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Journal of Rehabilitation Researchand Development Vol . 26 No . 1

Pages 25—32

Racing wheelchair crown compensation

Rory A. Cooper, MEngInstitute of Environmental Stress Human Performance Lab, and the Control Systems Lab, Department ofElectrical and Computer Engineering, University of California, Santa Barbara, CA 93106

Abstract—This paper is concerned with the directionalstability of racing wheelchairs on crown roads . Threetypes of crown compensators are described and evaluated:the push-pull, the push-push, and the pull-pull . It wasfound that the push-push and the push-pull types ofcompensators have the most desirable characteristics, andwere, in general, safer than the pull-pull type . Inaddition, the equations necessary to specify the minimumspring force required to compensate for the downhillturning moment, were derived and compared to theactual preset forces for the various compensators pres-ently in use. It was found that the force required tomaintain directional stability was less than that to deflectthe crown compensator . This was due to the preference ofathletes for additional stiffness needed for disturbancerejection, and to help compensate for any asymmetry intheir stroke kinematics . It was also more cost-effectivefor the manufacturer to build stiffer-than-necessarycrown compensators so that a range of individual andracing wheelchair combinations could use the same crowncompensator.

Key words: center of gravity, crown compensators,directional instability, racing wheelchairs.

INTRODUCTION

Wheelchair racing, the sport of propelling awheelchair with push-rings over a predesignated

Address all correspondence to : Rory A . Cooper, M .Eng ., Departmentof Electrical and Computer Engineering, University of California, SantaBarbara, CA 93106 .

course in a minimum amount of time, is animportant aspect of the rehabilitation of manyspinal cord injured patients (6) . The increasedpopularity of this sport has prompted athletes andmanufacturers to develop improvements in wheel-chairs . These wheelchairs (Figure 1) have severaldistinguishing features, such as tubular tires, light-weight rims, precision hubs, larger wheels, andsmaller push-rings.

Although racing wheelchairs have some of thesame control problems as everyday wheelchairs,these problems are amplified due to the speeds (inexcess of 40 mph on down grades) attainable by elitewheelchair athletes. Several factors affect racingwheelchair propulsion : weight, materials, design andphysical dimensions of the racing wheelchair ; levelof fitness, strength, and ability of the athlete;compatibility of the racing wheelchair and theathlete, along with external factors such as thetexture, hardness, and crown of the road . Signifi-cant efforts have been made by a number ofinvestigators to classify and quantify these relation-ships (2,3,4,7,8) . There is still a substantial amountof investigation required, especially in the analysisof wheelchair racing . The interaction of manyfactors involved in wheelchair racing performancemakes it difficult to change a single variable withoutaffecting other variables.

One problem that is of great significance is thedownhill turning moment induced by road crown . Inwheelchair racing, differential pushing or inducing adrag on the rear wheel are not acceptable, because

25

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Journal of Rehabilitation Research and Development Vol . 26 No. 1 Winter 1989

PUSH-RING

SEAT UPHOLSTERY

Figure 1.Racing wheelchair.

of the increased energy requirements or the de- FUNCTIONcreased speed (1).

PROBLEM DEFINITION

The purpose of this investigation was to analyzethe factors that have an effect on the directionalstability of racing wheelchairs on crowned roads(Figure 2), and to develop the relationships neces-sary for satisfactorily controlling the direction.

METHODS

Racing wheelchairs do not require the maneu-verability of everyday wheelchairs, because theirpurpose is to proceed in a forward direction asrapidly as possible under human power, usingpush-rings for propulsion. A spring-loaded deviceattached to a front wheel assembly can be used tocompensate for directional instability.

Three experienced spinal cord injured wheel-chair racers, using racing wheelchairs modified toaccept three types of crown compensator mecha-nisms, evaluated the properties of each crowncompensator type . They evaluated each compensa-tor mechanism after training with each one for aminimum of 14 days, over various types of courseswith differing degrees of road crown . Each individ-ual was then interviewed .

The crown compensator functions by exerting aforce on the fork or trailing arm of the front wheelopposing the force due to road crown . The threetypes tested are described below.

