Dynamics of a Parallel-kinematics Machine with Six Pairs of Offset Joints

The authors propose a systematic formulation of the dynamics of the 6-P-RR-R-RR parallel-kinematics machine (PKM) with offset RR-joints. The kinematics of the same system is reported in an accompanying paper. Based on the kinematics model developed in the former, the dynamics model of the limb-chain is derived using the Newton-Euler equations. Then, the constraint wrenches in the governing equations of the limb-chain are eliminated with the aid of the natural orthogonal complement (NOC). This is the twist-shaping matrix, which maps the joint-rate array of the limb-chain into the twist array of the PKM. Furthermore, the dynamics model of the whole PKM with offset joints is formulated. Moreover, the actuator forces are obtained. Finally, upon validation via simulation, the dynamics model is proven to be both precise and effective.