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Behaviors that are produced solely through geometrically complex three-dimensional interactions of soft-tissue muscular elements, and which do not move rigid articulated skeletal elements, are a challenge to mechanically model. This complexity often leads to simulations requiring substantial computational time. We discuss how using a quasi-static approach can greatly reduce the computational time required to model slow-moving soft-tissue structures, and then demonstrate our technique using the biomechanics of feeding behavior by the marine mollusc, Aplysia californica. We used a conventional 2nd order (from Newton’s equations), forward dynamic model, which required 14 s to simulate 1 s of feeding behavior. We then used a quasi-static reformulation of the same model, which only required 0.35 s to perform the same task (a 40-fold improvement in computation speed). Lastly, we re-coded the quasi-static model in Python to further increase computation speed another 3-fold, creating a model that required just 0.12 s to model 1 s of feeding behavior. Both quasi-static models produce results that are nearly indistinguishable from the original 2nd order model, showing that quasi-static formulations can greatly increase the computation speed without sacrificing model accuracy. 

ABSTRACT Lantern bugs are amongst the largest of the jumping hemipteran bugs, with body lengths reaching 44 mm and masses reaching 0.7 g. They are up to 600 times heavier than smaller hemipterans that jump powerfully using catapult mechanisms to store energy. Does a similar mechanism also propel jumping in these much larger insects? The jumping performance of two species of lantern bugs (Hemiptera, Auchenorrhyncha, family Fulgoridae) from India and Malaysia was therefore analysed from high-speed videos. The kinematics showed that jumps were propelled by rapid and synchronous movements of both hind legs, with their trochantera moving first. The hind legs were 20–40% longer than the front legs, which was attributable to longer tibiae. It took 5–6 ms to accelerate to take-off velocities reaching 4.65 m s−1 in the best jumps by female Kalidasa lanata. During these jumps, adults experienced an acceleration of 77 g, required an energy expenditure of 4800 μJ and a power output of 900 mW, and exerted a force of 400 mN. The required power output of the thoracic jumping muscles was 21,000 W kg−1, 40 times greater than the maximum active contractile limit of muscle. Such a jumping performance therefore required a power amplification mechanism with energy storage in advance of the movement, as in their smaller relatives. These large lantern bugs are near isometrically scaled-up versions of their smaller relatives, still achieve comparable, if not higher, take-off velocities, and outperform other large jumping insects such as grasshoppers.