Assessment of field rolling resistance of manual wheelchairs.
Ambulation aids (Analysis)
de Saint Remy, Nicolas
|Publication:||Name: Journal of Rehabilitation Research & Development Publisher: Department of Veterans Affairs Audience: Academic Format: Magazine/Journal Subject: Health Copyright: COPYRIGHT 2012 Department of Veterans Affairs ISSN: 0748-7711|
|Issue:||Date: Jan-Feb, 2012 Source Volume: 49 Source Issue: 1|
|Product:||Product Code: 3010000 Tires & Tubes; 3011000 Tires; 3841780 Wheelchairs NAICS Code: 326211 Tire Manufacturing (except Retreading); 339113 Surgical Appliance and Supplies Manufacturing SIC Code: 3011 Tires and inner tubes; 3842 Surgical appliances and supplies|
|Geographic:||Geographic Scope: France Geographic Code: 4EUFR France|
Evaluating resistances is critical to the study of manual wheelchair (MWC) propulsion. In fact, the impact of resistance on the mechanical efficiency of MWC propulsion induces a decrease in the user's mobility, with potential risks including musculoskeletal disorders (i.e., pain and/or injuries). This has caused clinicians, scientists, and mechanical engineers to focus on this topic with the goal of minimizing such resistances. During propulsion, most of the energy supplied by the user is dissipated by rolling, turning, slipping, bearing, and air resistances. Because bearing resistance and air drag have been proven to be negligible in daily locomotion , the rolling, turning, and slipping resistances remain as causes of energy loss. However, no turning resistance occurs in straight-forward propulsion. Therefore, under the assumption that the MWC does not slip, the present study focused on rolling resistance, which is mainly caused by inelastic deformations of the tires and ground .
Examining previous studies clarified the influences of tire type (pneumatic vs solid), pressure, rear wheel camber, and floor hardness on rolling resistance [3-8]. Furthermore, MWC propulsion models [1,9-13] have established the relation between wheel radius and rolling resistance; i.e., for a given laden weight, the wheel rolling resistance increases when the radius is reduced and vice versa. This relation thus explains the increase in MWC rolling resistance when the mass is brought forward [4,11-15]. Rear wheel toe-in/-out could also be an important source of resistance , but this mechanical phenomenon may not be considered part of rolling resistance because it is a consequence of the rear wheels' slipping (the wheel trajectories are not perfectly in their rotational plans, inducing a slipping friction of the wheels on the floor) and can be cancelled by appropriate rear wheel alignment. All the findings of the different studies conducted on MWC rolling resistance provide useful guidelines for clinicians and users when choosing and adjusting a MWC. However, these recommendations are not listed in terms of importance and may not all be satisfied at one time. Thus, compromises are usually made by clinicians when optimizing a MWC, with no quantified visibility for the benefits. Hence, a simple and fast tool to assess the rolling resistance in clinical practice is needed.
In order to quantify rolling resistance acting on a MWC, different experimental methods have been developed in the past. The first one measured the drag force (with a force transducer) occurring on a treadmill [2-3,5,16]. The main problem with this method was that rolling resistance depended on the material of the treadmill belt and did not allow evaluation of different surfaces. Other authors quantified the rolling resistance from deceleration tests (or coast-down tests) performed in the field by measuring the MWC deceleration with a subject sitting in the MWC [17-20]. These methods allowed evaluation of various surfaces but neglected the influence of the fore-aft distribution of the total mass, which conduces to major changes in rolling resistance. Hence, experiments were required to test the influence on rolling resistance of each adjustment of the MWC and each choice of wheels. Finally, a method also based on deceleration tests performed in the field with artificial masses and with various fore-aft distribution of the total mass was developed [11-13,21-22]. In this case, the rolling resistance offered by a MWC was calculated from coefficients linked to the loads applied on front and rear wheels. This method allows quantification of the rolling resistance of a MWC on various surfaces and simulates the effect of various adjustments, which change the fore-aft distribution of the mass. However, all these methods are time consuming during MWC adjustment. Therefore, they are not applicable in clinical routine.
In this context, the aim of this study was to develop a simple method for assessing subject-specific MWC rolling resistance in clinical practice.
