Development of a Mathematical Model to Investigate the Static and Dynamic Stability of a Wheelchair System

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atrc, assistive, technology, resource, center, graduate, thesis, mathematical, model, static, dynamic, stable, stability, wheelchair


The goal of this graduate thesis was to develop a mathematical model of a standard wheelchair with a humanoid model while the human is firmly secured in the wheelchair. In the United States, there are, on average, 50 wheelchair related deaths and 36,500 wheelchair related emergency room visits every year. About 3 out of every 4 of these incidents can be attributed to wheelchair instability, or more explicitly, the wheelchair’s ability to remain upright when moving up or down a slope or undergoing a collision with its surroundings. There have been investigations to examine the static and dynamic stability of wheelchairs in the past, but there is the need for a published theoretical analysis of wheelchairs under a range of experimental conditions. In order to analyze the stability of a wheelchair, Bruno stimulated a variety of tests by placing the wheelchair on a stable platform for static testing and by rolling the wheelchair down the ramp, for dynamic testing. The static stability was determined by measuring the maximum angle that the system of the wheelchair and human could be tilted without tipping over. Dynamic stability was evaluated by changing in the angle of the ramp that the wheelchair was pushed on and by noting any issues with the wheelchair. The results of the analysis showed a correlation with the experimental values and the mathematical model proved to be accurate in the case of static stability. The dynamic stability results showed some accuracy, but did not correlate as effectively with experimental data because of the instability and movement throughout the wheelchair system during dynamic testing conditions.