Kinematics and performance analysis for single-loop deployable polygonal mechanisms based on deployable paths

Abstract

Deployable polygonal mechanisms (DGMs) are widely used in various fields; however, their performance evaluation remains challenging due to limitations in existing indices. To address these shortcomings, this paper innovatively proposes several new evaluation indices for DGMs, aiming to improve the precision and comprehensiveness of performance analysis. Firstly, a velocity analysis method for single-loop DGMs based on deployable paths is introduced, eliminating the need to solve joint angle analytical expressions, reducing computational effort. Secondly, a method for calculating the transmission wrench screw of single-loop mechanisms is proposed. This method is applicable to overconstrained, non-overconstrained, and reconfigurable mechanisms, regardless of whether they possess a single or multiple degrees of freedom. Thirdly, an index for evaluating the deploying performance of $n$R DGMs that deploy into general planar polygons is developed, along with an algorithm for calculating folding length. Furthermore, novel evaluation indices for deploying$/$folding performance in various application scenarios, motion$/$force transmission performance, and transmission ratio stability are proposed. Finally, detailed analyses of deploying$/$folding performance, transmission ratio stability, global extreme velocity, global extreme stiffness, and motion$/$force transmission performance of $n$R DGMs are provided.