Model of Rolling Resistance
In order to quantify MWC rolling resistance, deceleration tests were performed on a horizontal surface [14-15,17-22]. During these tests, the MWC was first pushed forward (push phase) manually, released, and allowed to decelerate (deceleration phase). This deceleration was caused only by the rolling resistance, assuming that the MWC did not deviate and neglecting the bearing, slipping, and air resistances [1,4]. The mechanical model (detailed in Appendix 1, available online only) of the deceleration phase, linking the deceleration both to the forces and torques exerted on the MWC, was as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where is [[gamma].sub.G] the linear deceleration along the fore-aft direction (in meters per second squared); g is the gravitational acceleration (in meters per second squared); [[lambda].sup.f] and [[lambda].sub.r] are the front and rear wheel rolling resistance parameters (RPs) (in meters), respectively, characterizing the rolling resistance property caused by the contact between the wheels and floor and modeled as the fore-aft length between the theoretical and real centers of pressure in the contact area (Figure 1); [r.sub.f] and [r.sub.r] are the front and rear wheel radii (in meters); [d.sub.f] and [d.sub.r] are the fore-aft distances between the global center of mass (COM) and the front and rear wheel hubs (in meters), respectively; [w.sub.b] is the wheelbase (in meters), defined as the fore-aft distance between the front and rear hubs; m is the total mass (in kilograms); h is the height to the ground of the global COM (in meters); and [I.sub.f] and [I.sub.r] are the moments of inertia of the two front and the two rear wheels around their rotational axes (in kilogram-meters squared), respectively.
This equation was used as an exhaustive model for the MWC rolling resistance during the deceleration phase of the test. However, it could be simplified by leaving out some terms with an error that was lower than 5 percent (see details in Appendix 2, available online only):
[[gamma].sub.G] = -g([[[lambda].sub.f] / [r.sub.f]] [[d.sub.r] / [w.sub.b]] + [[[lambda].sub.r] / [r.sub.r]] [[d.sub.f] / [w.sub.b]]) (2)
[FIGURE 1 OMITTED]
Moreover, when replacing [w.sub.b], [d.sub.f], and [d.sub.r] with the masses applied to the front and rear wheels ([m.sub.f] and [m.sub.r], respectively) and the total mass (m), the model is close to those previously proposed [1,9].
[[gamma].sub.G] = - g ([[[lambda].sub.f] / [r.sub.f]] [[m.sub.f] / m] + [[[lambda].sub.r] / [r.sub.r]] [[m.sub.r] / m]) (3)
This equation shows that the MWC deceleration is inversely related to the wheel radii. Because the front casters have smaller radii than the rear wheels, the MWC deceleration would be more influenced by the mass distribution on the front wheels than the rear wheels [11-14]. Finally, the rolling resistance can also be expressed by means of a resisting force ([F.sub.roll]) sustained by the subject during propulsion:
[F.sub.roll] = m[[gamma].sub.G] [??] m[[gamma].sub.G] = - g ([[[[lambda].sub.f] / [r.sub.f]] [m.sub.f]] + [[[[lambda].sub.r] / [r.sub.r]] [m.sub.r]]) (4)
The RP characterizes the resistance acting at the contact level between the wheels and ground and greatly depends on the materials used for both. The rolling resistance factor (RF) is the ratio between RP and the wheel radius; it characterizes the wheel's specific rolling quality based on its size and the type of floor. Therefore, RF increases with an increase in RP or a decrease in wheel radius. The resisting force ([F.sub.roll]) characterizes the intensity of the MWC rolling resistance for a given subject during propulsion on a specific floor.
Two approaches could be used to characterize the rolling resistance properties (RP and RF) for different types of front and rear wheels. The first one uses a single chair and replaces the wheels, while the other uses several chairs already equipped with various wheels. If the same chair were to be used, then resistances such as the air drag and frame deformations would remain unchanged. However, all the wheels cannot be mounted on the same chair because of differences in the rear wheel axles and fork geometries, inducing the need for several chairs. Thus, we selected the second approach, while neglecting the air drag and frame deformation effects [1,4].
Thirty-three different MWCs (Table 1) were tested on two typical indoor surfaces: a hard smooth surface (polished concrete type) and carpet (loop pile carpet [5.4 mm] laid on concrete). For pneumatic rear wheels, the pressures were respectively set to their advised maximum values, which ranged from 43.5 to 87.0 psi. Rehabilitation experts performed the wheel alignments to minimize the toe-in/-out effect. A there-and-back procedure was undertaken to override possible flatness imperfections in the floor [16-17,20]. The deceleration was measured by use of a wireless three-dimensional accelerometer (sensitivity: [+ or -]2 g; Beanscape AX-3D; Neuvillesur-Oise, France) with a sampling frequency of 100 Hz [21-23] that was fixed to the loads placed on the seat.
