Inverse and forward kinematic analysis of a 6-DOF foldable mechanism with a circular rail (FoldRail mechanism)

Abstract

This article considers an inverse and forward kinematic analysis of a recently proposed foldable parallel mechanism with a circular rail (FoldRail mechanism). The mechanism has six degrees of freedom and three RRRS kinematic chains. Here, R and S indicate revolute and spherical joints, respectively, and the first and third R joints of each chain are actuated. First, the paper presents an algorithm to find a closed-form solution to the inverse kinematic problem. The analysis shows there can be four different solutions for each kinematic chain. Next, the paper studies forward kinematics and develops an elimination-based approach to handle this problem. The proposed method relies on the vector convolution operation and avoids symbolic computations inherent to most other similar techniques. It is shown that the forward kinematics has up to 16 distinct solutions, corresponding to 16 different assembly modes of the mechanism. Numerical examples illustrate the developed techniques for both the inverse and forward kinematic problems. The proposed algorithms provide the basis for subsequent performance evaluation and design optimization, and they can be applied to other parallel mechanisms.