Force-closure of spring-loaded cable-driven open chains: Minimum number of cables required & influence of spring placements

While cable-driven systems offer the advantages of being lightweight with low moving inertia, the unilateral driving property of cables generally require them to have a greater number of actuators than their rigid-linked counterparts. This paper investigates the use of springs in an attempt to reduce the number of cables required. Given an n-DOF spring-loaded cable-driven open chain, several important questions arise: (i) How can force-closure analysis be carried out for a given spring and cable routing configuration? (ii) Are n+1 cables still necessary to fully constrain the entire open chain? (iii) What is the influence of spring placement on force-closure and cable tension required? This paper will address these concerns by proposing a systematic approach based on reciprocal screw theory. The analysis shows that an n-DOF spring-loaded cable-driven open chain still requires a minimum of n+1 cables to fully constrain it. From preliminary analysis, spring placement can have a positive effect on altering the cable tension required and increasing the feasible workspace.