Perturbation analysis applied to eye, head, and arm movement models

Four types of human movements are compared: eye saccades, horizontal head rotations, the twisting motion of the forearm about its long axis, and the horizontal rotation of the forearm about the axis of the elbow. Each is a rotation about a single axis of a load, driven by muscle-generated torques. In each case, earlier investigators have modeled the load as a second-order linear system and have identified the three parameters of the model. The authors´ aim is to develop a hierarchy of descriptions of each kind of movement, by applying perturbation theory to the four second-order models. the amplitude, time, and maximum net torques are called to get a single-parameter equation for each movement system. Asymptotic series solutions are then developed for the response of each system to a step input, in terms of the single (small or large) parameter. The low-order terms of the expansions give the simplest approximations to the behavior of each system. These low-order approximate trajectories are used to compare the systems and to understand control strategies for different movements.