DEVELOPMENT OF A NOVEL THREE-WHEELED VEHICLE

V. Cossalter, N. Ruffo, F. Biral, R. Berritta

Department of Mechanical Engineering , University of Padua

Abstract

In the last few years the automotive and motorcycle industries, pressed by the need for better rider safety, have shown an increasing interest in innovative vehicles.

This paper focuses on a new three-wheeled vehicle concept. A three-wheeled vehicle is a fine synthesis between the manoeuvrability and compactness of a motorcycle and the stability and load-bearing capacity of a four‑wheeled car.

The solution presented in this paper is characterised by the innovative system of linking the rear frame to the front frame so that the latter tilts like motorcycles do whereas the rear frame does not. The linking system is a four bar linkage whose geometry can be adjusted to set the position of the instant tilting axis of the front frame with respect to the rear one closer to or further from the road surface. Moreover, it is possible to vary the inclination of the tilting axis on the longitudinal plane.

A model of this vehicle was developed using a multi‑body program. Many analyses have been carried out varying the geometrical parameters of the linking system in order to find the best handling and safety behaviour.

Finally a real working prototype of the vehicle was built. As in the virtual model, the prototype can change the geometry of the linking system. Different test drivers have accomplished many manoeuvres with different geometrical configurations. These tests confirmed the predicted simulations results.

1. Introduction

For decades two and four wheel vehicles have been the most important means of people transport by road. In the last few years the increase of traffic in cities, of parking problems and pollution have changed the concept of how vehicles are used.

Motorcycles and scooters are maneuverable and compact, but they have little storage space and no protection against bad weather.

Though cars do not have these problems, they are bigger, more complex and expensive. Moreover, nowadays more than 80% of cars in cities carry only one or two people thus wasting a lot of energy.

In this framework the market seems to be ready for a new type of vehicle which is useful as a car, but as small as a motorbike, which could transport one or two people and be safe in all kinds of traffic and situations.

In fact the car and motorbike industry has started to define new means of transportation especially in the field of three-wheeled vehicles.

In order to build a vehicle with stability typical of a four wheeled vehicle and the maneuverability and compactness of a two wheeled vehicle, the three wheeled vehicle must be capable of tilting. This kind of vehicle has a kind of tilting system to make it lean into corners like motorcycles.

The leaning motion can be controlled by the driver, or an automatic system. In the former case, the driver is directly responsible for maintaining the correct tilted position; while in the other the system controls the steering front wheel angle and the tilting angle.

Since the 1930’s many attempts have being made to develop a safe, compact and maneuverable vehicle /1-20/.

These vehicles can be divided into two groups: car derived and motorcycle derived. The first ones are driven with a steering wheel, with the aid of an automatic system for tilting.

The second ones look like scooters or motorcycles with two rear wheels and the front frame that can tilt.

The solution presented in this paper is a motorcycle derived type where the driver controls the roll motion of the vehicle without the aid of any system. The innovative feature of this vehicle is the system linking the front frame to the rear frame /21/.

The aim of this work is to examine the dynamic behavior of the proposed vehicle and, in particular, the effects of the linking system. The influence of the four-bar geometry on the kinematic and dynamic behavior is investigated and some results are presented in this paper.

Finally a comparison between the numerical results and the judgments of the test drivers about the prototype is proposed.

2. Vehicle description

This vehicle was first conceived, designed and simulated using a computer and then a prototype was built. First, the kinematic behaviour of the vehicle is presented and discussed because it has a large influence on the vehicle’s dynamic performance. Then the dynamic simulation results are shown and compared to the experimental results obtained from the driving tests using the prototype.

This vehicle is characterized by three main assemblies. The first one is the rear assembly, which consists of the rear frame, two wheels, the engine and the rear suspension. The second assembly is the tilting front frame which consists of the front wheel, the front fork and the suspension. The rear frame and the front frame are connected with a four bar linkage. This linkage is the innovative aspect of this vehicle and is significantly responsible for the vehicle’s dynamic behaviour.

The four-bar linkage is made up of the rear frame which do not tilt, the tilting front frame and two connecting bars that link the front and rear frame by means of four revolute‑joints, which have the same axis orientation (Figure 1).

