# Assessment of the mechanical power produced by a manual wheelchair user during ambulation in the field

Sauret C.<fnref n="1" />,<fnref n="2" />, Vaslin P.<fnref n="2" />, Dumas R.<fnref n="3" />, Bascou J.<fnref n="1" />,<fnref n="4" />, Pillet H.<fnref n="4" />, Chèze L.<fnref n="3" />, Cid M.<fnref n="5" />, Lavaste F.<fnref n="1" />,<fnref n="4" />

**Keywords: manual wheelchair, mechanical power, energy transfert, rehabilitation**

## 1. INTRODUCTION

Assessing the mechanical power produced by the user of a manual wheelchair (MWC) during daily ambulation is an important issue for both scientists and clinicians as it highlights the user's difficulties when he moves in his environment. On laboratory ergometers, this power was initially computed from the opposite of the rolling resistance during propulsion at a supposed “constant” speed [1]. Currently, this power is assessed by the power of the handrim (HR) propelling torque measured with one instrumented wheel mounted on one side of a MWC [1]. Although this latter method takes into account the obvious propulsive actions of the user on the instrumented HR, three assumptions are made: 1) the power computed on one side is assumed to be half of the total power produced by the user; 2) the powers of the user's actions on the seat, backrest and footrest are neglected; and 3) the kinetic power due to user's movements is also neglected.

The aim of this paper is to present a new method, which relies on classical mechanical principles, for assessing the total mechanical power developed by the user during MWC ambulation in the field.

## 2. APPLICATION OF MECHANICAL PRINCIPLES

In order to assess the mechanical power developed by any mechanical system, it is useful to isolate this system and to list all the external mechanical actions exerted on this system. Using this approach for the {user} system during actual MWC ambulation, the external actions applied on the {user} are his weight (w), the reaction wrenches of both HRs and those of the seat, the backrest and the footrest. The air drag can be neglected with respect to the velocity reached during daily ambulation [2].

On the other hand, according to classical mechanics, the {user} kinetic power ($P_{kin}$) is the time differentiation of the {user} kinetic energy and it is equal to the sum of the powers of all the external actions ($P_{ext}$) and of all the internal actions ($P_{int}$):

$$P_{kin} = P_{ext} + P_{int} \qquad (1)$$

where $P_{int}$ is the resulting power of all the mechanical actions produced by the user's musculo-skeletal system. Thus, $P_{int}$ corresponds to the mechanical power developed by a MWC user and can be calculated from the following equation:

$$P_{int} = P_{kin} - P_{ext} \qquad (2)$$

In this expression, $P_{ext}$ represents the sum of the power of the user's weight ($P(w)$) and the resulting power of all the reaction wrenches exerted by the MWC on the {user} on both HRs, the seat, the backrest and the footrest ($n_D = 5$), which is the opposite of the power put by the user in the MWC ($PI$) [3]. The resulting power $PI$ is calculated by the sum of the $n_D$ co-moments between the wrenches of mechanical actions {$T_A$} exerted by the user on the MWC and the respective kinematics wrenches {$T_C$}:

<footnote n="1">¹CERAH, Institution Nationale des Invalides, Woippy, France</footnote>

<footnote n="2">²LIMOS, Université Blaise Pascal, Clermont-Ferrand, France</footnote>

<footnote n="3">³LBMC, Université Claude Bernard Lyon 1 - IFSTTAR, Lyon, France</footnote>

<footnote n="4">⁴LBM, Arts et Métiers ParisTech, Paris, France</footnote>

<footnote n="5">⁵LMP, Université Bordeaux 1, Bordeaux, France</footnote>
$$PI = \sum_{k=1}^{n_D} \{T_{C_k}\} \otimes \{T_{A_k}\} \quad (3)$$

