Dynamics and energetics of dual-spring force couples in torque reversal systems

Latch-mediated spring actuation systems leverage the interplay of springs and latches to rapidly accelerate a load. In biological systems, elastic energy is often distributed across multiple structures, resulting in forces applied from multiple springs. Here, we specifically examine dual-spring force couples in torque reversal systems. A dual-spring force couple applies forces from recoiling springs at two locations to generate torque. Torque reversal systems transition from spring loading to spring actuation through a change in torque direction. We develop a mathematical model of a dual-spring force couple in a torque reversal system, where one spring is attached to the pivot point of a rigid body. During spring loading, this spring compresses to store elastic energy; during spring actuation, it recoils, driving pivot translation and contributing to rotation. We experimentally validate the model using a physical model. We then vary geometric parameters and the energy partition between the two springs to examine how these factors shape system dynamics. We show how variations in geometry and energy partition influence the rotational, translational and coupling terms in the mathematical model. Finally, we demonstrate that the energetics of these systems must be carefully accounted for to accurately capture how potential energy is transformed into kinetic energy. We hypothesize that dual-spring force couples in torque reversal systems may be prevalent in biological organisms, and that insights from this work can guide the design of spring-actuated mechanisms in robotics.