Mass perturbation of a body segment: 1. Effects on segment dynamics

Investigators often use mass perturbation of body segments as an experimental paradigm to study movement coordination. To analyze the effect of mass perturbation on small-amplitude oscillations, the authors linearize the equation of motion of a single segment moving in a vertical plane and derive the effect of added mass on the undamped eigenfrequency, the relative damping, and the low-frequency control gain of the segment. Mass addition results in a decrease in both the relative damping and the low-frequency control gain; the undamped eigenfrequency increases for mass addition between the pivot point and R0 (where R0 is the length of a point mass pendulum whose undamped eigenfrequency is identical to that of the unperturbed segment), decreases for mass addition beyond R0, and remains unaffected for mass addition at R0. For a typical lower leg + foot segment, R0 is just proximal to the ankle joint. That location may explain the absence of an effect on oscillation frequency in studies in which mass has been added to the ankle. The authors' analysis provides a basis for a more effective application of mass perturbations in future experiments.