Mechanical Design in Tube Feet.

Hydrostatic skeletons enable the transmission of mechanical work through a soft body. Despite the ubiquity of these structures among animals, we have a relatively rudimentary understanding of how they operate mechanically. Here we consider a mathematical model of the mechanics of a relatively tractable hydrostatic skeleton, the tube feet of sea stars. Tube feet drive locomotion by generating a pushing force against the environment. This pushing force is created by transmission of pressure from one chamber, the ampulla, to another, the stem, which extends from the oral surface of the body. This system operates as a compound machine with a mechanical advantage (MA, the ratio of output to input force) that varies with the geometry of its two chambers. We present an analytical approach for parameterizing the model from morphometric measurements and predictions for representative morphologies. Our analysis predicts that MA initially increases as the stem extends, but collapses to zero near maximum extension. The decrease in force output occurs because the angle of cross-helical fiber winding in the stem approaches the critical point of 54.7○, an angle at which the force components exactly balance the hoop and longitudinal forces from pressure. Though producing no axial force at full extension, a bent tube foot can still generate perpendicular forces that generate torque to lift and propel the body as the degree of bend changes, a proposition that is supported by kinematic observations of the tube feet. These results provide a framework for understanding tube foot mechanics across echinoderms and highlight the functional significance of helical fiber arrangements in hydrostatic skeletons.