Golfari Theorem: A Constructive Geometric Approach to the Foldability of Planar Four-Bar Linkages
Year: 2026
Type: preprint
Abstract: This paper introduces a unified geometric formulation, providing a comprehensive, Euclideanfoundation for planar four-bar linkages. Moving away from traditional algebraic frameworks thatclassify mechanisms through link length inequalities, this work establishes a complementary geometricframework by utilizing a rigid generating triangle as the fundamental evolutionary structure.By introducing a fourth hinge joint along the perimeter of the triangle, the system transforms intoa mobile kinematic linkage. The proposed framework proves that total collinear foldability is bothconstructively generated and universally characterized through a two-fold geometric law, supportedby rigorous synthetic proofs for both genesis and structural configuration. This formulation offersa coordinate-free approach that enriches the morphological analysis of linkage configurations.
Author: Golfari, Nicola
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168328003
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