Soft skeletons transmit force with variable gearing
A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A humans tongue, an octopus arm, and a nematodes body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore model 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 consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure, and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA x DA) or, equivalently, the ratio of output to input work), which changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.