THE RELATIONSHIP BETWEEN THE ANGLE OF CAMBER AND THE TRACKING MISALIGNMENT OF MANUAL WHEELCHAIRS

Pedro Barbosa Rodrigues, Arlindo F. Silva, António Carrilho, Pedro Antunes Instituto Superior Técnico, Lisbon, Portugal

ABSTRACT

Wheelchairs with camber on the propelling wheels require accurate setting to achieve tracking alignment. To this setting corresponds a seat/frame trim angle. A change from this seat/frame trim angle setting will cause some degree of rear wheel tracking misalignment. This effect will be greater for larger camber angles and since tracking misalignment increases the rolling resistance it is particularly relevant for sport wheelchairs which can have camber angles up to 20 . In this paper this effect is quantified and it can be shown that for a camber angle of 10º a change in trim angle of 8º will cause a tracking misalignment of 1.4º corresponding to a toe in/out of 32 mm for a 26 inch wheel.

BACKGROUND

It is recognised that rear wheel camber has an effect on the wheelchair stability (1,2) as well as on the propelling energy required (3). Additionally it has been shown that is necessary to set accurately the rear wheel axis to guarantee the parallel tracking of these wheels (4). Changes of seat/frame trim angle can occur either by; i) raising or lowering the axis of either the front or the rear wheels, ii) lifting the front wheels of the ground during the impulse on the push rims often seen in the riding/racing practice. These changes in trim will inevitably cause some degree of tracking misalignment of the real wheels. Wheel tracking misalignment will increase the rolling resistance and therefore it is important to quantify and minimise this effect.

OBJECTIVE

The main objective of this study was to identify the relationship between real wheels tracking misalignment and seat/frame trim angle quantifying this effect for different camber angles.

METHOD

Figure 1 show schematically a three wheel "Sports" type wheelchair. The variables shown are: L-the distance between the front and rear axis; b- seat/frame trim angle; H- distance from the ground of the front wheel; g- wheel tracking misalignment angle.

Fig. 1- Show schematically a "Sports" type wheelchair in the vertical and horizontal plane.

Fig. 2 - Rear view of the back wheels with camber.

Figure 2 shows the geometry of the back wheels. The variables shown are: R - the wheel radius; Q- the intersection point of the wheel axis; E- distance between the horizontal and the intersection point of the wheel axis Q; q- the camber angle; P- the centre point of the rear wheel hub; - the vector defining the rear wheel axis rotation due to changes in the seat/frame trim angle b. The co-ordinates of P are defined by: The co-ordinates of Q are defined by: The vector , is given by the difference of co- ordinates between points P and Q: As the trim angle b is increased the vector takes new positions. These new positions can be defined by a rotation matrix A: The new position of the vector after rotation is obtained by: The tracking misalignment angle,g is obtained by :

This expression can be rearranged as: (1) The trim angle b can be related to the distance of the front wheels from the ground by the following expression: H= (cos b-1) E + L sinb (2) The tracking misalignment angle g can also be converted into tow in/out. For a 26 inch wheel the following expression was used for the conversion Tow in/out = 4*R* sin g (3)

RESULTS

The values of tracking misalignment gº for different trim angles bº from 0º to 90º and for camber angles q from 6º to 20º were calculated using expression (1) are shown in table 1. The range of trim angles bº from 0º to 90º were chosen to show the non linearity of this relationship although it is recognised that for normal riding practice trim angles variation will be less than 20º.

Table 1 Values of tracking misalignment gº for different trim angles bº and camber angles q.

The figures 3 show the results of table 1 in graphical form.

Fig. 3 - Show the value of tracking misalignment gº for a range of trim values b from 0º to 90º for different camber angles.

The figure 4 shows the values of tracking misalignment gº corresponding to trim angles up to 20º which represents normal riding practice.

Fig. 4 - Shows the value of tracking misalignment gº for a range of trim values b from 0º to 20º for different camber angles.

For practical purposes it was considered useful to convert the trim angles b into the distance of the front wheels from the ground H using expression (2). The tracking misalignment angle g was also converted into tow in/out using expression (3). Figures 5 and 6 show in graphical form the relationship between distance of the front wheels from the ground H and the tow in/out for a wheel camber q of 10º.

Fig.-5 Show the relation between the tow in/out and H for a "Universal" type wheel chair with a L of 400 mm and a camber angle q of 10º.

Fig. 6- Show the relation between the tow in/out and H for a Sports type wheelchair with a L of 775 mm and a camber angle of 10º.

DISCUSSION

These results show that for a "Universal" type wheelchair with a camber angle of q 10º a change in trim angle b of 8º corresponding to a change in H of 55 mm will cause a tow in/out of 32 mm. For "Sports" type wheelchairs the values of misalignment will be reached at approximately the double of the change in H. This is due to fact that the distance between the front and back wheels of the "Sports" type wheel chair is approximately the double of the "Universal" type wheel chair. It is recommended to limit tow in/out to 12 mm for "Universal" wheelchairs and 6 mm for "Sports" wheelchairs therefore it can be concluded that the setting up of the trim angle of wheelchairs with camber is critical and that changes in trim angle will significantly influence the rolling characteristic and consequently riding confront.

REFERENCES

1. Trudel, G., Kirby, R.L. Effect of camber on wheelchair stability. Proceedings of the RESNA'94 Annual conference, June 17-22,1994

2. Trudel, G., Kirby, R.L., Bell, A.C. Experimental location of the axis of rotation for rear stability of wheelchairs with and without camber. Proceedings of the RESNA'95 Annual conference, June 9-14, 1995

3. Buckley, S.M., Bhambhani, Y.N., Madill, H, M., Proceedings of the RESNA'95 Annual conference, June 9-14, 1995

4. Homem, P.L. Carmo, E.F. Cadeira de rodas de competição. Report-IST-RT-1/1994.

ACKNOWLEDGEMENTS

The authors would like to thank Dr. L Teodoro for the support given to this work and to Prof. L Magalhães for the helpful discussions.

Prof. Pedro Barbosa Rodrigues Instituto Superior Técnico Departamento de Engenharia Mecânica Av. Rovisco Pais LISBOA 1096 CODEX PORTUGAL Tel: +3511 841 74 57 Fax: +3511 841 74 57