Department ofVeterans Affairs

Journal of Rehabilitation Research andDevelopment Vol . 36 No . 1, January 1999Pages 42-47

A steering linkage for short wheelbase vehicles : Design andevaluation in a wheelchair power base A technical note

David M . Brienza, PhD and Clifford E. Brubaker, PhDDepartment of Rehabilitation Science and Technology, University of Pittsburgh, Pittsburgh, PA 15260

Abstract—An Ackerman steering linkage for shortwheelbase, four-wheel vehicles has been developed . Thelinkage coordinates the steering angle of each wheelthrough a range of 180° with minimal misalignmentbetween wheels . Control of steering angles is accomplishedusing a single linear actuator. Control complexity is lowercompared to four-wheel systems using individuallycontrolled steering actuators for each wheel . A prototypelinkage that provides a minimum turning radius whilemaintaining maximum stability has been developed andevaluated for a power wheelchair base . The single-actuatorlinkage is well suited for this application, due to the cost-sensitive nature of wheelchair products.

Key words : spinal cord injury, steering linkage,wheelchair.

INTRODUCTION

Characteristics of Wheelchair Drive ConfigurationsThe ability of the user to maneuver a powered

wheelchair in confined spaces is closely related to thewheelchair's drive and steering configurations . Themost common drive configuration, differential rear-wheel drive, consists of fixed and driven rear wheels

This material is based upon work supported by the US Department ofEducation, National Institute on Disability and Rehabilitation Research,Rehabilitation Engineering Research Center, Washington, DC 22202.

Address all correspondence to : David Brienza, PhD, Department ofRehabilitation Science and Technology, University of Pittsburgh, Forbes Tower

Suite 5044, Pittsburgh, PA 15260 ; email : dbrienza+a,pitt.edu

with front caster wheels (1) . Direction changes aremade by individually varying the speeds of the rearwheels . In this configuration, the point about whichthe wheelchair pivots lies on a line perpendicular to,and running through, the center of the rear wheels.The minimum turning radius is achieved when thepivot point is located at the midpoint between the rearwheels . The minimum space required to turn thewheelchair is then determined by the maximumdistance from that point to any other point on thewheelchair, usually the front corner of the base or theuser's feet hanging off the front of the chair. A similaranalysis applies to drive configurations with fixed anddifferentially driven front wheels and rear casterwheels . The fixed rear wheel and caster front wheeldrive configuration is illustrated in Figure 1.

To minimize the turning radius for the fixed-wheel, differential-drive configuration, the fixed-drive wheels must be located as close as possible tothe geometric center of the chair. For fixed front-wheel-drive chairs, the drive wheels are movedrearward, and for fixed rear-wheel-drive chairs, therear wheels are moved forward . Several commerciallyavailable power chairs have achieved reduced turningradii using this approach : the Quickie P200 series(Sunrise, Longmont, CO), a fixed rear-wheel-drivemodel, and two front-wheel-drive chairs, the Jazzy®series (Pride Health Care Inc., Exter, PA) and theAction Ranger II Storm series (Invacare Corp ., Elyria,OH) . Another benefit of locating the drive wheelsclose to the geometric center of the chair is that alarger portion of the total weight of the wheelchair isborne by the drive wheels and less by the caster

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RRIENZA and BRUBAKER : Wheelchair 4-wheel Steering Linkage

Figure 1.Fixed rear-wheel differential drive configuration.

wheels . The greater the weight borne by the casterwheels, the more difficult it is to change directionswhen caster wheels must reverse directions and rotatethrough 180° . The approach, however, causes thedesigner to take extraordinary steps to providestability. Typically, stability is achieved bycounterbalancing the user's mass over and in front ofthe main drive wheels with the mass of the batteriesbehind the main drive wheels . It may be necessary toprovide caster or sprung wheels in the rear of the chairto avoid tipping backward while accelerating forward.The addition of these extra wheels, if small, may alsocompromise the chair's ability to climb low obstacles.

