 Manual wheelchair
 Wheelchair adjustments
 Wheelchair maneuverability
 Wheelchair stability
In the late 1970s, the introduction of new materials and, more importantly, new ideas has changed wheelchair users' potential for wheelchair mobility. The new generation of wheelchairs can be adjusted (Fig. 1) to provide a better fit to the user (legrest length, backrest height, armrest height, and width between the rear wheels), better posture (seat angle), and modifiable propulsion characteristics (axle position relative to user and rear wheel camber). The health care professional's challenge is to “optimize” wheelchair technology for each user. Decisions must be made about adjustments and configurations, and these decisions will determine how much effort will be required of the user and how stable the wheelchair will be. Simple decision criteria for wheelchair configuration are not found in the literature. The decisions are complex because the interaction of user, wheelchair, and environmental characteristics must be considered. The purposes of this article are to describe wheelchair characteristics and to discuss how adjustments can be made to manage these characteristics.
Factors in Manual Wheelchair Maneuverability
Brubaker^{1,2} identified biomechanical factors that affect wheelchair performance in order to illustrate the advantages of adjustable manual wheelchairs compared with “standard” wheelchairs. In the opinion of most experts, adjustable manual chairs have less rearward stability than standard chairs and, therefore, are more easily tipped backward. This increased potential to tip backward can be a disadvantage, although Brubaker argued that “standard” wheelchairs are more stable than they need to be for most users and, consequently, require more effort to propel. The adjustable wheelchair requires less effort to propel and turn than a standard wheelchair, which is its performance advantage. To propel a manual wheelchair, rolling resistance and the side slope effect need to be overcome.^{1} Rolling resistance is the force that must be overcome by the user to keep the wheelchair moving at a constant velocity over a level surface.^{3} The side slope effect is the tendency of a wheelchair to turn downhill on a side slope.^{4} Effort is required from wheelchair users, therefore, to maintain a straight path when the surface is not level.^{4}
Lemaire et al^{3} described a way to estimate rolling resistance for manual wheelchairs. The friction coefficients of the rear wheels and casters, the weight of the system (wheelchair and user), the surface over which the wheelchair is being propelled, and the distribution of weight between the rear wheels and casters determine the rolling resistance. Of these factors, only one is designed to be adjusted: the distribution of weight to the rear wheels. A wheel's rolling resistance is inversely proportional to its radius,^{5} so the rolling resistance coefficient is smaller for the rear wheels than the casters and total rolling resistance is reduced as a larger proportion of the weight is distributed to the rear wheels.^{1,3} Figure 2 illustrates the relationships that determine the effects of adjustments on rolling resistance. Dimensions that can influence the resistance are the length of the wheelchair (l_{wb}), the horizontal distance of the center of mass (COM) of the wheelchair and user forward of the rear axles (x), and the horizontal distance from the COM to the caster axles (l_{wb}−x). Equation 1 in Figure 2 can be used to calculate the vertical force on the casters (f_{c}), and equation 2 in Figure 2 can be used to calculate the vertical force on the rear wheels (f_{r}). An estimate of rolling resistance (f_{rr}) can be calculated using equation 3 in Figure 2 and is the vertical force multiplied by the wheels' coefficients of rolling friction (μ_{c} and μ_{r}). Equation 4 (Fig. 2) shows that the proportion of weight on the rear wheels (r_{wd}) will be increased as the distance from the COM to the casters (l_{wb}−x) is increased or as x is decreased. These changes will also decrease rolling resistance because rolling resistance is inversely related to the proportion of weight on the rear wheels.
Most outdoor surfaces are sloped for drainage or as part of the terrain, so the user must do more than overcome rolling resistance to propel the wheelchair. The side slope effect or downturning tendency (Fig. 3) is produced by a turning moment (μ_{dt}) that is a function of the angle of the side slope (θ_{s}), the weight of the system (mg), and the horizontal distance of COM to the rear axles (x).^{4} Equation 5 (Fig. 3) shows that the distance x is also the downturning moment arm, which can be decreased by moving the COM and rear axles closer together. Going one step further, the braking force (f_{b}) to the uphill pushrim necessary to keep the wheelchair traveling in a straight line is the turning moment divided by the distance (d) between the rearwheel surface contacts (equation 6). As the moment and braking force required on the uphill pushrim increase, the user must push the downhill rim to overcome rolling resistance and move forward.