Pull-pull compensatorThe springs of the pull-pull compensator are in

tension with equal, but opposite, forces when thereis no displacement of the tie-rod assembly . Itfunctions by exerting a force on the tie-rod armsopposite to the displacement . (The force is due tothe extension of one of the springs .) The compensa-tor lever is attached to the center of the frontcrossmember by a hinge (which has a high degree ofresistance) ; this lever is used to set the desireddirection, i .e ., the zero position of the springs . Theorientation of the pull-pull compensator is illus-trated in Figure 3a and Figure 3b.

Push-push compensatorThe casing of the push-push compensator is

fixed to one of the main frame members, while theshaft is affixed to the fork or trailing arm . Thespring encased in the compensator mechanism iscompressed when the front wheels are moved fromthe zero position, thus generating a force to returnthe wheels . The spring may be preloaded to preventmovement due to small forces . The orientation of

27

COOPER : Wheelchair Crown Compensation

Figure 2.Racing wheelchair on crowned road.

the push-push compensator is depicted in Figure 4a,and in greater detail in Figure 4b.

Push-pull compensatorThe orientation of the push-pull compensator is

shown in Figure 5a, and the mechanism is shown inFigure 5b . It is affixed to a lever at one end, and tothe fork or trailing arm at the other end . (The leveris resistive to movement, so that there is no changein position of the lever due to forces acting on thefront wheels .) When a force acting upon the frontwheels causes a displacement, one of the springs isin compression while the other is in tension, thusgenerating a force in opposition to the displacement .

The springs can be preloaded to prevent movementfor small forces at the wheels.

As can be seen in Figure 3a, Figure 4a, andFigure 5a, the steering lever(s) are rigidly attached tothe trailing arm(s) of the front wheel(s) . Thisrequires the individual to overcome the force of thecrown compensator when making voluntary direc-tional changes.

The forces required for initial compression andfor maximal compression for typical crown compen-sator mechanisms were measured using an Arborpress equipped with a load cell . (Table 1).

Table 1.Crown compensator mechanism spring forces.

SPRING FORCE

minimum maximum

Ray Stewart Self-Centering 20 lbs . 40 lbs.Compensator (Push-Push) 89 N 178 N

Bob Hall Crown Compensator (light) 30 lbs . 50 lbs.(Push-Pull) 133 N 222 N

(heavy) 35 lbs .

55 lbs.156 N

245 N

Typical Pull-Pull Spring Compensator

5 lbs .

20 lbs.22 N

89 N

Figure 3a.View of the front end of a racingwheelchair with a pull-pull compensa-tor . (a. front wheel, b . tie-rod, c.compensator lever, d . steering lever,e . compensator, f . tie-rod arm [stand-off]) .

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Journal of Rehabilitation Research and Development Vol . 26 No . 1 Winter 1989

STATIC ANALYSIS

A theoretical static analysis was done to de-velop a method for therapists and manufacturers todetermine the proper crown compensator setting foreach athlete.

The slope created by road crown for waterdrainage generates a downhill turning moment . Thisresults from the mass distribution of a racingwheelchair and athlete relative to the wheel orienta-tion (Figure 6a).

The downhill turning moment about the rearwheel is a consequence of the center of gravity beinglocated in front of the rear axles . The force whichcreates the turning moment is depicted in Figure 6b.

M is the mass of the athlete and racingwheelchair, g is the acceleration due to gravity(9 .81m/s2), 0 is the angle created by the roadcrown. The forces required for crown compensationby the use of a spring compensator mechanismattached to the front wheel assembly are depicted inFigure 6c.

Fspring is the force required to compensate forthe turning moment of the front wheels about thefront spindles ; Freaction is the force on the frontwheels acting against the road surface ; L is thedistance of the center of gravity of the athlete-racingwheelchair system to the rear axle intersection of the

Figure 4a.View of the front end of a racingwheelchair with a push-pull compen-sator . (a. front wheel, b. tie-rod, d.steering lever, e . compensator, f . tie-rod arm [stand off]) .

STIFFCOMPENSATOR

TENSION

LEVERSPRINGS

I

Figure 3b.Pull-pull crown compensator mechanism.

center line; 1 is the distance of the crown compensa-tor mechanism point of attachment to the frontwheel spindle ; and T is the trail of the front wheel.

To determine the required spring tension for thecrown compensator, the moments about the frontwheel spindle must be summed .

