Modeling the Determinants of Mechanical Advantage During Jumping: Consequences for Spring- and Muscle-Driven Movement

Systems powered by elastic recoil need a latch to prevent motion while a spring is loaded but allow motion during spring recoil. Some jumping animals that rely on elastic recoil use the increasing mechanical advantage of limb extensor muscles to accomplish latching. We examined the ways in which limb morphology affects latching and the resulting performance of an elastic-recoil mechanism. Additionally, because increasing mechanical advantage is a consequence of limb extension that may be found in many systems, we examined the mechanical consequences for muscle in the absence of elastic elements. By simulating muscle contractions against a simplified model of an extending limb, we found that increasing mechanical advantage can limit the work done by muscle by accelerating muscle shortening during limb extension. The inclusion of a series elastic element dramatically improves mechanical output by allowing for additional muscle work that is stored and released from the spring. This suggests that elastic recoil may be beneficial for more animals than expected when assuming peak isotonic power output from muscle during jumping. The mechanical output of elastic recoil depends on limb morphology; long limbs moving small loads maximize total work, but it is done at a low power, whereas shorter limbs moving larger loads do less work at a higher power. This work-power trade-off of limb morphology is true with or without an elastic element. Systems with relatively short limbs may have performance that is robust to variable conditions such as body mass or muscle activation, while long-limbed systems risk complete failure with relatively minor perturbations. Finally, a changing mechanical advantage latch allows for muscle work to be done simultaneously with spring recoil, changing the predictions for spring mechanical properties. Overall, the design constraints revealed by considering the mechanics of this particular latch will inform our understanding of the evolution of elastic-recoil mechanisms and our attempts to engineer similar systems.