New adjustable manual wheelchairs are usually assembled for delivery with the seat at an angle similar to a standard wheelchair and with the rear axles in the position that provides the most rear stability. In this configuration, adjustable manual wheelchairs are more maneuverable than standard wheelchairs for several reasons. Adjustment from the original wheelchair configuration may not be considered necessary when the adjustable manual wheelchair, in its most stable and least maneuverable settings, has better performance than the wheelchair being replaced.
Adjustable wheelchairs have rear wheels attached to the frame forward of the rear frame uprights, but standard wheelchairs have the rear wheels attached to the rear frame uprights. This design difference directly decreases the distance of the COM forward of the rear axles. The smaller distance x and larger rearwheel weight distribution will result in decreased rolling resistance and downturning tendency. The rear wheels are usually attached to the frame with 3 to 4 degrees of camber. Camber is a tilt of the top of the wheel toward the frame so that the distance between the wheels at the ground is wider (Fig. 1). The increased width of the rearwheel contacts increases the distance (d) and the space required for mobility. The combination of widened wheel contacts and a shortened turning resistance moment arm (x) contribute to the decreased required braking force on a side slope and the increased turning response felt on level surfaces. Weight distribution^{6} and the distance of the COM forward of the rear axle^{3,7} can be measured, but no guidance is readily available on how to use these measurements to decide whether further adjustments are indicated. The real question remains: Because rear stability decreases as maneuverability improves, how much maneuverability should a wheelchair have for a particular user?
Factors in Manual Wheelchair Stability
The rear stability of a wheelchair is generally decreased when adjustments are made that improve the ability to propel the wheelchair. Static rear stability of a manual wheelchair can be measured by tilting the occupied wheelchair rearward to find the critical angle at which it will fall backward.^{8–11} Stability data have been collected from manual wheelchairs in a variety of configurations and conditions.^{12–17} Kirby and Dupuis^{11} measured the critical angle of rear stability for 95 wheelchair users and found that the mean critical angle was 12.3 degrees (95% confidence interval=6.4°, 18.2°) with the rear wheels locked and 20.2 degrees (95% confidence interval=10.6°, 29.8°) with the rear wheels unlocked. Because of the varying needs and characteristics of their subjects, the authors did not recommend using the data for clinical decision making.
In static conditions, the stability of the wheelchair will be determined by the position of the COM of the system in relation to an axis of rotation.^{16} Stability can be evaluated with the rear wheels unlocked so that the rotation is occurring at the rear axles or with the rear wheels locked and rotation occurring between the rear wheels and the ground. The wheelchair depicted in Figure 4 will not fall backward at the rear axle with the rear wheels unlocked until the wheelchair is rotated rearward more than the critical angle θ_{a}.^{16} This is the angle at which the wheelchair will be balanced in a wheelie, assuming the user does not change posture. The “bedside test”^{10} was developed specifically to measure that angle and is meant to be a clinical tool. In this test, a goniometer is used to measure the angle through which an occupied wheelchair is tilted rearward to balance on the rear wheels. When the rear wheels are not free to roll, such as when the user is on an incline and holds the wheels so the chair does not roll downhill, the critical angle will be θ_{g},^{9} which is always smaller than θ_{a}. The critical angle of stability is determined by the height of the COM above the axis of rotation and the horizontal distance of the COM from the axis of rotation.
Equations 7 and 8 (Fig. 4) show that rear stability will increase as x in the numerator increases or as y in the denominator decreases. Adjustments that only change x will directly change stability and maneuverability. Adjustments that only change y will affect stability but not maneuverability. Although we can understand the implications of a particular adjustment to a wheelchair in terms of increasing or decreasing rear stability as summarized in the Table, it is more difficult to anticipate the magnitude of the effect on stability or maneuverability. Ultimately, the critical angle of stability must be large enough for the wheelchair to be stable in the user's environment. Stability beyond that angle can unnecessarily diminish maneuverability.
