Optimizing Racing Wheelchair Design Through Coupled Biomechanical-Mechanical Simulation

Abstract

The purpose of this study is to optimize the design of racing wheelchairs to improve the performances of the athletes. The design of manual wheelchair allows athletes to express their full potential. Two models have then been created. The first one to compute the optimal position of the shoulder of the athlete relatively to the wheelchair to obtain the maximal wheelchair speed for long distance races. The second one was designed to represent the 100 m race and to optimize the pelvis position of the athlete on the wheelchair to reduce the time to reach 100 m. Our model quantified the maximal speed reached by the wheelchair to 32 km/h and the optimal time to 14.35 s. To obtain these performances, the athlete would be in a lying position, with the vertical position of the pelvis centre close to the vertical position of the shoulder. The second program also returned the optimal speed curve of the wheelchair during the 100 m race. The coaches could then use the optimal acceleration curve found in this study to match the acceleration of the wheelchair of their athlete.

Annex

The formulas used to compute the kinematic parameters of the model are presented in this annex. This allowed us to find the shoulders and elbow angles.

The first step to calculate the kinematics parameters of the Long-distance model was based on the current position of the shoulder centre (${X}_{shoulder}$ and ${Y}_{shoulder}$ respectively the horizontal and vertical position):

$$ \begin{array}{*{20}c} {inc = \arctan \left( {\frac{{Y_{shoulder} }}{{X_{shoulder} }}} \right){;} \; D = \sqrt {(X_{shoulder}^2 + Y_{shoulder}^2 )} } \\ \end{array} $$

For the sprint model, the first step to compute the kinematic parameters was based on the dimension of the torso (${L}_{torso}$), the horizontal and vertical position of the pelvis (respectively ${X}_{pelvis}$ and ${Y}_{pelvis}$), and $\beta$, the angle between the torso and a horizontal line (figure attached).

$$ \begin{aligned} & X_{shoulder} { } = { }L_{torso} \cos \left( {\upbeta } \right) - X_{pelvis} {;} \; Y_{shoulder} = L_{torso} \sin \left( \beta \right) + { }Y_{pelvis} \\ & inc = \arctan \left( {\frac{{Y_{shoulder} }}{{X_{shoulder} }}} \right){;} \; D = \sqrt {{(X_{shoulder}}^{2} + {Y_{shoulder}}^{2} )} \\ \end{aligned} $$

Then, the next step was the same for both models. The parameters used were: $\alpha$, the

$$ \begin{aligned} & \nu =\alpha +\frac{\pi }{2}-inc \\ &L=\sqrt{\left({R}_{mc}^{2}+{D}^{2}-2D{R}_{mc}\mathrm{cos}\left(\nu \right)\right)} \\ & \theta =-\mathrm{arccos}\left(\frac{{L}_{arm}^{2}+{L}_{forearm}^{2}-{L}^{2}}{2{L}_{arm}{L}_{forearm}}\right)\\ &\psi =-\mathrm{arctan}\left(\frac{{R}_{mc}\mathrm{sin}\left(\nu \right)}{D-{R}_{mc}\mathrm{cos}\left(\nu \right)}\right) \\ & \mu =-\mathrm{arccos}\left(\frac{{L}^{2}+{L}_{arm}^{2}-{L}_{forearm}^{2}}{2{L}_{arm}L}\right)+\psi \\ & \varphi =\mu +\theta\\ &\delta =inc+\mu -\beta \end{aligned} $$