For each MWC, 4 sets of 20 deceleration tests (80 tests total) were performed on each surface and the mean deceleration of every set was computed. The number of deceleration tests for each set was defined to give both acceptable accuracy and a feasible protocol in terms of experiment time (around 1 hour for one MWC on the two tested surfaces). For each set, the mass distribution on the front and rear wheels was changed by alternatively placing the loads forward or backward (Table 1) and was measured with use of a specific weight-scale platform (resolution: 0.05 kg). In summary, 5,280 deceleration tests were performed (20 tests x 4 sets x 33 MWCs x 2 floors). The initial velocities at the beginning of the deceleration phase, computing from the acceleration signals, ranged from 1.5 to 2.5 m/s.
A system, comprising Equation 3 written four times and applied to the four sets, was thus available for each MWC for every surface and only included two unknown variables: the RP values for the front ([[lambda].sub.f]) and rear ([[lambda].sub.r]) wheels. Each system was then written in a matrix form:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
in which [[M.sub.A]] is the acceleration matrix containing the measured decelerations, [[M.sub.D]] is the distribution matrix containing the wheels' radii and mass distributions, and [[M.sub.RP]] contained the unknown RPs. The latter were then computed as follows:
[[M.sub.RP]] = [[-g[[[M.sub.D]].sup.T][[M.sub.D]]].sup.-1][[[M.sub.D]].sup.T][[M.sub.A]]. (6)
For the 33 MWCs, the system was respectively solved for each surface.
The RPs ([[lambda].sub.f]) and ([[lambda].sub.r]) for each MWC (on the two tested surfaces) were analyzed based on the types of front and rear wheels. A rehabilitation specialist sorted the front casters into three groups (Table 2): soft roll, standard, and roller casters. The rear wheels were gathered into four groups: three for pneumatic tires according to their inflating pressure (43.5, 65.0, and 87.0 psi) and one for solid tires.
A statistical analysis was carried out to ascertain whether significant RP differences existed between the various wheels and floor types. Because of the small sizes of the groups (ranging between 3 and 20), nonparametric tests were used (Kruskal-Wallis or Mann-Whitney to compare the wheel types and Wilcoxon signed-rank for floor types). All the comparisons were two-sided and p-values [less than or equal to] 0.05 were considered significant.
To validate the predicting model for the MWC rolling resistance per surface, we used a leave-one-out cross validation technique and evaluated the accuracy by means of the standard error of the estimate (SEE).
Manual Wheelchair Deceleration
The decelerations ranged from -0.02 to -0.34 m/[s.sup.2] on a hard smooth surface and from -0.12 to -0.59 m/[s.sup.2] on carpet. For both surfaces, the decelerations increased when the mass distribution on the front casters was augmented (Figure 2). In addition, this increase was more important on carpet than on the hard smooth surface. The MWC rolling resistances ([F.sub.roll]) ranged from -2.9 to -32.6 N on a hard smooth surface and from -11.2 to -61.6 N on carpet.
Wheel Rolling Properties (Rolling Resistance Parameter and Rolling Resistance Factor)
For each type of front caster, the RP value was significantly higher on carpet than on the hard smooth surface (Figure 3). The RP values of every type of rear wheel were also higher on carpet than the hard smooth surface, but the statistics could not be computed for all the groups because of the small sample sizes. The only significant difference was found for pneumatics inflated to 87.0 psi.
On both surfaces, the RP values were found to be significantly different according to the caster types (p < 0.001). Standard casters showed the highest RP, followed by soft and then roller casters. Therefore, for a given radius, standard casters had the biggest RF, whereas roller casters had the smallest (Figure 4). Figure 4 shows that the same RF value could be obtained for all the caster types when setting different radii. For the same caster, Figure 4 shows that RF decreased when the radius was augmented. However, the effect on RF of a caster radius variation evolved with the enlargement of the radius: the smaller the radius, the higher the effect and vice versa.
[FIGURE 2 OMITTED]
Surprisingly, the rear wheel pneumatics showed that tires inflated to 87.0 psi exhibited a higher RP than those inflated to 43.5 and 65.0 psi (Figure 3). However, the first group included six cambered wheels, which showed a slightly higher RP than the rest of the group on the hard smooth (1.91 [+ or -] 0.66 mm vs 1.10 [+ or -] 0.56 mm) and carpet surfaces (4.81 [+ or -] 0.90 mm vs 4.69 [+ or -] 1.11 mm). Nevertheless, the statistics did not reveal significant differences between the pneumatic types for either the hard smooth (p = 0.18) or carpet surface (p = 0.57). Then, all the pneumatic tires were gathered into the same group, which showed significantly lower RP values than the solid tires on both surfaces. Hence, the solid tires exhibited a higher RF than the pneumatic tires for any wheel radius (ranging from 0.25 to 0.35 m) (Figure 5).
