Spiral Wheel Shape Definition Given Applied Constant Weight and Reaction Force Function

by Wuthipat Brink

Submitted : Fall 2012

To help those suffering from asymmetric gait a rehabilitation shoe was designed to account for the lack of stride in one leg. Finding the wheel shape of the Gait Enhanced Mobile Shoe (G.E.M.S) will allow adjustments to be made and will allow when rehabilitative forces are applied. The given problem statement asks to derive an equation to find a spiral wheel shape that results in a desired horizontal ground reaction force when a known downward force is applied. Each wheel parameter is related to one another in order to find a differential equation that best describes the shape of this wheel. Given a few governing equations, these given relations are related to a specified parameter (which in this case is theta), the angle around the spiral. Solving the resulting differential equation for the radius determines the shape of the wheel. Nonetheless, a basic relation is formed that can be used to solve for a wheel shape that results in a desired reaction force. Slight differences in the exerted force can change the outcome in distance traveled, which can be beneficial for gait rehabilitation.

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