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Stiffness Analysis and Stiffness Mapping of 3-RRR Planar Parallel Mechanism Based on CCT Stiffness Matrix

Shujun Li

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Abstract

The analytical stiffness equations of the part concerning joint stiffness and configuration and the uncompleted analytical stiffness equations of the part affected by external forces of 3-RRR planar parallel mechanism were all deduced,based on the conservative congruence transformation(CCT) stiffness matrix.The method of stiffness mappings was given,and the maps of the mechanism were presented to illustrate the properties of the stiffness of the mechanism.The stiffness characteristics of the mechanism were analyzed and discussed.It was revealed that the stiffness of the mechanism are configuration dependent and proportional to the actuating forces and joint stiffness.The stiffness becomes higher towards the boundaries of working space and vise versa,which forms a stronger stiffness ring area near the boundaries,and a weaker stiffness zone near the center of working space.

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What this paper is about

The analytical stiffness equations of the part concerning joint stiffness and configuration and the uncompleted analytical stiffness equations of the part affected by external forces of 3-RRR planar parallel mechanism were all deduced,based on the conservative congruence transformation(CCT) stiffness matrix.The method of stiffness mappings was given,and the maps of the mechanism were presented to illustrate the properties of the stiffness of the mechanism.The stiffness characteristics of the mechanism were analyzed and discussed.It was revealed that the stiffness of the mechanism are configuration dependent and proportional to the actuating forces and joint stiffness.The stiffness becomes higher towards the boundaries of working space and vise versa,which forms a stronger stiffness ring area near the boundaries,and a weaker stiffness zone near the center of working space.

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Available abstract

The analytical stiffness equations of the part concerning joint stiffness and configuration and the uncompleted analytical stiffness equations of the part affected by external forces of 3-RRR planar parallel mechanism were all deduced,based on the conservative congruence transformation(CCT) stiffness matrix.The method of stiffness mappings was given,and the maps of the mechanism were presented to illustrate the properties of the stiffness of the mechanism.The stiffness characteristics of the mechanism were analyzed and discussed.It was revealed that the stiffness of the mechanism are configuration dependent and proportional to the actuating forces and joint stiffness.The stiffness becomes higher towards the boundaries of working space and vise versa,which forms a stronger stiffness ring area near the boundaries,and a weaker stiffness zone near the center of working space.

Key concepts: Stiffness, Direct stiffness method, Tangent stiffness matrix, Mechanism (biology), Planar, Stiffness matrix, Joint stiffness, Structural engineering

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Stiffness Analysis and Stiffness Mapping of 3-RRR Planar Parallel Mechanism Based on CCT Stiffness Matrix — Research Paper | ScholarLens