Finally, on the hard smooth surface, the pneumatic rear wheels showed a higher RP value than the roller (p < 0.001), soft (p = 0.04), and standard casters (p = 0.002). On carpet, the RP of the pneumatic rear wheels was also higher than those of the roller (p < 0.001), soft (p < 0.001), and standard (p < 0.001) casters. In addition, the effect of the radius variation on RF appeared to be significantly smaller than that for front casters.
Assessment of Manual Wheelchair Rolling Resistance
The accuracy of the MWC rolling resistance assessments was evaluated with a leave-one-out cross-validation technique (Figure 6). The SEE values were 4.4 and 3.9 N on the hard smooth and carpet surfaces, respectively. Finally, the mean RP values computed from all the data are summarized in Table 3.
[FIGURE 3 OMITTED]
Modeling the MWC rolling resistance (Equation 4) provided helpful information for decreasing it based on the geometric properties of the MWC. For example, enlarging the wheel radii made decreasing the rolling resistance possible. The rolling resistance could also be decreased by adjusting the MWC with a change in the rear wheel fore-aft position, which modified the masses applied to the front and rear wheels. For instance, when the front casters exhibited a higher RF than the rear wheels, the latter could be brought forward to decrease the load on the front casters and thus drop the MWC rolling resistance. When RP values for the front and rear wheels are previously known, the RF values can be easily calculated by measuring the wheel radii. Hence, the measurements of the masses applied on front and rear wheels (using weight scale plate-forms) when the user is sitting in the MWC allow estimation (using Equation (4)) of the specific rolling resistance sustained with this MWC. In this case, the required measurements are very easy and fast to do and the method becomes applicable in clinical routine by clinicians or other members of the rehabilitation team.
Because MWC rolling resistance is related to the type of floor, the RP values were determined for two different surfaces: a hard smooth surface and carpet. For that purpose, deceleration tests were performed directly in the field. This experimental setting made it possible to test any surface, which cannot be done with drum-dynamometers [6,8] or treadmills [2,5,16]. During the deceleration tests, the bearing resistance, air drag, and wheel toe-in/-out effect were neglected. However, so that these hypotheses could be assumed, the MWC velocity did not exceed 2.5 m/s, the ball-bearings were clean and not overused, and wheel alignments were carried out by rehabilitation experts.
In order to compute the RP values, we performed the deceleration tests with four load settings for each MWC on every surface. The results for these four conditions were then used to solve a system of four equations with only two unknowns. Even though two loads would have been enough, a system of four equations offered more reliable results. Therefore, the variations in RP with the load were neglected based on the good linearity previously found .
On the hard smooth surface, the decelerations were consistent with the previous ones obtained on a hardwood gymnasium surface [14-15,17]. On carpet, the decelerations were slightly higher than those obtained on short pile carpet  but in the same range as those obtained on an athletic track [11-12,15]. On both surfaces, the deceleration increased with the percentage of the total mass distributed on the front wheels as in the previous observations [4,11-15]. Furthermore, this result reveals that the rolling resistance of MWC could not be evaluated using a single load setting, as is often done [20,25].
The MWC rolling resistances obtained on the hard smooth surface were consistent with the previous results, ranging from -2.9 to -22.6 N [3,16-19]. On carpet, the rolling resistances were higher than on the hard smooth surface, which confirmed the conclusions of Koontz et al. . These authors found that, for a given velocity, the propelling torque was higher on carpet than on linoleum or tiled floors. Therefore, they suggested that this resulted from higher rolling resistance. Frank and Abel earlier showed that the rolling resistances of casters on carpet were higher than on a vinyl surface . However, they did not use a MWC but a trolley equipped with four casters. Finally, the results make it possible to advise home architects not to use carpet, both to increase the mobility of MWC users and to decrease muscle and joint strain.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
For every type of wheel, the RP values were found to be significantly higher on carpet than on the hard smooth surface, which explains the differences noted in the decelerations and rolling resistances. This result is explained by floor deformations for carpet that did not occur for the hard smooth surface. As a consequence, the use of a carpet surface should decrease the mobility of MWC users and increase the risk of musculoskeletal disorders.