An alternate approach to minimizing the turningradius is to steer all four wheels ; this avoids theproblems associated with caster wheels, yet retainsminimum turning radius and maximizes stability.Added benefits of four-wheel steering are the trackingof front and rear wheels along the same path andenhanced obstacle climbing capability.

The challenge in designing a mechanical four-wheel steering mechanism is to design a device withthe ability to turn each wheel through 180° whileminimizing Ackerman errors (misalignment of the

Figure 2 . Wheel alignment for four-wheel steering about a singlepivot point.

wheels) . Ackerman steering linkages, such as thoseused in automobiles, owe their simple design to therelatively small turning angles required by that typeof vehicle . For highly maneuverable wheelchairs, therange of steering angle is much greater, and the wheelsmust maintain proper alignment over that entire rangeto avoid undesirable scrubbing when the wheelchairmoves . Scrubbing results in excessive tire wear,wrinkling of carpets, and/or undesirable tire noise.

The wheels are properly aligned whenever linesprojected from the axis of each intersect at a singlepoint . In four-wheel steering configured for minimumturning radius, this point lies on a line between thefront and rear wheels running perpendicular to thefore-aft direction of the base, as illustrated in Figure2. In two-wheel steering, the perpendicular bisectorsof the front steered wheels intersect at a point alongthe line through the centers of the fixed rear wheels.

Another significant advantage of four-wheelsteering over two-wheel differentially driven and two-wheel steering is that in the four-wheel configuration,the rear wheels track the front wheels . This is not thecase when either the front or rear wheels are fixed.What this means to the user is that when the front ofthe wheelchair clears a corner, the rear will also clear,if course direction is not changed. The problem isanalogous to that facing automobile drivers when theyattempt to enter a parking space head in between twoother cars, or the one tractor trailer drivers havemaking turns at right angle intersections . In bothsituations, the drivers are required to make coursecorrections during the maneuver to avoid collisionswith the obstacles on the inside of the turn . In otherwords, course corrections must be made to avoidclipping the corner.

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Journal of Rehabilitation Research and Development Vol . 36 No . 1 1999

A disadvantage of steering all four wheels is therestriction placed on the power delivery to the drivewheels . Two possible drive configurations are eitherto mount the motors directly onto the wheels andconfigure the power base to allow for rotation of theentire motor and wheel assembly, or to deliver powerto each of the steered wheels through a right-angledrive assembly along the wheel 's turning axis . Ineither case, power delivery is more cumbersome thanto a fixed wheel . In our protoype, we have choosenthe first option, direct motor mounting.

METHODS

Design AlternativesThe problems associated with designing a

complicated mechanical linkage to achieve four wheelsteering can be circumvented using individualcomputer-controlled steering actuators on each wheel.However, the cost of such a system is likely to behigher than that of a mechanical system, due to theneed for three additional actuators and threeadditional channels of control . The specific designobjectives for this project were to develop andevaluate a four-wheel steering mechanism, driven bya single actuator and achieving minimal misalignmentover the entire range of steering angles . Although the

prototype system implements four-wheel steering,two-wheel steering could be achieved with only aslight modification of the design methods.

A photograph showing a section of the prototypesteering linkage is shown in Figure 3 . The completelinkage consists of two sliding members (A), four camfollower slots (B) cut into a flat plate (C), and twolinks (D) for each wheel.

The initial design was achieved using graphicalmethods in a CAD program (CadKey, Inc ., Windsor,CT) . Subsequent analysis of the graphical methodsresulted in the formation of a general mathematicaldescription that allowed for the cam follower slot tobe determined given arbitrary link lengths and vehicledimensions . Using the model, two prototype linkageswere developed . A full-size physical model of just oneof the four sections of the mechanism (i .e ., the linkagesection necessary to steer one wheel) was constructedto investigate the feasibility of manufacturing thedevice. Based on positive results from that exercise,a full-scale working prototype integrated into awheelchair power base was designed and constructedso that evaluation of the concept could be completedunder actual operating conditions.

