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Jpn J Biomechanics Sports Exercise 10(3):146-158, 2006

A 3D dynamical model for analyzing the motion-dependent torques of upper extremity to generate throwing arm velocity during an overhand baseball pitch


Graduate School of Design Science and Technology, Tokyo Institute of Technology


In the present study, we proposed a dynamical model for analyzing the segment motion interaction of the throwing arm during an overhand baseball pitch. The model consisted of three segments(upper arm, forearm and hand)and 7 degrees of freedom(shoulder horizontal adduction-abduction, adduction-abduction, external-internal rotation, elbow extension-flexion, wrist ulnar-radial deviation, extension-flexion and pronation-supination). The throwing motion of a collegiate baseball pitcher was filmed using high-speed cameras, and 3D coordinates and Euler's angles were calculated using the DLT method. Joint torques in the throwing arm were calculated using the Newton-Euler equation. The calculated data from the model were used to test the model's performance, and the test indicated that the model numeration was accurate. In this model, the endpoint, wrist and elbow velocities in the throwing arm were decomposed into the joint torque-dependent, angular velocity-dependent, gravity-dependent, external force-dependent and trunk motion-dependent components. The results from the present study implied the following;(a)the joint torque-dependent component primarily contributed to production of the endpoint velocity at the instant of ball release, (b) the angular velocity-dependent and trunk motion-dependent components contributed to production of the wrist and endpoint velocities at the instant of ball release, and(c)sequential segmental rotations of throwing arm segments was influenced by angular-dependent interaction through the multi-joint limb system.
Since the findings from the present model could not be understood from knowledge of joint torque alone, the present model for analyzing the motion-dependent interaction of a multi-joint limb movement should be useful for more detailed study on coordination in skilled throwing movement.

Key Words: pitching, dynamical model, contribution, motion-dependent interaction, kinetic link principle

Submittted for Publication : May. 18, 2005,

Accepted for Publication : May. 25, 2006



JJBSE バイオメカニクス研究