Optimum timing of muscle activation for simple models of throwing

Abstract

In diverse throwing activities, muscles contract in sequence, starting with those furthest from the hand. This paper uses simple mathematical models, each with just two muscles, to investigate the consequences of this sequential contraction. One model was suggested by shot putting, another by underarm throwing and the third by overarm throwing, but all are much simpler than real human movements. In each case there is an optimum delay between activation of the more proximal muscle and of the more distal one, that maximizes the speed at which the missile leaves the hand. If the delay is shorter than optimal, the throw is completed sooner and less time is available for contraction of the proximal muscle: it may shorten faster, exerting less torque, or through less than its full range of movement, and so do less work. If it is longer than optimal, less time is available for contraction of the distal muscle, which therefore does less work. The optimal delay is in some cases longer than would maximize total work because the delay influences the proportion of the work that appears as kinetic energy of the missile.