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Modular Kinematic Reduction of Closed-Chain Mechanisms Using Path Assembly and Defect Homotopy

arXiv · AI, language, vision and robotics · article · Sep 10, 2026 · UTC

Closed kinematic chains complicate modular modeling by coupling active and passive coordinates through nonlinear closure constraints. This paper presents a Path-Assembled Closure Differential Mapping (PACDM) framework for modular closure resolution and kinematic reduction. Each closure element compares two ordered transformation paths with common endpoints, with their mismatch expressed through the logarithm on SE(3) and the corresponding Jacobian assembled from local transformation derivatives. Multi-path modules are constructed from a minimal set of pairwise closure elements, while rank-reve

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