Closed-Form Dynamic Modeling and Performance Evaluation of a 4-Degrees-of-Freedom Parallel Driving Mechanism

Kinematic estimations and dynamic performance assessments are fundamental theoretical issues to realize the mechanism from conceptual design to engineering application. In this article, the closed-form dynamic formulations of a 4-degrees-of-freedom (DoFs) parallel driving mechanism are derived by combining the Lagrange method and the virtual work principle. The selection principle of generalized coordinates and the steps for inverse dynamics modeling of the manipulator are proposed. Simulation results verify the correctness of the dynamic model, and a physical prototype has been built. Based on the dynamic modeling, the concise algebraic expression of the operational space inertia matrix of the parallel driving mechanism is deduced. Because the translation and rotation degrees-of-freedom are inconsistent in the operational space, the Jacobian matrix is adopted to map the inertia matrix from the operational space to the joint space. Based on the inertia matrix in joint space, the average energy transfer efficiency (AETE) index is proposed. Finally, two control techniques for the manipulator implementable in joint space are compared. The AETE index and dynamic modeling method suggested in this article can be further used in other manipulators for dynamic analysis and motion system design.