Ellers, O.; Ellers, K.-I.; Johnson, A. S.; Po, T.; Heydari, S.; Kanso, E.; McHenry, M. J.

A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human\'s tongue, an octopus\' arm, and a nematode\'s body illustrate the ubiquitous presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, the capacity of hydrostatic skeletons to transmit force remains largely unclear. We therefore modeled the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly considered the tube feet of a sea star and the body segments of an earthworm, and contrasted the properties of both against a hydraulic press and a piston-plus-McKibben actuator. All of these soft skeletons feature a helical winding of stiff fibers that play a critical role in hydrostatic mechanics. In contrast to conventional examples such as levers, pulleys, and the hydraulic press, in which MA remains constant as the machine transmits force, soft hydrostats have a variable MA that changes as the hydrostatic skeleton changes shape as it transmits force. For example, in an extending piston-plus-McKibben, MA decreases as the helically-wrapped structure extends towards a fiber angle of 54.7 deg. In comparison, an ampulla-plus-tube foot system similarly extending first increases in MA and then decreases as it approaches 54.7 deg. Deformations in cylindrical hydrostats also often store elastic energy, which adversely affects the transmission efficiency, which is the ratio of output to input work. This transmission efficiency equals unity when DA is equal to the inverse of MA and declines due to elastic energy storage or through energy dissipation. These findings demonstrate the capacity of soft skeletons to transmit force with variable gearing.