29

COOPER : Wheelchair Crown Compensation

Freaction (T) = Fspring (1)The moments about the downhill rear wheel,

the pivot point, must also be summed.

Freaction (WHEELBASE) = MgLsinO

Now solving for Fspring

Fspring (1/T) = FreactionFspring (1/T) WHEELBASE = MgLsinOFspring = MgLTsinO / 1 (WHEELBASE)

Thus, the crown compensator spring force mustbe preset to a force equal to or greater than thecalculated value for static directional stability.

A method for determining the location of thecenter gravity for the athlete and racing wheelchairis depicted in Figure 7 (5).

The center of gravity can be calculated by usingthe linear relationship between the position of thecenter of gravity as follows:

when y = z then F = Wthus F = W (y / z) and y = x + Land y = (z / W) Ftherefore F (z / W) = x + Lso L=F(z/W)–x

Where F is the value of the load cell or scaleforce, z is the distance from the center of thefulcrum to the point where the platform touches theload cell or scale; W is the combined weight of theathlete and racing wheelchair ; and, x is the distancefrom the point where the rear wheels touch theplatform to the center of the fulcrum.

An athlete and racing wheelchair weighing622.7 N (140 pounds) were tested to determine theproper crown compensator spring force for an angleof 10 degrees (the maximum angle one might expect

NUT

BOLTCASING

SHAFTSPACER

SPACER

Figure 4b.Push-push crown compensator mechanism .

to encounter), using the equations derived in thestatic analysis . The racing wheelchair had a trail of7 .62 cm (3 inches), the crown compensator wasattached 5 .08 cm (2 inches) from the spindle, andthe wheelbase was 68 .58 cm (27 inches).

The distance of the center of gravity from therear axles must first be found . In this case theplatform length (z) was 2 m, the distance from thefulcrum to the rear axles (x) was 30 cm, and F wasmeasured to be 135 N (30 .4 pounds).

Thus:

L = 135 N (200 cm / 622 .7 N) – 30 cm =13 .36 cm

The distance of the center of gravity from therear axles is 13 .36 cm . The compensator spring forcerequired (Fspring) is as follows:

F spring = (622 .7 N) (sin(10)) (13 .36 cm) (7 .62 cm) = 31 .6 N(5 .08 cm) (68 .58 cm)

Thus, the force for initial movement for thecrown compensator must be at least as great as 31 .6N (7 .1 pounds).

RESULTS

The three athletes made the following observa-tions about the characteristics of the three types ofcrown compensator mechanisms:

The pull-pull crown compensator was deter-mined to be the least desirable, as it required thegreatest amount of adjusting for changes in the roadcrown, and it had the most difficulty tracking . Thisis probably due to the negating effect of theopposing tension of each spring, which translates tosmall reaction forces for small perturbations. Inaddition to these problems, the pull-pull crowncompensator is, in the event of failure, not self-centering . When a spring breaks, or otherwisebecomes detached, the front wheels rapidly turn tothe side, which can cause injuries.

The push-push crown compensator and thepush-pull crown compensator have nearly equalhandling characteristics . Their designs allow thesprings to be preloaded to prevent most movementdue to directional instability or external distur-bances . Both of these crown compensators areself-centering, thus avoiding the problem of abruptdirectional changes because of crown compensatorfailure. No force is exerted on the wheel assembly in

n

.~ %um 311w.NIL

CAP

SPRING

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Journal of Rehabilitation Research and Development Vol . 26 No. 1 Winter 1989

Figure 5a.View of the front end of a racingwheelchair with a push-pull compen-sator . (a . front wheel, b. tie-rod, c.compensator lever, d . steering lever,e . compensator, f. tie-rod arm [standoff]) .

/WALL

TENSION

PLUNGER

Figure 5b.Push-pull crown compensator mechanism.

the absence of road crown reducing the stress on thefront wheel assemblies, making alignment of thefront wheels simpler. The only undesirable charac-teristic noted seems to be some internal binding thatmakes accurate control less than optimal whilevoluntarily turning.

The crown compensator force is limited by theability of the athlete to overpower the crowncompensator when voluntarily making directionalchanges. This is of special concern to quadriplegicathletes because of their reduced arm strength anddexterity .

