A two-dimensional model has been developed to predict and explain the effects of the variation of muscle moment arms during dynamic exercises involving heavy external loads. The analytical dependence of the muscle moment arm on the joint angle and on the origin and insertion position was derived for an ideal uniaxial hinge joint, modeling the muscle as a cable following an idealized minimum distance path from the origin to insertion that wraps around the bony geometry. Analytical expressions for the ratios of muscular force and the joint restraining reaction components to the external load weight were deduced, for isokinetic and static exercises, as a function of joint angle, joint angular velocity, and the other geometric parameters defining the model. Therefore, external load weight, joint angular velocity, and constraints to joint range of motion may be adjusted reciprocally in order to control in advance the peak value of the components of the joint load during isokinetic exercises. A dynamic formulation of forearm flexion/extension was solved numerically under the condition of constant biceps force in order to highlight the key role played by the variation in muscle moment arm in preventing injury during lifting of external loads against gravity. For example, our analysis indicates that the mean and peak resultant joint loads decrease by 5% and 14%, respectively, as a result of the change in muscle moment arm that occurs over the range of motion.
Andrea Biscarini is with the Laboratorio delle Attività Motorie e Sportive, Dipartimento di Fisica, Università di Perugia, Via Pascoli, 06100 Perugia, Italy.