Origami Inspired Integrated Planar Spherical Overconstrained Mechanisms

Abstract

This paper presents two integrated planarspherical overconstrained mechanisms that are inspired and evolved from origami cartons with a crashlock base. Investigating the crashlock base of the origami cartons, the first overconstrained mechanism is evolved by integrating a planar fourbar linkage with two spherical linkages in the diagonal corners. The mechanism has mobility one and the overconstraint was exerted by the two spherical linkages. This mechanism is then evolved into another integrated planarspherical overconstrained mechanism with two doublespherical linkages at the diagonal corners. The evolved mechanism has mobility one. It is interesting to find that the doublespherical linkage at the corner of this new mechanism is an overconstrained 6R linkage. The geometry evolution is presented and the constraint matrices of the mechanisms are formulated using screwloop equations verifying mobility of the mechanisms. The paper further reveals the assembly conditions and geometric constraint of the two overconstrained mechanisms. Further, with mechanism decomposition, geometry and kinematics of the mechanisms are investigated with closedform equations, leading to comparison of these two mechanisms with numerical simulation. The paper further proposes that the evolved overconstrained mechanism can in reverse lead to new origami folds and crease patterns. The paper hence not only lays the groundwork for kinematic investigation of origamiinspired mechanisms but also sheds light on the investigation of integrated overconstrained mechanisms.