So, $P_{ext}$ is given by equation 4:

$$P_{ext} = P(\bar{w}) - PI \quad (4)$$

Besides, the user's kinetic power ($P_{kin}$) is calculated from the half sum of the $n_S$ co-moments between the respective kinetics {$T_K$} and kinematics {$T_C$} wrenches of the $n_S$ {user} segments:

$$P_{kin} = \frac{1}{2} \sum_{i=1}^{n_S} \{T_{K_i}\} \otimes \{T_{C_i}\} \quad (5)$$

Then, the power of all the internal actions produced by the user can be calculated from the following expression:

$$P_{int} = \frac{1}{2} \sum_{i=1}^{n_S} \{T_{K_i}\} \otimes \{T_{C_i}\} - P(\bar{w}) + \sum_{k=1}^{n_D} \{T_{C_k}\} \otimes \{T_{A_k}\} \quad (6)$$

### 3. MATERIALS AND METHODS

In order to assess $P_{int}$ during actual propulsion on a horizontal floor, the mechanical actions (i.e. forces and torques) applied by the user on both HRs and on the {seat + footrest + backrest} system of an instrumented MWC (FRET-1) [4] were measured with three six-component dynamometers (TSR-mesures, France). Kinematics of both rear wheels and of the frame was computed from the measurements of two angular potentiometers (Spectrol 601-1045, Vishay, USA) fixed on rear wheels axles, while assuming the MWC rolled without slipping. All sensors data were synchronized and sampled at 500 Hz using a 16-bit A/D conversion card (DAQCard-6036E, National Instruments, USA) plugged into an embedded mini-computer (TC1100, Hewlett-Packard, USA). The data were transmitted in real time to a remote computer (M5200N, ASUS, Taiwan) using IEEE 802.11b and TCP/IP wireless transfer protocols, where they were recorded.

The {user} was segmented into 16 segments (2 feet, 2 legs, 2 thighs, 1 pelvis, 1 trunk segmented in two parts: abdomen and thorax, 1 head & neck, 2 arms, 2 fore-arms, 2 hands). The body segment inertial parameters were assessed from [5-6] in segment reference frames recommended by the International Society of Biomechanics [7-9]. Kinematics of user's segments was determined from the measurement of the 3D positions of 54 reflective markers placed on the user's skin, recorded by a motion capture system (Motion Analysis, USA) composed of 6 digital cameras recording at a video rate of 100 Hz.

Synchronization between the measurements of the instrumented MWC and those of the motion capture system was processed a posteriori from signals resulting from a little stroke on the left instrumented HR with a sledge-hammer equipped with a reflective marker.

Kinematic data provided by the motion capture system were used to compute the kinetic and kinematic wrenches of the user's segments ($n_S = 16$), and then $P_{kin}$ according to equation (1). These data were also used to compute the vertical velocity of the user's center of mass, and then $P(\bar{w})$. Dynamic and kinematic data provided by the instrumented MWC were used to compute the wrenches of mechanical actions applied by the user on the {seat + footrest + backrest} system and on both HRs ($n_D = 3$), and the associated kinematic wrenches. These wrenches were then used for computing $PI$ according to equation (3). Finally, the resultant mechanical power produced by the user ($P_{int}$) could be calculated from equation (6).

The outcomes of this method are illustrated by the results obtained by one able-bodied subject familiar with MWC locomotion (26 y.o., 1.75 m, 63.0 kg) who performed 8 trials of a 7-m long straightforward displacement on a level floor covered with a short-pile carpet. During each displacement, the subject crossed the calibrated volume of the motion capture system allowing the measurement of the subject's kinematics during one complete propulsion cycle. Each trial was performed at a self-selected comfortable velocity, and it began at least two pushes before the MWC went into the calibrated volume, and finished one or two pushes after it was out of this volume.
## 4. RESULTS

Results of the 8 trials showed a cycle mean velocity of 1.21 m/s. The cycle time was 1.14 s (±0.04 s) in which push and free-wheeling phases represented 46 and 54 % of the cycle time (±3 %), respectively. However, the time course of the kinetic power ($P_{kin}$) varied so much that it would not have had any sense to present the results of a mean cycle. Consequently, the following analysis is only focused on one trial (the first one) without any *a priori* on the results obtained in this trial.

