Dynamics of wrist rotations.

Understanding the dynamics of wrist rotations is important for many fields, including biomechanics, rehabilitation and motor neuroscience. This paper provides an experimentally based mathematical model of wrist rotation dynamics in Flexion-Extension (FE) and Radial-Ulnar Deviation (RUD), and characterizes the torques required to overcome the passive mechanical impedance of wrist rotations. We modeled the wrist as a universal joint with non-intersecting axes. The equations of motion of the hand rotating about the wrist joint include inertial, damping, and stiffness terms, with parameter values based on direct measurements (stiffness) or measurements combined with data available in the literature (inertia, damping). We measured the wrist kinematics of six young, healthy subjects making comfortable and fast-paced wrist rotations (±15° in FE, RUD, and combinations) and inserted these kinematic data into the model of wrist rotation dynamics. With this we quantified the torques required to overcome the impedance of wrist rotations and evaluated the relative importance of individual impedance terms as well as interactions between the degrees of freedom. We found that the wrist's passive stiffness is the major impedance the neuromuscular system must overcome to rotate the wrist. Inertia and passive damping only become important for very fast movements. Unlike elbow and shoulder reaching movements, inertial interaction torques are negligible for wrist rotations. Interaction torques due to stiffness and damping, however, are significant. Finally, we found that some model terms (inertial interaction torques, axis offset, and, for moderately sized rotations, non-linearities) can be neglected with little loss of accuracy, resulting in a simple, linear model useful for studies in biomechanics, motor neuroscience, and rehabilitation.