The Behavior of Single-Input Super-Articulated Mechanisms

Super-articulated mechanical systems tems have more degree of freedom than actuators. For these systems, the relationship between actuator inputs and configuration space trajectories in nonholonomic in the sense that when the input variables return to their initial values it will not generally be the case that configuration variables also return to the initial values. Ih this paper, the long-term effects produced by periodic forcing of super-articulated mechanical systems are studied. For a certain class of Lagrangian control systems with symmetry, it is shown that the stability of equilibrium motions may be assessed in terms of a quantity which we call the averaged potential. For systems in which there is great complexity in the periodically forced dynamics (for instance in the rotating kinematic chains studied in [2] and [4]), appears to afford an attractively simple approach. The method is illustrated in solving the classical problem of stabilising an inverted pendulum by forced vertical oscillation of the point of suspension.