The high RP of standard casters reflects the low rolling properties of their materials, which require improvements to decrease the rolling resistance. Conversely, roller casters showed materials with high rolling properties. Unexpectedly, although the soft casters were the most deformable, their RP was not the highest. This result could be explained by the high elastic properties of these caster materials. Hence, the RP value depended not only on the wheel softness but also on the elastic properties of their materials. The effect of the tire pressure, previously demonstrated [2,4], was not found in our results. However, the inclusion of six cambered wheels--which showed slightly higher RP values than noncambered wheels--in the group of tires inflated to 87.0 psi could partially explain the highest RP found for this group. In addition, the pneumatics inflated to 43.5 and 65.0 psi exhibited larger widths than the pneumatics inflated to 87.0 psi, which could also partially explain the fact that the highest RP was obtained for the latter group. Indeed, under the same load and pressure conditions, the contact area would be the same for any tire width. Hence, the main axis of the ellipse area drops with an increase in tire width, which decreases the RP. Therefore, the expected decrease in the RP with tire pressure might have been impaired by the negative effects of both the camber and thinness of the pneumatics inflated to 87.0 psi. In addition, these results clarify the low effect of the tire pressure from 43.5 to 87.0 psi. However, keep in mind that MWC users generally do not maintain tire pressure, which could lead to a significant increase in the rolling resistance when tire pressure falls below 43.5 psi. Thus, further experiments carried out with different pressures on the same tires would allow both verification and quantification of the influence of the tire pressure on RP. Finally, the solid tires exhibited significantly higher RP values than the pneumatics. Considering that the solid and pneumatic rear wheels had similar radii, the fact that the former exhibited a higher RF than the latter is consistent with the previous results [5-6,27]. Thus, even if solid tires do not need to be maintained, improvements in their materials are required to reach the rolling properties of pneumatic tires. Thus, solid tires would decrease the mobility of MWC users and could lead to potential risks of muscle and joint disorders.
Beyond wheel comparisons, this knowledge of RP values makes determining the wheel radii that provide the same RF possible. For that, the ratio between the radii of the wheels must be the inverse of this between RP. As an example, the standard casters would need radii 5.4 times higher than those of roller casters to provide the same RF on a hard smooth surface. In the same way, pneumatic rear wheels would need radii 3.6-, 1.5-, and 0.7-fold those of roller, soft, and standard casters, respectively, to provide the same RF on a hard smooth surface. Considering that the radii of the front casters generally range from 0.03 to 0.10 m, the RF values of the rear wheels are lower than those of the front casters. Consequently, both clinicians and MWC users should probably not focus on the choice of rear wheel pneumatics but rather on the front casters.
The method presented in this article would help clinicians to make trade-offs, both when choosing MWCs and when making adjustments, based on a quantitative evaluation of the subject-specific MWC rolling resistance. The method includes a mechanical model (Equation (4)) and input data (Table 3), which just require measurements of the wheel radii and load applied to the front and rear wheels when a user sits in the MWC. Furthermore, the model can be applied to any mechanical system equipped with front and rear wheels (e.g., wheelchairs, strollers, or medical beds) and only needs a few inputs: wheel radii, masses applied on front and on rear wheels, and specific RP. The input data (RP summarized in Table 3) makes reducing the measurements possible, thereby making the method usable in a clinical environment. The validity of the method was investigated with a crossvalidation technique and gave acceptable results when predicting MWC rolling resistances on both tested surfaces. Further experiments performed on other surfaces (indoor and/or outdoor) would be useful to assess the specific MWC rolling resistance on the surface on which the user mainly rolls. However, the use of different types of front and rear wheels will be required on each surface.
Finally, clinicians could use the method to adjust the MWC for users with regard to subject-specific MWC rolling resistance. The method could also be used by engineers to enhance MWCs and by architects to improve the accessibility of private and public buildings for MWC users.
This study presented a simple and convenient method for the assessment of subject-specific MWC rolling resistance during propulsion on hard smooth and carpet surfaces. Rolling resistance properties were quantified from experiments and used as input data in the model. Thus, the method could be easily incorporated into a clinical routine.
The experiments allowed us to confirm various considerations, such as the higher rolling resistance of (1) solid tires on the rear wheels compared with pneumatic tires, (2) front casters compared with rear wheels, and (3) carpet compared with a hard smooth surface. Thus, carpet and solid tires should be avoided to improve both the mobility and accessibility of MWC users and decrease the potential risk of upper-limb disorders. Although these recommendations already exist, this study provided quantified data comparing several parameters like surfaces and wheel types and sizes.
