# Design Considerations Concerning an Innovative Drive System for a Manual Wheelchair
## 2 Materials and Methods  
### Kinematic Scheme  
To address the problem described, the research team decided to create a design of a manual, pushrim-propelled wheelchair with the ability to change the gear ratio (between pushrim and wheel): in both automatic and semi-automatic modes. Meeting such an assumption requires the separation of the pushrim and wheel functions, which are permanently connected in classic wheelchairs. To this end, the solution being developed is based on the patent application P.434936 (Patent Office of the Republic of Poland, 2023), which describes a pushrim ratio assembly for a manual wheelchair, and on the patent application P.443054 (Patent Office of the Republic of Poland, 2023), which refers to the wheelchair's drive wheel hub for multi-gear drive units. The kinematic system of the developed system is shown as a diagram in Figure 1. The system's most important element is the Shimano Acera CS-HG400 cassette (Shimano Inc., Sakai, Japan) enabling eight ratios including the derailleur. This is a standardized mechanism used in bicycles. For this reason, it works in a specific arrangement, because bicycles have a drive system with the chain on the right side, looking towards the direction of travel. A wheelchair has a different spatial arrangement of the driven wheels than a bicycle, so it was impossible to mirror the drive system for the right wheel relative to the wheelchair seat axis (shown on the right in the diagram), because the Shimano Acera derailleur is not able to work properly in a mirrored position [16; 17; 18]. Instead, it was decided to add a gear transmission to the right drive system, which allowed us to change the rotation direction of the chain located between the drive chain wheel and the derailleur hub. This solution also required moving the Shimano derailleur system towards the front of the wheelchair. This enabled maintaining fully identical gear ratios in the entire chain for both the wheelchair's left and right wheels, as well as a more favorable weight distribution, improving the wheelchair's stability. Table 1 presents a list of specific parameters that characterize the developed solution. As a result, it is possible to distinguish the system's gear ratios determined by Equations (1) to (6):  
\[i_{0}=d_{w}/d_{p}=609.6\ /520, \tag{1}\]  
\[i_{1}=z_{4}/z_{3}=23/20, \tag{2}\]  
\[i_{g}=z_{21\to 28}/z_{1}=0.44;0.52;0.60;0.72;0.88;1.08;1.32;1.60, \tag{3}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Designation** & **Value** \\ \hline Diameter of a wheel & \(d_{w}\) & 609.6 mm \\ Diameter of a pushrim & \(d_{p}\) & 520 mm \\ Number of sprocket teeth at the input from the wheel hub & \(z_{1}\) & 23 teeth \\ Number of teeth of Shimano cassette sprockets & \(z_{21};z_{22};z_{23};z_{24}\) & \\ Number of teeth on the countershaft sprocket & \(z_{3}\) & 20 teeth \\ Number of sprocket teeth at the exit from the wheel hub & \(z_{4}\) & 25 teeth \\ The number of gear teeth changing the direction of chain & \(z_{1g}\) & 90 teeth \\ movement for the right wheel gear & \(z_{3g}\) & 80 teeth \\ The number of gear teeth changing the direction of chain & \(z_{3g}\) & 80 teeth \\ movement for the right wheel gear & TG & - \\ Torque gauge & E & - \\ Encoder & \(d_{e1}\) & 54 mm \\ Output encoder pulley diameter & \(d_{e2}\) & 24 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the designed drive system. Figure 1: Kinematic diagram of the drive system of a wheelchair with a chain transmission. \[i_{1g}=z_{1g}/z_{1g}=90/9, \tag{4}\] \[i_{3g}=z_{3g}/z_{3g}=85/85,\] (5) \[i_{e}=d_{e2}/d_{e1}=24/54. \tag{6}\]  
The total instantaneous ratio for the left side of the \(i_{c1}\) system and the right side of the \(i_{c2}\) system is the product of the gear ratios in each stage of the mechanism included in the drive system.