Abstract

Kinematic synthesis design typically relies on predefined motion types, but traditional mechanism synthesis theories are primarily applied at the theoretical level, limiting their practical application in engineering. Therefore, a novel rigid-body motion identification method is developed to identify the quotient manifold G/H (in the coordinated motion of two mechanism modules used to realize the left-and-right hand system of the Lie group G, G/H is defined by one of the modules realizing the complement of the Lie subgroup H in G). First, based on the synthesis of the quotient mechanism MG/H, a Lie subgroup motion generator synthesis theorem is introduced. Second, based on the finite screw displacement motion theory, Chasles decomposition models for MG/H are developed. Finally, utilizing the transversality conditions and normalizer subgroups, an effective G/H identification method is proposed, where the SO(3) submanifold is identified first, followed by the preselection of the product of exponential (POE) cross-sectional submanifold containing the T(3) submanifold, using the hierarchical relationship of G/H. This method successfully relates rigid-body motion to G/H, advancing the development of mechanism synthesis theory in engineering practice.

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