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The simplest model with which to examine the dynamics of the human eye consists of a rigid body which is free to rotate about a fixed point. Two classical laws governing monocular vision, which are known as Listing's law and Donders' law, can be enforced in this model using a single holonomic constraint. While there has been considerable attention paid to the kinematics of the eye, the dynamics of the eye predicted by rigid body models has not received the same level of attention. In the present paper, the unforced dynamics of the resulting rigid body model are examined with particular emphasis placed on the geodesics of the configuration manifold. A comprehensive portrait of these motions is presented, and the insight gained is related to the dynamics of the gaze direction and saccadic motions of the eye. Among our results, we find that modeling the eye as an asymmetric rigid body produces a nonintegrable system of governing equations and that the geodesics on the configuration manifold provide a wealth of potential motions for the gaze direction.

With the goal of robustly designing and fabricating a soft robot based on a caterpillar featuring shape memory alloy (SMA) actuators, analytical and numerical models for a soft robot were created based on the forward crawling motion of the Manduca sexta caterpillar. The analytical model features a rod theory and the mechanics of undulation were analyzed using a motion pattern based on the 'Witch of Agnesi' curve. Complementing these models, experiments on a SMA actuator sample were performed in order to determine its flexural rigidity and curvature as a function of the actuation voltage. A series of these actuators can be modeled as a system of rigid bodies connected by torsional springs. As these bodies are actuated according to the motion pattern based on the individual caterpillar segments, ground contact forces are calculated and analyzed to determine the requirements of successful forward locomotion. The energetics of the analytical and numerical models are then compared and discussed.