Isolated mechanical systems—e.g., those floating in space, in free-fall, or on a frictionless surface—are able to achieve net rotation by cyclically changing their shape, even if they have no net angular momentum. Similarly, swimmers immersed in “perfect fluids” are able to use cyclic shape changes to both translate and rotate even if the swimmer-fluid system has no net linear or angular momentum. Finally, systems fully constrained by direct nonholonomic constraints (e.g., passive wheels) can push against these constraints to move through the world. Previous work has demonstrated that the displacement induced by these shape changes corresponds to the amount ofconstraint curvaturethat the gaits enclose. Properly assessing or optimizing the utility of a gait also requires considering the time or resources required to execute it: A gait that produces a small displacement per cycle, but that can be executed in a short time, may produce a faster average velocity than a gait that produces more displacement, but takes longer to complete a cycle at the same instantaneous effort. In this paper, we consider gaits under two instantaneous measures of effort. For each of these costs, we demonstrate that fixing the average instantaneous cost to a unit value allows us to transform the effort costs into time-to-execute costs for any given gait cycle. We then illustrate how the interaction between the constraint curvature and these costs leads to characteristic geometries for optimal cycles, in which the gait trajectories resemble elastic hoops distended from within by internal pressures.

For the state-of-the-art of soft robotics, the current actuation mechanisms cannot produce shear forces, neither are the current stiffening mechanisms adaptive to various deformations. Consequently, the soft robots gain strength at the price of losing flexibility. To fill this gap, we proposed a new mechanism based on the muscle arrangements and incompressible property identified in biological hydrostatic skeletons. Beside longitudinal and transverse muscles, the proposed mechanism includes the oblique arrangement which is proved to play an indispensable role of producing shear forces. The effectiveness of the new mechanism is demonstrated through a benchmark problem - carrying a distributed load at the initial horizontal configuration, thus indicating an improved direction to realise shape-independent load-carrying capability of soft robotics. Furthermore, the proposed mechanism may explain how elephants coordinate the two contradicting properties, strength and flexibility, during their trunk manipulations.

Jumping spiders are capable of targeted jumps by using their front legs to guide the release of energy from their rear legs. In this paper, we present a simplified model of the jumping spider based on the anatomy of the real spider. The immediate goal of this model is to understand how the geometry of the legs affects the jumping motion, with the further goal of using this geometry in the future development of jumping robots. Through a set of simulations, dynamic analysis, and experiments with a physical realization of our model, we identify several features of the spiders' jumping mechanism, most notably that “vaulting” with the front legs allows the system to generate flatter take-off trajectories than could be achieved by simple aiming of a spring-release mechanism.