The primary purpose of this study was to determine the optimal release conditions and corresponding arm movement pattern for the free throw for players classified as 3 to 4.5 on the international player classification system in wheelchair basketball. A 2-D, three-segment simulation model was used to investigate this problem. The computational process involved a two-step optimization scheme in which an outer computational loop was used to optimize the magnitude and timing of the muscle torques that generate the arm's motion, and an inner computational loop was used to determine the optimal angle and speed of the ball at the moment of release. The inner optimization loop revealed that Brancazio's (1981) and Hay's (1993) approaches to determining the optimal release angle produced identical results. The lowered seated height of the wheelchair basketball player required that the ball be released at a steeper angle with greater vertical velocity, and hence the need for greater shoulder torque. For the wheelchair player, the peak shoulder flexion torque generated by the model was reduced by approximately 43% when the upper arm was initially positioned at an angle approximately 40° below the horizontal, as compared to being positioned at an angle of 10° above the horizontal. For the wheelchair player, the optimal release angle and speed for a ball released at a horizontal distance of 4.09 m from the center of the basket, and 1.30 m below the rim, was computed to be 53.8° and 7.4 m/s, respectively.
The authors are with the College of Kinesiology, University of Saskatchewan, Saskatoon, SK, Canada S7N 5C2.