Research on the Dynamic Model of an Over-constrained Parallel Mechanism

Due to their redundant links and redundant restriction forces,it has been a different problem for dynamic modeling and analysis of over-constrained parallel mechanism.A planar 2-DOF over-constrained parallel mechanism is discussed as an example.On the basis of kinematics analysis,the equilibrium equations for the force and moment of this mechanism are established by using Newton Euler method and D'Alembert principle.The model cannot be solved because the number of equations is less than that of unknown variables.So a novel method,which can provide feasible supplementary equations through analyzing the deformation compatibility to establish the relationships between constraint forces and position errors of terminal platform,is put forward.Thus the dynamic model can be solved.This method is applied to the dynamic modeling and analysis of parallel mechanism in a hybrid machine tool.By numerical example,driving forces and platform error are simulated.The result shows that this method is feasible and reasonable.The research provides a new method to the dynamic modeling and analysis of over-constrained parallel mechanism.