Dynamics of wrist and forearm rotations

Human movement generally involves multiple degrees of freedom (DOF) coordinated in a graceful and seemingly effortless manner even though the underlying dynamics are generally complex. Understanding these dynamics is important because it exposes the challenges that the neuromuscular system faces in controlling movement. Despite the importance of wrist and forearm rotations in everyday life, the dynamics of movements involving wrist and forearm rotations are currently unknown. Here we present equations of motion describing the torques required to produce movements combining flexion-extension (FE) and radial-ulnar deviation (RUD) of the wrist and pronation-supination (PS) of the forearm. The total torque is comprised of components required to overcome the effects of inertia, damping, stiffness, and gravity. Using experimentally measured kinematic data and subject-specific impedance parameters (inertia, damping, and stiffness), we evaluated movement torques to test the following hypotheses: the dynamics of wrist and forearm rotations are (1) dominated by stiffness, not inertial or damping effects, (2) significantly coupled through interaction torques due to stiffness and damping (but not inertia), and (3) too complex to be well approximated by a simple, linear model. We found that (1) the dynamics of movements combining the wrist and forearm are similar to wrist rotations in that stiffness dominates over inertial and damping effects (p<0.0001) by approximately an order of magnitude, (2) the DOF of the wrist and forearm are significantly coupled through stiffness, while interactions due to inertia and damping are small, and (3) despite the complexity of the exact equations of motion, the dynamics of wrist and forearm rotations are well approximated by a simple, linear (but still coupled) model (the mean error in predicting torque was less than 1% of the maximum torque). The exact and approximate models are presented for modeling wrist and forearm rotations in future studies.