Design and optimization of compliant constant-torque mechanisms utilizing arbitrary pre-curved beams

Compliant constant-torque mechanisms (CCTMs) have the potential to be used in precise manipulation and (force or torque) balance devices. In this paper, we propose two types of CCTMs utilizing varying-curvature beams. The stiffness-combination compliant constant-torque mechanisms (SC-CCTMs) are designed by combining positive-stiffness structures and negative-stiffness structures, whereas direct-zero-stiffness compliant constant-torque mechanisms (DZS-CCTMs) are designed by using zero-stiffness structures. In this paper, we develop a comprehensive methodology to analyze the mentioned CCTMs. Based on the methodology, a straight beam and a varying-curvature beam are optimized for negative stiffness and positive stiffness respectively to design SC-CCTMs. Besides, a constant-curvature beam is optimized for zero stiffness to design DZS-CCTMs. Then, the optimized SC-CCTM has the characteristic of adjustable constant-torque, and the optimized DZS-CCTM has a smaller preload range and a wider constant-torque range compared to existing results. Finally, the kinetostatic model has been verified using finite element method (FEM), with an error of less than 3% compared to FEM. The prototype of the optimized DZS-CCTM and SC-CCTM have been fabricated and tested to further verify the feasibility of the proposed design methodology.