| The purpose of this study was to develop the tools for the three-dimensional (3D) inverse dynamics calculations during manual wheelchair propulsion (MWP). Three parts are necessary to a complete inverse dynamic analysis (a) the forces applied at the wheel, (b) the kinematics analysis, and (c) an algorithm that combines parts (a) and (b).; As there is no standardized transducer to measure the forces applied to the pushrim, the first purpose of the study was to develop a transducer for the measurement of the forces and moments during MWP. The results showed that a six strain-gauge configuration and two more variables, the position of the wheel and the position where the hand touches the pushrim, is a viable way to measure the forces. However, a configuration with more strain gauges could increase the signal-to-noise ratio.; A tertiary purpose was to formulate the 3D kinematic analysis during MWP with a new method based on quaternions. The method proved to be superior to other traditional approaches, because there were no points where a transformation could not be defined or could be parametrized in more than one way. Using the quaternion model transformations from frame to frame were unique. Additionally, the quaternion model was used to develop a new smoothing technique that simultaneously smooths the data in 3D. The method had a 50% less mean-square-error than a linear Butterworth filter when both methods were applied to simulated MWP data superimposed with known error.; Another purpose of the study was to formulate a method that can evaluate stability during MWP. The method used the Floquet multipliers of a Jacobean matrix, which maps the position of the hand from cycle to cycle, to examine whether a repetitive movement is converging to a stable pattern or not. The method was implemented in linear space, and in angular space with the use of quaternions. Both methods proved to discriminate between stable and unstable conditions predicting the same results. However, the results suggest that the point where the analysis takes place could affect the final outcome, agreeing with the theoretical formulation and disagreeing with research from gait analysis.; Finally, using a detailed mathematical formulation and experimental data, it was proved that local coordinate systems should be used not only because they are more meaningful in describing 3D kinematic analysis, but also because the equations of the kinetic analysis require, during calculations from frame to frame, to transform either the inertia properties or to use local angular velocities. |
