Optimizing simulation for lower limb motion during throwing in water polo

The objective of this study was to clarify the optimized lower limb motion during throwing in water polo by the simulation. The flexion/extension angles of the hip joint around the ball release were optimized in order to maximize the ball velocity, which corresponded to the hand velocity at the ball release, under the constraint in terms of the hip joint torque and power. The following findings were obtained from the results of optimization: The ball velocity in the case of original joint torque and power limit was 20.8 m/s. The increase in velocity from that of the original motion was 7%. In the case of doubled joint torque and power limits, the increase reached 15%. The characteristic motion in the optimized cases was the kicking forward (flexing) of both lower limbs just before the ball release. The preceding extending motion that was needed to increase the flexing velocity was also found. The increase in the ball velocity in the optimized motions can be explained as the sum of two components. One is the velocity relative to the center of mass of the whole rigid body, and the other is the absolute movement of the rigid body itself. With respect to the relative velocity, the flexing rotation of the lower half of the body produces the counter-rotation of the upper half of the body because of the conservation law of angular momentum. This effect contributed 70% of the total increase in the ball velocity. With respect to the absolute velocity, the rotations around the longitudinal and lateral axes of the inertia were induced by the reaction of kicking the fluid forward. This effect contributed the remaining 30% of the total increase in the ball velocity