Kinetostatic Synthesis of Coupled Serial Chains

Single Degree-of-freedom Coupled Serial Chain (SDCSC) mechanisms are a novel class of modular and compact mechanisms with single degree-of-freedom actuation and control. In this paper, the kinetostatic synthesis of SDCSC mechanisms is addressed. Using the principle of virtual work, the static force equilibrium equations are developed for two-link SDCSCs. These are combined with the previously developed kinematic loop-closure equations to solve the kinetostatic precision point synthesis problem. Since the ratios of the angular velocities at the joints are constants by virtue of cable-pulley coupling in SDCSCs, it possible to render the kinetostatic equations linear in terms of the mechanism parameters. As a result, the solution of the precision point synthesis problem of SDCSCs becomes simpler compared to that of the four-bar mechanism. In order to meet additional criteria such as minimizing the maximum torque required over the entire range of motion of the mechanism, an optimization problem is formulated. The free choices in the precision point synthesis are used as variables in the optimal synthesis problem. The paper also addresses how torsional springs at the joints can be utilized to reduce the required input torque in supporting a specified load at the end-effector. Numerical examples are presented to illustrate the precision point and the optimal synthesis of two-link SDCSC mechanism with and without torsional springs at the joints.