Proper alignment of the wheels is maintained toavoid undesirable scrubbing of the wheels as thevehicle turns . To maintain alignment, the steeringangle on each wheel must be tangent to concentriccircles . In the case of the four-wheel steered vehicle,the inside wheels (i .e ., the wheels on the right duringa right turn and those on the left during a left turn)will be traveling along the path described by a circlewith radius r t (circle 1 in Figure 4) while the outsidewheels travel along a circle with the longer radius r,(circle 2 in Figure 4) . The turning rate of the vehicleincreases as those radii shorten and the center pointof the circles moves toward the center of the vehiclealong its midline . Maximum turning rate is achievedwhen the centers of the circles coincide with the centerof the vehicle. For the vehicle to have full turningrange, that is, have the ability to rotate about its centerin either direction, each wheel must be free to rotatethrough 180° . Proper alignment is maintainedthroughout the 180° range if

qL = - ArcTan2 (Cot (qs [1]vl .r .baseb

ien ., J

Figure 3.Section of steering linkage shows (A) sliding member, (B) camfollower slot, (C) flat plate, (D) link members .

where Q and Qs are the angles of the wheels on theinside and outside wheels, respectively.

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BRIENZA and BRUBAKER : Wheelchair 4-wheel Steering Linkage

Figure 4.Wheel alignment constraints for four-wheel steering.

The steering linkage provides proper alignmentof the wheels through the shape of the cam path.Furthermore, the cam path is constrained to besymmetric about its midline, so that there is a linearrelationship between the translation along the path in

Figure 5.A series of linkage positions showing the cor respondence betweenthe endpoints of each member in the steering linkage .

the fore and aft direction and the turning motion ofthe inside and outside wheels of the vehicle.Symmetry of the cam path allows for the use of asingle, linear motion steering actuator to drive thesteering motion of all four wheels.

The shape and location of the cam path isdetermined by the wheelbase and track length of thevehicle and the specification of the lengths ofmembers linking the cams to the wheel spindles . It isalso necessary to specify the maximum deviation inangle between the two links from 90° . An arbitrarypoint on the cam path (x,y) is determined by solvingthe equation

for y in terms of ay, a y , bX , and b y

where

r is the length of the link between the camand crank arm.

)( midpointis determined by the specification

of the constraint on the angle between thelinks at the extreme positions . Themethod for computing xmdpo t follows.(a ,a y) and (b x,b y) are coordinates ofpoints on the circular path of the end ofthe crank arm corresponding to the linkend positions of the inside and outsidewheels, respectively. xa is the xcoordinate of the point on the cam pathcorresponding to the location of the endof the crank arm (a . ,ay).xb is the x coordinate of the point on thecam path corresponding to the locationof the end of the crank arm (b a,b ).y is the y coordinate of the point on thecam path and is the same for the a and bpoints due to the constraint on thegeometry requiring linear motion of theactuator.The reference coordinate system is centered

at the wheel spindle with the y axis parallel to theside of the vehicle and pointed toward the front

axis

Y

x „ [2]— x n

2

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Journal of Rehabilitation Research and Development Vol . 36 No . 1 1999

of the vehicle.To generate a cam path given the wheelbase,

B, the track length, L, the crank arm length, r,and the crank arm to cam link length, r, wegenerated a series of points (a ,a) and (b ,b) onthe circular path described by the path of the crankarm where

ax = r Sin (ci s + f)

= re Cos(gs + f)

= r Sin Gi l + f)

= r Cos(q . + f)

and

=-ArcTan2(Cot(q , - 2B )) ]

f is the angular offset of the crank arm whenthe wheel is pointed in the neutral position.

The use the solution for y from Equation 2 andcompute the points on the cam path, (x a ,y) .,corresponding to the points (ax ,a y), and the points(x b ,y)., corresponding to the points (b ob) , (see Figure5). This solution can also be used to generate a linkagethat steers the two front wheels and assumes that therear wheels are fixed. For this condition, substitute2B for B in Equation 4, and everything else remainsthe same.

