Date of Award

Fall 1999

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

H. Michael Lacker

Second Advisor

John Kenneth Bechtold

Third Advisor

Denis L. Blackmore

Fourth Advisor

Ellen C. Ross

Fifth Advisor

Michael Siegel

Abstract

Wheelchair racing strokes are very complicated movements, which involve a coupling between the athlete and his or her racing chair. Each body segment, as well as the wheel, follows a distinct trajectory as the motion is performed. Understanding the kinematics and kinetics of various stroke techniques would provide the athletes and their coaches with information, which could help guide the racers toward improved performances.

In this thesis, a mathematical model is developed, which is capable of providing such valuable kinematic and kinetic information. This two-dimensional model represents the body segments as a coupled pendulum system of point masses and the wheel as a distributed-mass disk. Furthermore, the model incorporates several fundamental assumptions, including that the stroke cycle can be divided into an arbitrary number of consecutive ballistic phases such that segment positions are continuous at phase boundaries.

Each phase is mathematically a second-order, nonlinear ordinary boundary value problem (BVP). Numerical methods are used to solve the BVPs independently, resulting in velocity discontinuities at the phase boundaries. These instantaneous velocity increases or decreases must be caused by impulsive forces. In turn, these impulsive forces are interpreted as muscular input and/or physical impacts.

In this research, the model is used to produce numerous stroke techniques, which are consistent with a given racer's structural parameters and prescribed stroke characteristics (racing speed, cycle time, recovery cycle time, the athlete's orientation in the racing chair, and wheel contact and release angles). The kinematics of these different techniques are contrasted. In addition, the muscular mechanical energy costs of these strokes are determined and an interpretation as to the mechanical energy efficiency of each technique is given.

The model is used to provide insight into the intricacies of an actual wheelchair racing stroke. In this thesis, the kinematics and energetics of model-produced techniques guide the analysis of these characteristics of an empirical stroke. One conclusion of this analysis is that this model may be able to provide more mechanically efficient alternative strokes from which the athlete can choose. Finally, suggestions are offered toward improving the model.

Included in

Mathematics Commons

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