Effects of Adjustments to Common Designs
The reported relationships can be used to predict the effects of adjustments to a manual wheelchair on stability and maneuverability. To examine the effects of adjustments to manual wheelchairs predicted by use of the equations, I will use a simulated wheelchair and user. The combined mass of the user and wheelchair is 80 kg (176 lb). The rearwheel diameter is 61 cm (24 in). The caster diameter is 12.6 cm (5 in). The wheelchair initially has a 40cm wheelbase. The center of mass is 10 cm forward of the rear axles. The rear wheels are cambered 3 degrees, and the width of the rear wheelbase is 56 cm. The only characteristic that cannot be easily measured in the clinic is that the COM is 33.7 cm higher than the rear axles. From these values, estimates of wheelchair performance and stability can be made (Fig. 5). Seventyfive percent of the weight of the system (r_{wd}) is on the rear wheels. Using the coefficients of rolling resistance for the casters (0.041) and rear wheels (0.011) reported by Lemaire et al,^{3} the rolling resistance that the user will encounter when propelling the chair over a level surface at 2.5 km/h can be estimated to be 14.5 N. The braking force needed on a 3degree side slope can be estimated to be 7.3 N. The angle through which the wheelchair can be tilted (assuming the user maintains the posture that existed before the wheelchair was tilted) before becoming unstable with the rear wheels unlocked (θ_{a}) is 16.5 degrees. The wheelchair is stable with the rear wheels locked, by the user's hands or wheel locks, on inclines up to 8.9 degrees. These characteristics will be the starting point for adjustments to 3 basic designs used in adjustable wheelchairs today. The simplest design has a movable seat on a rigid base. A newer design being used more frequently in rigidframe wheelchairs has rear axles that slide on a horizontal frame member. The most common design has an axle plate as the adjustment mechanism. The effects of adjustments to each of these frames can be predicted.
Adjustments to a RigidFrame Wheelchair
Rigidframe manual wheelchairs have fixed rear axles and caster positions and, therefore, a fixed wheelbase length (Fig. 6). This design preserves the relationship between the rear wheels and casters. The seat can be moved forward or backward, and it can also be angled with respect to the base. I believe that a reasonable approach is to find the best seat angle and height for posture, transfers, and the shoulderpushrim relationship and then move the seat forward or rearward to adjust the propulsion characteristics and stability of the wheelchair. The effect of adjusting the seat rearward 2.5 cm (a_{x}) can be evaluated for the simulated user. This adjustment will change the distance x from 10 to 7.5 cm, a 25% change. Characteristics proportional to x should change by 25%, as well. As shown in Figure 6, the vertical force on the casters, the downturning braking force, and the critical angles of stability will be similarly affected. The change in weight distribution is determined by the change in x relative to the wheelbase. For this adjustment, 2.5 cm is 6.25% of 40 cm, and that is the calculated change in rearwheel and casterweight distributions. The vertical force on the rear wheels is determined by the distance of the wheelbase forward of the rear axles (l_{wb}−x), so the change is 2.5 cm out of 30 cm, or 8.3%, which is the calculated change in the vertical force on the rear wheels (f_{r}). The change in rolling resistance (10%) is determined by the weight on the casters and rear wheels, which change at different rates, so the change is between 8.3% and 25%. For adjustments that change only x, we should be able to predict the effect on maneuverability if we know the wheelbase and either x or the weight distribution, and we should be able to predict the effect on stability if we know a critical angle. The effect on stability is larger than the effect on maneuverability.
Rigid Frames With Horizontally Movable Rear Wheels
An increasingly popular design incorporates rearwheel axles that can only be moved forward or backward on horizontal frame members (Fig. 7). This is important in that the design does not allow vertical adjustments to the rear wheels and makes angular adjustment of the casters relative to the frame unnecessary. The caster structure, therefore, is simpler and more durable than an angle adjustable caster. On some wheelchairs, the caster can also be moved horizontally to adjust the length of the wheelbase. With this frame design, the rear axles would be moved 2.5 cm forward (a_{x})to effect the same adjustment made with the rigidframe wheelchair, but the length of the wheelbase is also decreased. Calculations of the adjusted wheelchair characteristics are shown in the formulas in Figure 7. The change in downturning braking force and stability angles will again be 25% because they are only related to x. Changes in weight distribution and rolling resistance will be smaller for this frame because the length of the wheelchair is also changing. For approximately the same adjustment and same decrease in stability, there is apparently a smaller benefit to maneuverability.
