# Use of a 3D accelerometer for kinetic analysis of wheelchair propulsion

Philippe Vaslin, Michel Dabonneville

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## To cite this version:

Philippe Vaslin, Michel Dabonneville. Use of a 3D accelerometer for kinetic analysis of wheelchair propulsion. 12th Conference of the European Society of Biomechanics, Trinity College, Aug 2000, Dublin, Ireland. pp.345. hal-05000521

HAL Id: hal-05000521

https://uca.hal.science/hal-05000521v1

Submitted on 21 Mar 2025

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# Use of a 3D accelerometer for kinetic analysis of wheelchair propulsion

Ph. Vaslin and M. Dabonneville

Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes, Université Blaise Pascal, Clermont Ferrand 2, France.

## Introduction

Since accelerometry has been recommended for kinetic and kinematic analysis of human movement [1], it has not been widely applied in the field of biomechanics. Some studies [2, 3] used this technique for computing joint forces during walking and running. However, it seems that it has never been applied to the analysis of wheelchair propulsion. In that research field indeed biomechanical parameters are mostly studied with various devices (treadmills, ergometers) which restrain investigations within the laboratory. In the present study, a 3D accelerometer has been used for kinetic analysis of wheelchair propulsion with some simplifying assumptions.

## Materials and methods

### Experimental procedure

One able-bodied sedentary subject (50 years, 180 cm, 80 kg) accustomed to wheelchair locomotion propelled himself straight forwards over 7 metres on a flat ground according to two modalities ('normal' and 'fast'). The subject performed five trials of each modality and he had to stay stock-still at the beginning and the end of each trial.

A 3D accelerometer (Analog Devices: ADXL05EM-3, range: +/-5 g) was fixed under the seat of a standard basketball wheelchair, approximately at the level and in the middle of the rear wheels axles. The sensor was connected with a 10 metres cable to an A/D conversion card (National Instrument, AT-MIO-64E-3) slotted in a PC and the three components of the acceleration were recorded at a sampling rate of 1000 Hz.

### Theoretical considerations and simplifying assumptions

In the general case of a non Galilean reference frame $R^*$ moving in an absolute Galilean reference frame $R$, the driving acceleration of $R^*$ with respect to $R$, $a(R^*/R)$, can be written:

$$a(R^*/R) = a(O/R) + (d\omega/dt) \times r + \omega \times (\omega \times r) \quad (1)$$

where $a(O/R)$ is the linear acceleration of the origin $O$ of $R^*$ with respect to $R$, $\omega$ is the instantaneous rotation vector of $R^*$ with respect to $R$ and $r$ is the position vector of a fixed point in the moving reference frame $R^*$.

Assuming that the subject's action is symmetrical so that the movement of the wheelchair is only a translation along the fore-and-aft axis of $R$ ($\omega = 0$), the accelerometer measured the linear acceleration $a(O/R)$ of the origin $O$ of the moving reference frame $R^*$ linked to the wheelchair. As it is quite impossible to precisely fix the accelerometer so that the axes of $R^*$ are strictly parallel to those of $R$, the measurement of the gravitation acceleration ($g$) in the initial static position of the wheelchair has been used to correct the orientation of the accelerometer's axes with respect to $R$, following a two-sequence rotation described by the transformation matrix $M$:

$$a(W/R) = M \cdot [a(O/R) - g] \quad (2)$$

where $a(W/R)$ is the absolute wheelchair's acceleration.

This correction allowed to rotate $R^*$ so that its vertical axis became parallel to $g$, but it did not permit to orient any of its horizontal axes along the fore-and-aft axis of $R$. It was thus assumed that the horizontal acceleration measured by the accelerometer was oriented in the displacement's direction.

Although this correction was satisfying for acceleration data, both components of the horizontal velocity, obtained by first time integration, presented a negative 'drift' at the end of each trial whereas the wheelchair remained immobile and its trajectory was linear. A second correction was thus applied to the acceleration data by computing the mean 'acceleration

drift' between the starting and the ending instants of the movement, manually identified on X and Y velocity curves. Assuming this quantity was constant during the wheelchair's displacement, it has been subtracted to the corrected accelerations before computing the horizontal velocity again.

## Results

This calculation method has been applied to all the trials performed by the subject in this pilot study. The velocity curves presented on Figure 1 could indicate that both corrections were founded and that $V(\text{correct})$ depicts the actual wheelchair's velocity along the fore-and-aft axis of $R$.

<figure><img src="image_3.png" /><figcaption>Figure 1: Corrected horizontal velocity ($V$) of a 'normal' trial.</figcaption></figure>

## Discussion

The first correction is well known [2, 3] and might be suitable to the purpose of this study. However, the wheelchair is not perfectly rigid and the vertical movements of the subject's upper body may squash the rear wheels tyres thus producing a vertical oscillation of the frame during propulsion. In this case the accelerometer may record a small component of $g$ along its horizontal axes which could not be corrected.

The second correction implies to precisely control the initial and final orientations of the wheelchair. It may allow to subtract from the horizontal components of $a(W/R)$ both the signal 'drift' and the centripetal component of the driving acceleration [$\omega \times (\omega \times r)$] created by asymmetric pushes on the handrims and which may exist even if the instantaneous axis of rotation goes through the origin of the accelerometer, depending on its sensing mode. In most other cases however the tangential component [$(d\omega/dt) \times r$] could not be corrected.

## Conclusion

This calculation method has been used to compute power output of wheelchair propulsion and the obtained results withstand the comparison with those of a previous study realized on a stationary wheelchair ergometer during a 30-s sprint test [4]. Nevertheless, the corrections and assumptions discussed above should be verified in future investigations on wheelchair propulsion with a 3D accelerometer.

## References

[1] J. R. W. Morris (1973) J. Biomech. 6: 729-736. [2] Z. Ladin and G. Wu (1991) J. Biomech. 24: 1173-1187. [3] A. J. van den Bogert, L. Read and B.M. Nigg (1996) J. Biomech. 29: 949-954. [4] H.E.J. Veeger, E.M.C. Lute, K. Roeleveld and L.H.V. van der Woude (1992) Eur. J. Appl. Physiol. 64: 158-164.