Analysis of a gymnastic maneuver on the horizontal bar as a goal-directed motion under a nonholonomic constraint

This paper addresses motion generation of a basic gymnastic maneuver on the horizontal bar, referred to as the kip motion, as a difficult goal-directed movement under a nonholonomic constraint. First, we show the results of the motion measurement of the kip movements performed by two expert gymnasts, where the movements of each subject are very similar among trials. Second, we attempt to elucidate whether the kip motion of the expert gymnasts can be understood by the criteria proposed for explaining the hand reaching movements or not. To this end, the body of the expert gymnasts is modeled as a rigid 3-link with an unactuated joint at the hand and actuated joints at the shoulder and the hip, where the angle profiles of the actuated joints are approximated by fifth spline functions. Moreover, it is confirmed that the model's motion is approximately consistent with the measured motion. By using the above model, the kip movements are generated with the minimum torque change criterion explaining the hand reaching movements, and motion segmentation assuming the initial, via- and final postures. The results of the numerical analysis suggest that the measured movements of the expert gymnasts could be almost reproduced in this way. Thus, it is suggested that motion determination/generation of the hand reaching and kip movements could be understood by the common criterion