A Two-dimensional Underactuated Model of Double-leg Circle on Pommel Horse

Abstract

A gymnastic technique on the pommel horse, called the double-leg circle, was modeled in the horizontal plane by using a rigid-body segment and variable-length arms. The model has three degrees of freedom, and two control inputs in the single support phase or three control inputs in the double support phase. The inter-joint coordination during the circle was modeled as a virtual constraint with respect to the center-of-mass position and the body orientation, and controlled by the feedback linearization. The result showed that the model has a periodic solution partially similar to the horizontal motion of the circle performed by gymnasts.