DISCUSSION

The problem of the downhill turning momenthas been investigated, and three methods of control-ling the racing wheelchair direction were evaluated.Crown compensation mechanisms appear to satis-factorily solve most of the directional instabilityproblems induced by road crown and small distur-bances . The pull-pull crown compensator mecha-nism, though widely used for racing, was the leastdesirable of the mechanisms evaluated, and forreasons of safety, not to be recommended . Thepush-pull crown compensator mechanism wouldinitially seem to be the best for road racing andtrack competition ; however, the push-push crowncompensator works equally as well on the road.

A static analysis of the road crown directionalstability problem was performed, and equationswere developed to help therapists and manufacturersselect the proper compensator for each athlete . Thebest results were obtained when the center of gravitymeasurements were made with the athlete's chestresting on his/her knees, and with his/her armshanging to the side.

Admittedly, the sample size for this study wassmall, and the results based upon their evaluationsmay thus be biased. Small sample size is a common

CASING

COMPRESSIONSPRING

/

PLUNGER

[NNAl

/SPRING

31

COOPER : Wheelchair Crown Compensation

Figure 6a.Downhill turning moment .

Figure 6b.Distribution of forces.

Figure 6c.Compensation analysis.

problem when evaluating rehabilitation research;however, by using experienced spinal cord injuredwheelchair racing athletes (who are very familiarwith the performance of their racing wheelchairs),the validity of these results should be greater thanfor a comparable random sample.

The results of the static analysis indicate thatthe forces required to compensate for road crown

are 2 to 4 times less than the initial compressionforce for the sample push-push and push-pullcompensator mechanisms . These crown compensa-tors are constructed to function satisfactorily for anumber of individuals of various weights . In addi-tion, wheelchair athletes prefer the added stiffnessthat results, and the greater force helps to compen-sate for any asymmetry in the athlete's stroke (dueto dominant side or on the occasion of missing astroke with one arm).

Special care must be taken to insure that thesteering levers are properly located and are ofsufficient length to give the athlete adequate controlduring voluntary directional changes, especially ondown grades.

CONCLUSION

The problem of directional instability of racingwheelchairs can adequately be solved by using thecrown compensator mechanisms discussed in thispaper. However, several problems deserve furtherinvestigation, in order that more disabled people cansafely enjoy the benefits of the physical exercisemade possible through wheelchair racing . One areaof particular importance seems to be that ofdetermining the optimal position of the body withrespect to the racing wheelchair.

mg sin e

/TIE-ROD LINKAGE

Fspring

T Freaction01 ++

WHEELBASE

i

PIVOTPOINT

1+

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Journal of Rehabilitation Research and Development Vol . 26 No. 1 Winter 1989

L —)-

Z

Figure 7.Center of gravity measurement.

REFERENCES

1. Brubaker CE, McLauren CA, McClay IS : Effects of sideslope on wheelchair performance . J Rehabil Res Dev23(2) :55-57, 1986.

2. Glaser RM, Collins SR : Validity of power output estima-tion for wheelchair locomotion . Am J Phys Med60(4) :180-189, 1981.

3. Kauzlarich JJ, Bruning T, Thacker JG : Wheelchair castershimmy and turning resistance . J Rehabil Res Dev21(2) :15-29, 1984.

4. Kauzlarich JJ, Thacker JG : A theory of wheelchairwheelie performance . J Rehabil Res Dev 24(2) :67-80,1987.

5. Loane TD, Kirby RL : Static rear stability of conventional

lightweight variable-axle-position wheelchairs . Arch PhysMed Rehabil 66(3) :174-176, 1985.

6. Madorsky JGB, Madorsky A : Wheelchair racing : Animportant modality in acute rehabilitation after paraple-gia . Arch Phys Med Rehabil 64(4) :186-187, 1983.

7. Pitetti KH, Snell PG, Stray-Gundersen J : Maximalresponse of wheelchair-confined subjects to four types ofarm exercise . Arch Phys Med Rehabil 68(1) :10-13, 1987.

8. York S, Kimura I : An analysis of basic constructionvariables of racing wheelchairs used in the 1984 Interna-tional Games for the Disabled . Res Q Exerc Sport58 :16-20, 1987 .