Optimal wrist prosthesis kinematics : three-dimensional rotation statistics and parameter estimation

Abstract

This thesis presents new theoretical results related to the statistical analysis of three-dimensional rotational data, as well as experimental results on the rotational kinematics of exoskeletal prosthetic wrist joints.

The statistical methods that are traditionally applied to rotational data are inadequate for rotations that have an arbitrary range. A set of rotation-specific statistical operators, referred to as the cosine statistics, are presented and interpretedfrom a geometrical point of view. The resulting cosine average operator is equivalent to the maximum likelihood estimator for the mean of a matrix Fisher distribution. A strong feature is that it is isotropic in its function, completely decoupling its value from the choice of reference coordinate frame. The novel concept of definity constitutes a measure of the degree of rotational symmetry in a given data set, providing a confidence measure for the cosine average. The operators related to data dispersion are simpler than those previously presented.

An experiment is designed and conducted in order to provide new insight into the utilization of the human wrist joint. Eight healthy subjects are instrumented and their range of elbow and finger motion is mechanically restricted to that obtainable with a commercial hand prosthesis. This construct is denoted a simulated prosthesis. The freedom of motion at the wrist is kept intact. Data on forearm and hand movement are recorded during the performance of activities of daily living (ADL) and subsequently analysed with respect to wrist motion.

Simple kinematic models are fitted to the data, and an ANOVA-inspired analysis is carried out. Considerable variability is found in wrist utilization between the different activities, while between-subject variations are only moderate.

For the zero-Degree-of-Freedom (0-DoF) prosthetic wrist, the overall optimal orientation is found to imply a slight pronation, extension and ulnar deviation. In the 1-DoF case, the overall optimal axis of rotation closely resembles that of a prosupination movement, which is the functionality offered by most commercial electric wrist prostheses. In some activities, however, the optimal axis of rotation exhibits significant obliquity with respect to the forearm and hand, indicating that there is potential for a better adaptation of prosthesis kinematics to these tasks.