Bundle folding type III Bricard linkages

Abstract

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.This research has been supported by the National Natural Science Foundation of China under Grant 51605011, 51635002(Key Program), the Fundamental Research Funds for the Central Universities (YWF-19-BJ-J-336), the State Key Laboratory of Robotics and System (HIT), and the AUTORECON project funded under the Seventh Framework Program of the European Commission (Collaborative Project NMP-FOF-2011-285189). The authors gratefully acknowledge the supporting agencies