Figure 1: i.r.c. and rolling axis definitions.

Figure 2: Four bar linkage elements.

With this configuration the front frame rotates around an instantaneous tilting axis.

The intersection of the tilting axis with the four bar linkage plane defines the instantaneous rotation centre (referred to as i.r.c.). The i.r.c. position in the linkage plane is defined by the intersection of the two axes of the connecting rod, as shown in Figure 2.

Hence, the distance a between the two superior revolute-joints, the length c of the connecting bars and the distance b between the two inferior revolute-joints (Figure 2), define the instantaneous rotation centre position. Height h is defined as the vertical distance between road plane and i.r.c.; its value is positive when the i.r.c. is above the road plane, negative if the i.r.c. is below the road plane.

The instantaneous tilting axis can be moved up and down with respect to the road surface by decreasing or increasing the distance between the revolute-joints (parameters a and b) as shown in Figure 3. As in general the instantaneous tilting axis is not parallel to the road plane, when it moves up and down, its intersection with the road plane moves back and forth.

Figure 3 – Tilting axis vertical translation

It is also possible to fix the position of the i.r.c (its height from the ground, parameter h) and rotate the tilting axis around this point changing the orientation of all the revolute-joint axes (see Figure 4). Again the intersection with road plane moves back and forth, except the case with the axis parallel to the ground. In this case there is no intersection at all.

All these possible configurations can be gathered into three main groups: the i.r.c. positioned over the ground (parameter h positive), on the ground (parameter h equal to zero), or under the ground (parameter h negative), These three different configurations influence significantly the dynamic behaviour of the vehicle.

Figure 4 – Tilting axis rotation about i.r.c. on four bar linkage plane

The above mentioned kinematic considerations are based on the hypothesis that the vehicle is in its vertical position. When the front frame tilts towards one side, the i.r.c moves towards the same side and height h from the road plane changes. If the i.r.c. is above the road, its distance from the road surface increases when the vehicle tilts. On the contrary, if the i.r.c. is under the ground its distance from the road surface decreases; in some cases the i.r.c. can even shifts over the ground (Figure 5).

Figure 5 – Main four bar linkage possible configurations

The vertical and lateral position of the i.r.c. and the tilting axis inclination affect the load transfer from the inner rear wheel to the external rear one during a curve.

The equilibrium of the torques of the forces acting on the rear frame, with respect to the i.r.c. point, gives the load transfer DN, between the rear wheels, as a function of the position of the i.r.c. and of the centre of mass of the rear frame.

where is the lateral displacement of the i.r.c., is the vertical position of the rear mass centre, F_l and F_r are the lateral forces on the rear wheels and 2N is the total vertical load on the rear wheels in static condition.

The forces transmitted by the connecting bars from the front frame to the rear frame do not give any contribution to the momentum because they pass through the i.r.c.

It is possible to observe that the load transfer depends both on mass forces (centrifugal and gravity) and on tyre lateral forces.

The more the i.r.c. is closer to the centre of mass the more the contribution of the centrifugal forces diminishes, but on the other hand the influence of the tyre lateral force increases its importance. The contrary happens if the i.r.c. is under the road surface because the momentum of the lateral forces changes sign.

Summarising, three relevant cases have to be investigated: the i.r.c. over the ground, on the ground and under the ground. Of course the effect of the inclination of the tilting axis has its own importance in all the three cases.

3. The Virtual Model

The components of the virtual vehicle were modelled and assembled using a 3D modelling software, which is integrated in the multi-body program Working Model 3D.

Figure 6 – Tricycle virtual model screenshot

Exploiting the CAD associativity, it was possible to change the design parameters of the vehicle in the drawing environment and get the model updated automatically in the multi-body software.

Working Model 3D lacks of a tyre model, thus it was necessary to develop a motorcycle tyre model /22/. This tyre model represents the reactions of the road surface on the tyre by means of three torques (overturning, rolling resistance and yaw torques) and three forces acting on the geometric contact point.

It was also necessary to add a driver model capable to follow a given path. This was accomplished with a proportional derivative and integrative control. The tyre and driver model codes were written in Visual Basic and used the OLE technology (Object Linking Embedding) to send inputs (such as tyre forces, engine, brake and steering torques) and retrieve the vehicle motion state from Working Model.

