Low-cost variable stiffness joint design using translational variable radius pulleys

Robot joints are expected to be safe, compliant, compact, simple and low-cost. Gravity compensation, zero backlash, energy efficiency and stiffness adjustability are some desired features in the robotic joints. The variable radius pulleys (VRPs) provide a simple, compact and low-cost solution to the stiffness adjustment problem. VRP mechanisms maintain a preconfigured nonlinear force-elongation curve utilizing off-the-shelf torsional spring and pulley profile. In this paper, three synthesis algorithms are presented for VRP mechanisms to obtain desired force-elongation curve. In addition, a feasibility condition is proposed to determine the torsional spring coefficient. Using the synthesis methods and the feasibility condition, a variable stiffness mechanism is designed and manufactured which uses two VRPs in an antagonistic cable driven structure. Afterwards, the outputs of three synthesis methods are compared to force-elongation characteristics in the tensile testing experiment. A custom testbed is manufactured to measure the pulley rotation, cable elongation and tensile force at the same time. Using the experiment as the baseline, the best algorithm achieved to reproduce the desired curve with a root-mean-square (RMS) error of 13.3%. Furthermore, VRP-VSJ is implemented with a linear controller to reveal the performance of the mechanism in terms of position accuracy and stiffness adjustability.