Analysis and synthesis of LinWWC-VSA, a Variable Stiffness Actuator for linear motion

This work presents the principle of operation of LinWWC-VSA, a Variable Stiffness Actuator (VSA) suitable to perform linear motions, conversely to the vast majority of VSAs typically designed to perform rotational movements and often affected by limits in the actually exploitable range of motions. It features two antagonist nonlinear equivalent springs, each of them made up of a cam wrapped by a wire and constrained by a torsion spring. This work presents methods both for the analysis and the synthesis of the actuator. Two synthesis methods, one numerical and one analytic, are described to design the cam profile as function of the desired stiffness-displacement characteristic of each equivalent nonlinear spring. The analytic method exploits the peculiar formulation of the logarithmic spiral. The theoretical aspects of the actuator are accompanied by numerical simulations.