Latch-based control of energy output in spring actuated systems

The inherent force-velocity trade-off of muscles and motors can be overcome by instead loading and releasing energy in springs to power extreme movements. A key component of this paradigm is the latch that mediates the release of spring energy to power the motion. Latches have traditionally been considered as switches; they maintain spring compression in one state and allow the spring to release energy without constraint in the other. Using a mathematical model, we demonstrate that changing the parameters of a simplified contact latch (latch radius and release velocity) can enable both this instantaneous energy release behavior as well as a regime that reduces and delays the energy released by the spring. This is true even for latches found in biology that have rounded edges and do not geometrically disappear instantaneously. We also identify a critical threshold between these instantaneous and delayed regimes. We validate this model in both a physical experiment as well as with data from the Dracula ant, Mystrium camillae, and propose that latch release velocity can be used in both engineering and biological systems to control energy output.

Methods
Data from Latch Physical Model:

Experiments with the latch physical model described in the associated paper were recorded with a Photron AX-200 high-speed camera (pixel resolution: 896 x 768, calibrated ruler) at 10000 fps (shutter duration: 1/60000 second) and both latch motion and projectile motion were analyzed using tracking software (Image Systems, TEMA). Take-off velocity was calculated from these images at the point when the spring and mass separated from the substrate.

Measuring latch delay was more challenging. In theory, the point of maximum projectile acceleration should equate to the instant at which latch force goes to zero, but this was not the case in the physical system. Instead, latch delay was measured when physical separation was visually observed between the projectile and the latch. While this method is expected to slightly overpredict delay, it provided consistent results. 

Data was processed in Matlab using the scripts provided.

Dracula ant data processing:

Mandible tip position data captured on high speed video from two types of Dracula ants (larger major and smaller minor workers) was made available in [Larabee 2018, doi: 10.5061/dryad.4863215]. This dataset provides x-y coordinates of the mandible tips for each frame along with the camera frame rate. Four ants of each type were analyzed over 4-5 strikes per ant as available in the dataset. The first mandible to move during each strike was designated as the latch mandible, and unlatching time was defined as the time difference between the start of latch mandible and strike mandible motion. Average latch mandible velocity was calculated as the angle over which the latch mandible displaced before the strike mandible began to move, divided by the unlatching time. The maximum strike velocity was calculated using the maximum angular motion of the strike mandible between two frames and dividing by the time interval between frames. The Matlab script used to process this data is included in the dataset, but the dataset itself is available from Larabee (doi: 10.5061/dryad.4863215).