RESULTS

Evaluation of Static ForcesThe losses in the linkage were estimated using a

static analysis of torques and forces . The force appliedto the sliding member of the linkage was determinedas a function of the torque on each wheel for operatingpoints throughout the full range of motion . The resultfor the linkage dimensions of a 7 .62 cm lower

member, 15 .24 cm upper member, 50 .8 cm wheelbase

and 45.72 cm track is shown in Figure 6e The curve

in the figure estimates the sum of linear force requiredon the sliding member of the linkage per unit torqueon the wheels (the sum required to turn all fourwheels) as a function of the angle of the inside wheelrelative to the straight ahead null position. As the nearwheel moves through 45°, the outside wheel movesthrough 135° to avoid misalignment . At the extremepositions, the perpendicular bisectors of each wheel

7,62 ern crank15.24 crn link45 .72 cm track50.3 cm wheelbase

20

30

ale of outside front wheel (dog.)

Figure 6.Relationship between linear actuator force and steering torgr

intersect one another at the geometrical center of thewheelchair base . This analysis demonstrates that thereis not any significant loss of mechanical advantagebetween actuator force and resulting torque on thewheels.

DISCUSSION

Control IssuesThe use of four-wheel steering in wheelchairs

introduces a dilemma for the control of that vehicle.Optimum performance is likely attained when thewheels can be left at arbitrary, but known, steeringangles while the chair is idle . Under these conditionsthe driver knows in which direction the chair willinitially go and there is no delay in initiating a move.However, making the direction of the wheels knownto the driver while the chair is at rest requires thedriver to either visually inspect the wheels or obtainthe direction information through some otherfeedback mechanism . Three options come to mind:1) a visual display on the controller panel ; 2) tactilefeedback through the control stick using a rotationabout either the unused vertical axis or a rotat1O11abo~~t the st.ee.xI.r axisx and 35 m £aadbm k at all.

Although no solution is ideal, a rotation of the stick

seems more desirable from the user's PCTSPCctiVC

because it will not require reading a display, therebynot diverting his or her attention away from theenvironment . The rotation option is likely morecomplex and expensive to implement . The thirdoption, no feedback at all, will require the driver tosense the wheel direction by sensing the direction oftravel once motion is initiated ; this option is likely to

z Z 7 .62c102

.54

[3]

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BRIENZA and BRUBAKER : Wheelchair 4-wheel Steering Linkage

be problematic in confined spaces.The other alternative for control of the vehicle

is to program the controller to self-center the wheelseach time the chair stops . This solution is also lessthan ideal . In this configuration, there will be a delaybetween the time when the user steers the wheels andwhen the chair is able to travel in the desired direction.If there is no direction feedback for the wheels, theuser is required to perform a visual inspection of thewheel direction or sense the direction after initiatinga move by observing the direction of travel.

Drive Wheel OptionsIn the prototype used to evaluate the steering

linkage, all four wheels are powered . The range ofoptions available are to power both rear wheels, powerboth front wheels, and power one rear and one frontwheel on opposite sides of the vehicle . Powering allwheels gives maximum performance, and, since eachwheel on the same side of the vehicle travels at thesame velocity, four completely independent channelsof control are not necessary. If the drive wheels areoperated open loop, only two channels are required.Either of the other two options requires twoindependent control channels . The advantage ofpowering one front and one rear wheel is to retain

the ability of the vehicle to climb over low obstacleswhile traveling either forward or backward, whileminimizing the control requirements and the cost ofmotor drives.

CONCLUSIONS

An innovative feature of this steering linkagedesign is its ability to drive all four (or two) wheelsusing a single steering actuator. Its successfulimplementation will allow for the development of afour-wheel, steered power base with maximummaneuverability, uncompromised static stability,front- and rear-wheel tracking, and optimum obstacleclimbing capability.

REFERENCES

1 . Brubaker CE, editor. Wheelchair IV: report of a conferenceon the state-of-the-art of powered wheelchair mobility; 1988Dec 7-9 ; Charlottesville, VA . Washington, DC: RESNAPress ; 1989.

Submitted for publication December 31, 1997 . Accepted inrevised form March 4, 1998 .