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The Stiffness Analysis of 4UPS-PU Parallel Mechanism Based on Conservative Congruence Transformation Model

Xie Li-chen

Abstract

In order to show the effect on stiffness of parallel manipulators due to derivation changes of Jacobian matrix of parallel manipulator cause by external forces,here the stiffness performance of the spatial 4UPS-PU parallel manipulators is investigated.This paper focuses on the stiffness analysis of the 4UPS-PU parallel mechanism based on CCT method and compared with the traditional stiffness model.First the Jacobian matrix of 4UPS-PU manipulator is determined.Then the distribution of CCT stiffness of 4UPS-PU parallel mechanism in every direction and the distribution of tradition stiffness model in every direction are analyzed.Finally,the stiffness mappings considering the geometric changes in the manipulator due to the effect of external forces and the conventional stiffness mappings are compared.Through comparison one can see that the external force effect on the stiffness of the manipulator cannot be neglected.

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Key concepts: Jacobian matrix and determinant, Stiffness, Tangent stiffness matrix, Direct stiffness method, Parallel manipulator, Screw theory, Stiffness matrix, Mechanism (biology)