The RCRRC Five-Link Space Mechanism—Displacement Analysis, Force and Torque Analysis and Its Transmission Criteria

Abstract

Displacement, and force and torque analyses of the RCRRC five-link space mechanism are performed using 3 × 3 screw matrix and dual vectors. Expressions for all the displacements in the mechanism are given. Input-output displacement equation is obtained in both eighth order and 16th order polynomials in half-tangents of the angular displacement. The solution of the 16th order displacement equation shows that the RCRRC mechanism may have 16 geometric inversions for a set of dimensions. The eighth order displacement equation, which conforms with that obtained by the Unified Theory which uses dual spherical trigonometry, is an incomplete relationship and it only gives the displacements of half of the existing geometric inversions. Numerical examples and photographs of the geometric inversions are given. The force and torque analysis of the RCRRC five-link space mechanism is performed by joint force analysis. Dual inertia forces are neglected, and the motion of the mechanism is known. Explicit expressions for the dual force components at the pair locations are given, as well as the matrix solution. Transmissivities of the mechanism are defined. Force and torque analysis of one of the geometric inversions is performed in a numerical example.