Isokinetic dynamometers are widely used in testing of muscular strength, as they allow simultaneous measurement of joint torque, angle and angular velocity. However, the torque measured by a dynamometer does not equal the torque applied about a joint by active muscle loading due to contributions from gravitational torque and passive joint torques. Gravitational torque is due to the weight of the limb and dynamometer arm (Herzog, 1988). Passive joint torque is caused primarily by elastic deformation of tissues crossing the joint, including muscles, tendons and ligaments (Yoon and Mansour, 1982). Passive torque may be modeled as the sum of gravitational torque and passive joint torques. The gravitational torque has frequently been modeled as a simple sine or cosine function (Herzog, 1988, Nelson & Duncan, 1983) based on measurements at specific joint angle(s). For these models, the angle of maximum gravitational torque is 90° or 0°, respectively. However, this assumes that the center of mass of the limb distal to the joint plus the dynamometer attachment is aligned with the centerline of the segment defining the joint angle. This assumption is not valid in all cases. Passive joint torques have typically been modeled as exponential functions (Hoang et al., 2005, Yoon and Mansour, 1982). Previously, we have used optimization to fit a model of passive torque to measured passive torque data (Anderson et al., 2007). The purpose of this work was to create a simple algorithm for directly calculating the model parameters.
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