Multi-loop Mechanisms Inspired by Flexible Polyhedrons: Construction and Mobility

Abstract Inspired by flexible polyhedrons, this paper proposes a construction method that converts flexible polyhedrons into the multi-loop mechanisms. Several multi-loop mechanisms with single degree-of-freedom are obtained through this method. To analyze this class of mechanisms, this paper applies screw theory to examine the equivalent motions between kinematic chains, which significantly simplifies the steps and computational workload for analyzing complex mechanisms. In this process, methods including structural decoupling and virtual coupling nodes are utilized. The effectiveness and intuitiveness of the methods are demonstrated in the mobility analysis and structural simplification of the Steffen mechanism. Finally, the mobility analysis of the Steffen mechanism inspires a method for constructing flexible polyhedrons with a single or multiple degrees of freedom.