The author derived the exact analytical expression of the instantaneous joint power in exercises with single-joint, variable-resistance, selectorized strength-training equipment, taking into account all the relevant geometric, kinematic, and dynamic variables of both the movable equipment elements (resistance input lever, cam–pulley system, weight stack) and of the user’s exercising limb. A numerical algorithm was also designed to express, in the presence of a cam, the rectilinear kinematic variables of the weight stack as a function of the rotational kinematic variables of the resistance input lever, and vice versa. Given that information, one can measure the value of the instantaneous and mean joint power exclusively by means of a linear encoder placed on the weight stack or, alternatively, only by the use of an angular encoder placed on the rotational axis of the resistance lever. The results highlight that, for knee extension exercises with leg extension equipment, the real values of both instantaneous and mean joint power may differ by more than 50% in comparison with the values obtained by taking into account only the mass and velocity of the weight stack. These differences are notable not only in explosive exercises, but also whenever considerable joint velocities/accelerations occur within the range of motion.
Andrea Biscarini is with the Department of Surgical, Radiologic and Odontostomatologic Sciences, Medical Physics Section, University of Perugia, and with the LAMS laboratory, University of Perugia, Perugia, Italy.