Assessments of MWC rolling resistances from the method showed acceptable accuracy on both tested surfaces. In addition, this method could easily be implemented in a calculus sheet that would help clinicians to choose a MWC, its wheels, and its adjustments based on the subject and environment. It should also help MWC manufacturers during the development of their products and should help architects enhance the accessibility of buildings. Finally, daily use of this method in various fields should decrease the rolling resistance sustained by MWC users in their daily life, which would improve their mobility and contribute to the prevention of muscle and joint disorders.
In the future, it would be interesting to enlarge this study to other common indoor or outdoor floors such as asphalt or clay ground. The modeling of the tire pressure effect on the rolling resistance could also be interesting, particularly to quantify the rolling resistance for low pressures, which are often used by MWC users.
JRRD at a Glance
Pushing a manual wheelchair is strenuous and frequently causes muscle and joint problems. Rolling resistance during manual wheelchair propulsion also causes energy loss that decreases users' ability to get around and increases their risk of musculoskeletal pain and injuries. This article presents a method for evaluating subject-specific rolling resistances with respect to the types and sizes of front and rear wheels and the fore-aft distribution of the total mass. The method is easy to use and could be used clinically to ensure that the most appropriate wheels and wheelchair adjustments are chosen.
Study concept and design: C. Sauret, J. Bascou, N. de Saint Remy, H. Pillet, P. Vaslin.
Acquisition of data: C. Sauret, J. Bascou, N. de Saint Remy.
Analysis and interpretation of data: C. Sauret, J. Bascou.
Drafting of manuscript: C. Sauret, J. Bascou.
Statistical analysis: C. Sauret, J. Bascou.
Critical revision of manuscript for important intellectual content: H. Pillet, P. Vaslin, F. Lavaste.
Obtained funding: F. Lavaste.
Study supervision: F. Lavaste.
Financial Disclosures: The authors have declared that no competing interests exist.
Funding/Support: This material was based on work supported by the SACR-FRM project, French National Research Agency (ANR-06TecSan-020) and the Centre d'Etudes et de Recherche sur l'Appareillage des Handicapes (loaned all MWCs required to fulfill this work).
Abbreviations: COM = center of mass, MWC = manual wheelchair, RF = rolling resistance factor, RP = rolling resistance parameter, SEE = standard error of the estimate.
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Submitted for publication March 18, 2011. Accepted in revised form July 26, 2011.
This article and any supplementary material should be cited as follows:
Sauret C, Bascou J, de Saint Remy N, Pillet H, Vaslin P, Lavaste F. Assessment of field rolling resistance of manual wheelchairs. J Rehabil Res Dev. 2012;49(1):63-74.
ResearcherID: Christophe Sauret, PhD: H-2410-2011; Joseph Bascou, MS: H-2414-2011.
Christophe Sauret, PhD; (1) * Joseph Bascou, MS; (1-2) Nicolas de Saint Remy, PhD; (1) Helene Pillet, PhD; (1) Philippe Vaslin, PhD; (3-4) Francois Lavaste, PhD (1-2)
