Geometry and Constraint Analysis of the Three-Spherical Kinematic Chain Based Parallel Mechanism

Abstract

This paper presents a three-spherical kinematic chain based parallel mechanism that evolved from an origami fold. The new parallel mechanism with symmetrical structure consists of a base, a platform, and three-spherical six-bar chains as chain-legs connecting to both base and platform via revolute joints. This paper investigates the constraint of the mechanism by constructing a virtual symmetric plane that is based on the three virtual centers of the spherical chains. Revealing the geometric characteristics and constraint disposition of the constraint screw system, singularity is identified related to the constraint configuration based on Grassmann line geometry and dependency of the constraint screw system, leading to selection of the design parameters that avoid the platform singularity.