Within the propulsion cycle, the internal power ($P_{int}$) showed wide variations with values ranging from 3 to 104 W during the push phase and from -13 to 46 W during the free-wheeling phase (Fig. 1, left). $P_{int}$ strongly increased during the first three quarters of the push phase before suddenly decreasing during the last quarter, though remaining positive. During the free-wheeling phase, $P_{int}$ continued to decrease and became negative during a few instants before it became positive again until the end of the cycle. In average, $P_{int}$ was 51 W during the push phase, 12 W during the free-wheeling phase and 31 W for the whole cycle.

<figure><img src="image_1.png" /><figcaption>Figure 1. Normalized time course of the {user} internal power and its components (left), and of the MWC linear velocity (right).</figcaption></figure>

When detailing the components of $P_{int}$ expressed in equation 6, it can be shown that during the push phase, $P_{int}$ was principally communicated to the MWC. Indeed, during the push phase, $P_{int}$ almost followed $PI$, which is the sum of the power put by the user into the HRs, the seat, the backrest and the footrest. However, $PI$ was slightly higher than $P_{int}$ during the first three quarters of the push phase and slightly lower during the last quarter. During the same period, $P_{kin}$ reached negative values (-20 W) during the first three quarters and positive values (24 W) during the last quarter. During all the push phase, the power required to raise up the {user} center of mass ($-P(\bar{w})$) exhibited positive values while it became negative at the beginning of the free-wheeling phase before reaching again positive values at the end of this phase.

Finally, the {user} internal power induced visible effects on the MWC linear velocity (Fig. 1, right), which slightly decreased during the first third of the push phase, reaching 0.84 m/s. Then, it increased until the first half of the free-wheeling phase, reaching 1.50 m/s, before decreasing until the end of the cycle. At the end of the propulsion cycle, the MWC velocity was about 0.2 m/s higher than at the beginning.

## 5. DISCUSSION

Despite the propulsion cycle analyzed in this paper cannot be generalized to the other trials of this study, the obtained results are original in comparison to those related in the literature. Indeed, the method has shown that the user did not only produce mechanical power ($P_{int} > 0$) during the push phase but also during the free-wheeling phase, which can no longer be considered as a recovery phase or a resting time. In addition, during a short period of the free-wheeling phase, the subject himself dissipated ($P_{int} < 0$) a small part of the energy he had produced before.

The analysis of the components of $P_{int}$ reveals that the energy put by the user into the MWC ($PI$) was partly due to a transfer of the {user} kinetic energy ($P_{kin} < 0$) and inversely. Finally, both at the beginning and at the end of the propulsion cycle, the MWC slowed down whereas $PI$ was positive and almost equal to $P_{int}$, which indicates that the power produced by the user is not sufficient to compensate the energy lost in the rolling resistance.

The main difficulty of this study was to obtain a reproducible cycle when propelling a MWC on the floor, which is expressed by the variable time courses of $P_{kin}$ between trials. One explanation could be that the analyzed cycles were not performed at a steady state but at a transient rhythm. This hypothesis is supported by the difference noted between the MWC velocity at the beginning and at the end of the propulsion cycle of trial 1. This problem could be solved by increasing the distance before the MWC crossed the motion capture calibrated volume, but that was not possible in the room where these trials were recorded.
## 6. CONCLUSION

The method presented in this paper demonstrated that the strict application of the classical mechanical principles to the {user} system allows to better understand MWC propulsion than previous methods related in the specific literature [1]. For instance, this method enlightens on the energy transfers between the user and his MWC.

However, since this method implies to determine the {user} kinetic power, its accuracy depends on 1) the refinements of user's segmentation model, 2) the body segment inertial parameters, and 3) the markers movements (skin movements and numerical filtering method).

## 7. REFERENCES

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