(1) Arts et Metiers ParisTech, Laboratoire de Biomecanique, Paris, France; (2) Institution Nationale des Invalides, Centre d'Etudes et de Recherche sur l'Appareillage desHandicapes, Woippy, France; (3) Clermont Universite, Universite Blaise Pascal, Laboratoire d'Informatique, de Modelisation et d'Optimisation des Systemes, Clermont-Ferrand, France; (4) Centre National de la Recherche Scientifique, Unite mixte de recherche, Laboratoire d'Informatique, de Modelisation et d'Optimisation des Systemes, Aubiere, France
* Address all correspondence to Christophe Sauret, PhD; Laboratoire de Biomecanique--Arts et Metiers ParisTech, 151 boulevard de l'Hopital, Paris 75013, France; +33144246364; fax: +330144246366. Email: email@example.com
Table 1. Manual wheelchair properties and load settings used for experiments. Company Front Casters Rear Wheels (Model) Type Radius Psi vs Width (m) Solid (in.) Dietz GMBH Standard 0.064 87.0 1-3/8 (Pro Activ Traveler) Invacare Soft 0.063 87.0 1 (Kuschall Champ Carb) Sunrise Medical Soft 0.071 87.0 1 (Quickie Easy Max) Sunrise Medical Roller 0.040 87.0 1 (Quickie Matchpoint) Otto Bock Soft 0.072 87.0 1 (Avant-Garde T) Livestand Standard 0.059 87.0 1 (LSA Helium) Sunrise Medical Standard 0.061 87.0 1-3/8 (Quickie 2HP) Sunrise Medical Soft 0.070 Solid 1-3/8 (Classic 160 Recline) Progeo Soft 0.060 87.0 1 (Exelle Vario) Rehateam Soft 0.062 87.0 1 (Projeo Jocker) Dupond Medical Standard 0.097 Solid 1-3/8 (Optimo Confort) Invacare Standard 0.099 87.0 1-3/8 (Rea Azalea) Otto Bock Standard 0.074 87.0 1-3/8 (Innov XXL) Invacare Standard 0.063 Solid 1-3/8 (Action 3 Junior) Meyra Roller 0.040 87.0 1 (Offense 1.879) Invacare Soft 0.096 65.0 1-3/8 (Action 4 XLT) Meyra Standard 0.063 65.0 1-3/8 (X2 3.351) Dupond Medical Standard 0.097 87.0 1 (Alto Plus F) Dupond Medical Standard 0.095 43.5 1-3/8 (Primeo C) Meyra Soft 0.074 87.0 1 (FX One) RGK Roller 0.036 87.0 1 (Interceptor) Invacare Roller 0.040 87.0 1 (Top End Transformer) Bischoff & Bischoff Standard 0.086 Solid 1-3/8 (Triton) Dietz GMBH Standard 0.090 65.0 1-3/8 (Primo Amico) Invacare Standard 0.097 43.5 1-3/8 (Rea Clematis) Invacare Standard 0.074 65.0 1-3/8 (Action 3 Positioning) Invacare Standard 0.051 87.0 1 (Kushall AG) RGK Roller 0.051 87.0 1 (Hi Lite) Rupiani Standard 0.072 65.0 1-3/8 (Fuze T20 PDG) Invacare Roller 0.036 87.0 1 (Top end Pro Tennis) Dupond Medical Standard 0.062 87.0 1 (Energy ASB 600) Vermeiren Standard 0.101 Solid 1-3/8 (795 TII) Vermeiren Standard 0.101 43.5 1-3/8 (R708 TII) Company Rear Wheels Load Setting (Model) [set 1, set 2, set 3, set 4] Tread Radius Total Design (m) Mass (kg) Dietz GMBH Street 0.312 [67, 64, 103, 103] (Pro Activ Traveler) Invacare Smooth 0.299 [75, 75, 99, 90] (Kuschall Champ Carb) Sunrise Medical Smooth 0.298 [67, 68, 106, 107] (Quickie Easy Max) Sunrise Medical Smooth 0.297 [83, 83, 106, 106] (Quickie Matchpoint) Otto Bock Street 0.299 [68, 68, 107, 107] (Avant-Garde T) Livestand Street 0.299 [83, 83, 102, 107] (LSA Helium) Sunrise Medical Street 0.307 [69, 69, 117, 117] (Quickie 2HP) Sunrise Medical Smooth 0.306 [83, 84, 115, 115] (Classic 160 Recline) Progeo Smooth 0.297 [80, 83, 103, 108] (Exelle Vario) Rehateam Smooth 0.297 [66, 67, 106, 103] (Projeo Jocker) Dupond Medical Street 0.302 [92, 93, 131, 132] (Optimo Confort) Invacare Smooth 0.306 [102, 102, 125, 125] (Rea Azalea) Otto Bock Street 0.310 [100, 100, 141, 141] (Innov XXL) Invacare Smooth 0.279 [56, 62, 84, 82] (Action 3 Junior) Meyra Smooth 0.292 [75, 75, 97, 102] (Offense 1.879) Invacare Street 0.313 [73, 80, 112, 113] (Action 4 XLT) Meyra Street 0.308 [79, 84, 102, 103] (X2 3.351) Dupond Medical Smooth 0.293 [71, 72, 110, 11] (Alto Plus F) Dupond Medical