Wheelchairs With Axle Plates
The most common adjustable wheelchair frame design has an axle plate that is bolted to vertical frame members and can be moved up or down on the frame (Figs. 1 and 8). Axle plates can be used on rigid frames and on frames that fold from side to side. The plate has a slot or holes that allow the axle to be moved forward or backward on the plate. The effects of a horizontal adjustment to the rear axle position have already been discussed. Vertical adjustments to the axle plates change the rear seat height and cause the frame to rotate around the caster axles. The rotation presents a considerably more complex problem because the COM is moved in an arc relative to the caster axles that changes the vertical and horizontal positions of the COM relative to the rear axles. If the axle plates are moved 2 cm up on the frame, the rear seat height will decrease and there will be counterclockwise rotation of the seat about the caster axles (Fig. 8). Assuming that the wheelbase remains the same, the height of the COM above the rear axles decreases 1.6 cm (a_{y}), and the distance of the COM forward of the rear axles decreases 2.5 cm (a_{x}), the effects of the adjustment can be calculated. Maneuverability will be the same as for the rigidframe wheelchair because x is changed 25% and the length of the wheelbase forward of the COM (l_{wb}−x) is changed 6.25%. Rear stability decreases less than is seen with a strictly horizontal adjustment because the height of the COM also decreases.
Although the effects of the adjustments to a manual wheelchair on several variables can be predicted, we still do not know whether the wheelchair is “optimized” from the user's perspective. Each of the adjustments resulted in a wheelchair that is stable on a 7degree slope compared with the Americans With Disabilities Act (ADA) standard for public facilities of 1:12^{18} or 4.8 degrees. We may determine that 7 degrees is adequate and be confident that the adjustment would not be unsafe but still not know whether the wheelchair is “optimized.”
An alternate approach would be to determine the stability angle that must be maintained. Five degrees of stability may be enough if the user can produce limited pushrim force and will propel the wheelchair only over surfaces not steeper than the ADA standard of 4.8 degrees.^{18} Equation 8 (Fig. 4) can be used to solve for the x that will provide 5 degrees of stability. For the rigidframe wheelchair, I believe that a 4.4cm adjustment can safely be made in order to reduce rolling resistance 18% and steering effort 44%. This large adjustment, in my view, should dramatically change the user's ability to propel the wheelchair in the identified environment. In contrast, if the user is active in the community and needs 8 degrees of stability, the adjustment, in my opinion, would be too large. The calculated “optimal” adjustment would be to move the seat rearward 1.0 cm. These 2 examples show that the optimization process could be shortened, thus saving considerable time. The problem with the scenario is that we do not currently have established clinical methods to find the height of the COM or the necessary angle of stability. In addition, clinical trials are needed to determine whether decisions made as illustrated in this article lead to improved wheelchair fitting.
Conclusion
The best answer to the question “How much maneuverability should be adjusted into the wheelchair?” is: as much as possible. It seems obvious that it is better to use less effort to be mobile. The real constraining factor is stability, which diminishes as maneuverability improves. The length of the wheelbase and either the distance of the COM forward of the rear axle or the proportion of weight on the rear wheels determine the maneuverability characteristics of the wheelchair for the user, and these can be measured. These values can be used to predict the effect of horizontal adjustments on rolling resistance, downturning braking force, and weight distribution. Although we cannot currently measure the height of the COM to calculate the critical angles, we can use the “bedside test”^{10} to measure the critical angle with the rear wheels unlocked. The effect of horizontal adjustments on this measured angle can also be estimated from the percentage of change in distance of the COM forward of the rear axles. To predict the effects of vertical adjustments to the wheelchair, a clinical method for determining the COM height is needed. To take full advantage of the biomechanical relationships, a method for determining how stable the wheelchair must be for the user to be safe and functional in the user's environment is also needed. The advantages of this approach should be a decrease in the time and effort required to “optimize” the wheelchair for a user and more confidence in the clinical decisions that are made in the process. Further research is needed to determine whether the theoretical considerations discussed in this article do, indeed, result in more functional wheelchairs and greater user satisfaction.
Footnotes

Mr Tomlinson provided concept/design and writing.
This work, in part, has been supported by the Foundation for Physical Therapy.
 Physical Therapy