Force Analysis of the Overconstrained Mechanisms Based on Equivalent Stiffness Considering Limb Axial Deformation

Abstract Overconstrained mechanism has the advantages of large bearing capacity and high motion reliability, but its force analysis is complex and difficult because the mechanism system contains overconstraints. Considering the limb axial deformation, taking typical 2SS+P and 7-SS passive overconstrained mechanisms, 2SPS+P and 7-SPS active overconstrained mechanisms, and 2SPS+P and 7-SPS passive-input overconstrained mechanisms as examples, a new force analysis method based on the idea of equivalent stiffness is proposed. The equivalent stiffness matrix of passive overconstrained mechanism is derived by combining the force balance and deformation compatibility equations with consideration of axial elastic limb deformations. The relationship between the constraint wrench magnitudes and the external force, limb stiffness is established. The equivalent stiffness matrix of active overconstrained mechanism is derived by combining the force balance and displacement compatibility equations. Here, the relationship between the magnitudes of the actuated wrenches and the external force, limb stiffness is investigated. Combining with the equivalent stiffness of the passive overconstrained mechanism, an analytical relationship between the actuated forces of passive-input overconstrained mechanism and the output displacement, limb stiffness is explored. Finally, adaptability of the equivalent stiffness to overconstrained mechanisms is discussed, and the effect of the limb stiffness on overconstrained mechanisms force distribution is revealed. The research results provide a theoretical reference for the design, research and practical application of overconstrained mechanism.