulator is divided into the limb parts and the platform part at the passive spherical joints. For both parts, the equivalent dynamic equations related to the passive joints are obtained based on the transformation principles of dynamics between different spaces. Then, in acceleration level, the dynamic model for both parts can be rewritten in the form of linear equations on the generalized constraint forces and the linear accelerations of the passive joints on the condition that the state (position and velocity) of the manipulator is specified. According to the force coupling and geometry constraint of passive joints, the closed form solution for the generalized constraint forces can be derived readily from the linear equations combined by the separated parts. In the level of position and velocity, task variables of the manipulator, namely the position and orientation of the moving platform, are chosen as the system's generalized coordinates, which results in the utilization of the inverse kinematics for the state transformation between the workspace and the passive joints space. Consequently, by virtue of the obtained constraint forces, the dynamics of the manipulator can be replaced by a single free rigid body (the platform) with specified external forces provided by the environment through the end-effector and the limbs through the passive spherical joints, respectively. At last, some numerical results are provided and compared to validate the correctness and effectiveness of the proposed approach.