Position and Force Analysis of a Planar Tensegrity-Based Compliant Mechanism

Abstract

This paper presents an analysis of a planar tensegrity-based mechanism. In this study, a moving body is joined to ground by four compliant leg connectors. Each leg connector is comprised of a spring in series with an adjustable length piston. Two problems are solved in this paper. In the first, the values of the four spring constants and free lengths are given and the lengths of the four pistons are determined such that (1) the top body is positioned and oriented at a desired pose, (2) the top body is at equilibrium while a specified external wrench is applied, and (3) the total potential energy stored in the four springs equals some desired value. In the second problem, the values for the four spring free lengths are given and the values for the four spring constants and the lengths of the four pistons are determined such that conditions (1) and (2) from above are met and also the instantaneous stiffness matrix of the top body equals a specified set of matrix values. The paper formulates the solutions of these two problems. Numerical examples are presented.