Street 0.305 [84, 92, 112, 112] (Primeo C) Meyra Smooth 0.299 [76, 79, 108, 111] (FX One) RGK Smooth 0.295 [64, 65, 103, 103] (Interceptor) Invacare Smooth 0.298 [74, 74, 106, 103] (Top End Transformer) Bischoff & Bischoff Smooth 0.300 [107, 107, 133, 133] (Triton) Dietz GMBH Street 0.309 [84, 90, 107, 111] (Primo Amico) Invacare Street 0.305 [89, 90, 127, 128] (Rea Clematis) Invacare Street 0.304 [75, 79, 116, 117] (Action 3 Positioning) Invacare Street 0.299 [70, 71, 97, 98] (Kushall AG) RGK Smooth 0.297 [81, 81, 99, 99] (Hi Lite) Rupiani Street 0.307 [99, 99, 121, 121] (Fuze T20 PDG) Invacare Smooth 0.298 [78, 78, 101, 101] (Top end Pro Tennis) Dupond Medical Smooth 0.298 [65, 65, 104, 104] (Energy ASB 600) Vermeiren Smooth 0.282 [110, 116, 148, 159] (795 TII) Vermeiren Street 0.306 [69, 71, 108, 110] (R708 TII) Company Load Setting (Model) [set 1, set 2, set 3, set 4] Front Distribution (%) Dietz GMBH [10, 57, 8, 60] (Pro Activ Traveler) Invacare [29, 63, 22, 69] (Kuschall Champ Carb) Sunrise Medical [9, 68, 10, 58] (Quickie Easy Max) Sunrise Medical [6, 24, 12, 24] (Quickie Matchpoint) Otto Bock [12, 83, 12, 65] (Avant-Garde T) Livestand [17, 51, 17, 56] (LSA Helium) Sunrise Medical [46, 78, 29, 85] (Quickie 2HP) Sunrise Medical [39, 50, 44, 55] (Classic 160 Recline) Progeo [14, 39, 17, 42] (Exelle Vario) Rehateam [6, 77, 7, 53] (Projeo Jocker) Dupond Medical [13, 79, 11, 77] (Optimo Confort) Invacare [41, 68, 44, 66] (Rea Azalea) Otto Bock [27, 52, 26, 54] (Innov XXL) Invacare [26, 46, 29, 49] (Action 3 Junior) Meyra [14, 32, 16, 26] (Offense 1.879) Invacare [29, 83, 23, 74] (Action 4 XLT) Meyra [15, 45, 14, 54] (X2 3.351) Dupond Medical [25, 83, 24, 72] (Alto Plus F) Dupond Medical [32, 58, 31, 62] (Primeo C) Meyra [12, 34, 17, 49] (FX One) RGK [7, 69, 5, 53] (Interceptor) Invacare [12, 24, 17, 32] (Top End Transformer) Bischoff & Bischoff [38, 62, 42, 54] (Triton) Dietz GMBH [24, 62, 24, 62] (Primo Amico) Invacare [15, 83, 20, 73] (Rea Clematis) Invacare [15, 68, 8, 66] (Action 3 Positioning) Invacare [9, 84, 8, 82] (Kushall AG) RGK [22, 51, 24, 51] (Hi Lite) Rupiani [32, 57, 32, 72] (Fuze T20 PDG) Invacare [3, 23, 2, 22] (Top end Pro Tennis) Dupond Medical [9, 72, 12, 77] (Energy ASB 600) Vermeiren [29, 45, 40, 49] (795 TII) Vermeiren [20, 80, 22, 74] (R708 TII) Table 2. Properties (mean [+ or -] standard deviation) of three types of front casters and four types of rear wheels. Type No. Radius (m) FW Soft Casters 8 0.071 [+ or -] 0.011 Standard Casters 19 0.079 [+ or -] 0.019 Roller Casters 6 0.040 [+ or -] 0.005 RW Solid Tires 5 0.296 [+ or -] 0.016 Pneumatic Tires 43.5 psi 3 0.306 [+ or -] 0.009 Pneumatic Tires 65.0 psi 5 0.308 [+ or -] 0.003 Pneumatic Tires 87.0 psi 20 0.300 [+ or -] 0.005 FW = front wheels, RW = rear wheels. Table 3. Mean [+ or -] standard deviation rolling resistance parameters (RPs) of front and rear wheels according to wheel type. Type RP Hard Smooth Carpet (x [10.sup.-3] m) Front Soft Caster 0.83 [+ or -] 0.34 2.67 [+ or -] 0.52 Standard Caster 1.94 [+ or -] 0.85 3.54 [+ or -] 0.68 Roller Caster 0.36 [+ or -] 0.14 1.84 [+ or -] 0.54 p < 0.001 p < 0.001 Rear Solid Tire 4.93 [+ or -] 1.83 6.92 [+ or -] 1.60 Pneumatic Tire 1.28 [+ or -] 0.73 4.84 [+ or -] 1.23 p < 0.001 p < 0.001 Type RP p-Value (x [10.sup.-3] m) Front Soft Caster 0.006 Standard Caster < 0.001 Roller Caster 0.01 Rear Solid Tire Pneumatic Tire < 0.001
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