We have developed a 2-D analytical biomechanical model for monoarticular open kinetic-chain exercises with lever selectorized equipment, and different relative placement between the joint center of rotation (J) and the center of rotation (C) of the resistance input lever (“off-center” exercises). All the relevant geometrical aspects of such exercises have been characterized: the change with the joint angle of the distance between the resistance pad (P) and J, and of the angle between CP and JP (i.e., the angle between the resistance input lever and the exercising limb). These changes may strongly affect the joint load and the muscle torque in inverse dynamic problems, given the joint kinematics and the mass of the selected weight stack. Therefore, the muscle torque, the shear and axial components of the joint load have been calculated analytically as a function of the relative positioning of C and J, and the length CP, in addition to the parameters that define the joint kinematics, the equipment mechanics, and the external load. From these results we have derived the optimal cam profiles for “off-center” exercises, as well as the geometrical “off-center” setting that minimizes the shear component of the tibiofemoral joint load in leg extension equipment.
Biscarini is with the Department of Surgical, Radiological and Odontostomatologic Sciences, Medical Physics Division, University of Perugia, and also with LAMS Laboratory, University of Perugia, Perugia, Italy.