Bundle folding type III Bricard linkages

Description

The paper presents a set of one-degree-of-freedom overconstrained linkages, which can be folded into a bundle and deployed into a polygon on a plane. The proposed mechanisms are movable Bricard octahedra of type III, characterized by the existence of two configurations where all joints are coplanar. The possible geometries of doubly-collapsible Bricard linkages are parameterized and their kinematics is analyzed. A line-intersection method is proposed to construct a bundle-folding mechanism of this type. Necessary and sufficient conditions are derived for the deployed-configuration polygon to be a square. Simulation and prototype experiment results validate the analysis and design.

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