Position-dependent characterization of passive wrist stiffness

Because the dynamics of wrist rotations are dominated by stiffness, understanding wrist rotations requires a thorough characterization of wrist stiffness in multiple degrees of freedom. The only prior measurement of multivariable wrist stiffness was confined to approximately one-seventh of the wrist range of motion (ROM). Here, we present a precise nonlinear characterization of passive wrist joint stiffness over a range three times greater, which covers approximately 70% of the functional ROM of the wrist. We measured the torque-displacement vector field in 24 directions and fit the data using thin-plate spline smoothing optimized with generalized cross validation. To assess anisotropy and nonlinearity, we subsequently derived several different approximations of the stiffness due to this multivariable vector field. The directional variation of stiffness was more pronounced than reported previously. A linear approximation (obtained by multiple linear regression over the entire field) was significantly more anisotropic (eigenvalue ratio of 2.69 ± 0.52 versus 1.58 ± 0.39; p < 0.001) though less misaligned with the anatomical wrist axes (12.1 ± 4.6° versus 21.2 ± 9.2°; p < 0.001). We also found that stiffness over this range exhibited considerable nonlinearity - the error associated with a linear approximation was 20-30%. The nonlinear characterization over this greater range confirmed significantly greater stiffness in radial deviation compared to ulnar deviation. This study provides a characterization of passive wrist stiffness better suited to investigations of natural wrist rotations, which cover much of the wrist's ROM. It also provides a baseline for the study of neurological and/or orthopedic disorders that result in abnormal wrist stiffness.