# Laboratory Assessment of Manual Wheelchair Propulsion
## 2 Experimental Testing Methods
### Determining Changes in the Position of the Center of Mass (COM)  
One of the most essential biomechanical parameters impacting the efficiency of wheelchair propulsion is the position of the COM of the human-wheelchair system. This parameter directly impacts both the propulsion efficiency and stability of the wheelchair. In the so-called active wheelchairs, intentional instability of the human-wheelchair system is deliberately incorporated into the wheelchair's design to reduce reliance on torso balancing while maintaining proper push-rim propulsion. This intentional instability enhances maneuverability and obstacle-crossing capabilities [4]. However, because active wheelchairs are less stable, they require specific skills from the user to control them effectively. As a result, active wheelchairs are typically tailored for individuals with enhanced physical fitness and maneuvering abilities, enabling them to fully capitalize on the advantages of this intentional instability. In human-wheelchair anthropo-technical systems, studying changes in the COM under dynamic conditions is essential. Numerous factors influence the current position of the COM. In addition to the constantly changing position of the torso, the wheelchair frame dynamics are influenced by the moving masses of the user's arms during manual wheelchair propulsion [49]. Measuring the COM position under dynamic conditions has been extensively documented in the literature [50; 51; 52]. The method presented in [53] involves determining the COM (barycenter) of the person-wheelchair system using four strain-gauge-measuring scales (Figure 10). Each scale measures the vertical reaction \(R_{i}\) at one of the four support points of the system. These signals allow for determining the projections of the COM in the XY plane, simplifying the analysis to a two-dimensional area. To determine the position of the COM, the distances \(f_{12},f_{23},f_{43}\), and \(f_{14}\) between successive points of applied reaction forces \(R_{i}\) are measured, balancing the moments in each of the four analyzed planes \(\pi_{i}\) (Figure 11). These distances indicate the distribution of forces between pairs of scales, simplifying the calculations to a one-dimensional space. The distances \(f_{i}\) (Figure 12) are marked on the sides of the rectangle defined by the points of application of the reaction forces  
Figure 10: Schematic diagram of the test stand with the reactions determined using strain gauge scales in four measurement planes (source: [34]). \(R_{i}\). Then, through points \(P_{i}\) on the sides of the rectangle, two lines can be drawn that intersect at a single point in the XY plane, determining the coordinates of the COM of the person-wheelchair system for a single measurement (Equations (5) and (6)). \[x=\frac{-\frac{L_{2}f_{12}}{f_{43}-f_{12}}-f_{14}}{\left(\frac{L_{23}-f_{14}}{L_ {1}}\right)-\left(\frac{L_{2}}{f_{43}-f_{12}}\right)} \tag{5}\]  
\[y=\frac{\left(\frac{f_{23}-f_{14}}{L_{1}}\right)\left(\frac{L_{2}f_{12}}{f_{43 }-f_{12}}\right)-\left(\frac{f_{23}-f_{14}}{L_{1}}\right)f_{14}}{\left(\frac{ f_{23}-f_{14}}{L_{1}}\right)-\left(\frac{L_{2}}{f_{43}-f_{12}}\right)}+f_{14} \tag{6}\]  
The described method allows the coordinates of the position of the COM in the horizontal plane to be determined [53; 54; 55]. Considering the use of this method in the stand described in Section 2.1, the measurement signal from the strain gauges is accessed. Delivering a measurement signal at 100 Hz is of significance in this case. Due to a simple method of converting the measurement signal and a high measurement frequency, it was possible to measure changes in the position of the COM under dynamic conditions characteristic of wheelchair propulsion. The disadvantage of the above method is that it does not measure the position of the COM in the vertical plane. However, this problem was solved by analytically determining the position of the COM vertically using data obtained from human body motion capture (Section 2.2).