Different kind of manoeuvres typically used for handling tests can be selected like U turn, steady state turn, lane change and slalom test.

4. Simulation results

The simulations were carried out considering principally U turns because these manoeuvres highlight the effect of the load transfer between the two rear wheels. The load transfer is important because it influences the total lateral adherence of the vehicle. In particular during a curve at very high speed or during obstacle avoiding manoeuvre, the load transfer may be so large that the internal wheel vertical load becomes equal to zero and the wheel rises from the road surface. This situation should be avoided to prevent rear frame roll over.

In addition, the U turn manoeuvre is useful to analyse the behaviour of the vehicle on entry and exit a curve, and evaluate the general handling behaviour of the vehicle /23/.

Simulations were grouped in three main configurations:

· i.r.c. over the ground

· i.r.c. on the ground

· i.r.c. under the ground

and for some cases the inclination a of the revolute joints of the four bar linkage (and consequently of the tilting axis) was changed from –5° to +5°.

In the graph of Figure 7 the vertical loads on the two rear wheels are shown for a vehicle having an horizontal tilting axis considering several values of height h (in the range -0.15 ÷ 0.15 m). It is possible to see that the vertical load on the internal wheel (internal with respect to the turning side) decreases less if height h decreases. When height h = -0.150 m the internal wheel is more loaded than the external one.

Figure 7 Load transfer between rear wheels varying h

Figure 8– i.r.c. position varying h, for different roll angle values

In fact, as stated above, the load shift depends mainly on the position of the i.r.c. and on the position of the centre of mass of the rear frame. This phenomenon is better explained in Figure 8, which depicts the trajectory of the i.r.c. on vertical plane y-z, as a function of the front frame roll angle f. The more the i.r.c. is under the road plane the more the tilting axis shifts towards the internal wheel for a given roll angle. Moreover, for negative values of h, the i.r.c. moves vertically much more than for positive values of h.

In order to reduce the movements of the i.r.c. during tilting motion, it is necessary to shorten the connecting bar length c and to increase the length b. Then the effect of four bar linkage geometry on the steering torque is considered, because steering torque is closely related to vehicle handling.

Figure 9 - Steering torque against time for different values of parameter h

The graph of Figure 9 shows that when h decreases the absolute value of the steering torque in steady turning condition decreases, whereas the steering torque that the rider has to apply to begin the curve increases ( e.g. the initial peak of the torque with h equals to -0.150 is greater than the peak of the torque with h equals to +0.150). This means that a configuration with the i.r.c. under the ground is more stable than the ones having the i.r.c. over the ground. Moreover, handling diminishes because a greater torque is required to tilt the front frame to perform a given manoeuvre.

The improvement of stability achieved with negative values of h is highlighted by the manoeuvre represented in figure 10 (h = - 0.30m) in which the steering torque and the roll angle are plotted against time. The first part of the plot represents the entry in the curve followed by a steady turning condition. At time 4.5 s the rider suddenly stops exerting the steering torque and the vehicle returns to the vertical equilibrium configuration with small overshoots.

Figure 10 –Four bar linkage stable configuration

The angle of the axes of the revolute joints affects the orientation of the tilting axis and consequently the intersection of the tilting axis with the road plane. With positive angle a, the intersection with the road surface moves forwards and vice versa for negative values.

Figure 11 shows that the load transfer decreases when a increases.

The steering torque value is almost the same for different values of a, as it is shown in Figure 12.

Other parameters that influence the steering torque and vehicle stability are tyre properties (and in particular the self-aligning torque and the twisting torque), castor angle and front fork offset which affect the vehicle trail /24/, see Figure 13.

Figure 11 Load transfer between rear wheels varying a

Figure 12 – Steering torque varying a

Figure 13 – Steering torque varying e

5. The prototype

A working prototype based on the design parameters obtained from the simulation results was built (Figure 14 and Figure 15).

Figure 14 – Prototype during roll motion. Front and rear view.

As the virtual model the prototype four bar linkage geometry can be adjusted to achieve the desired set-up. This was accomplished creating a slot both in the rear and in the front frame in which the superior and inferior couple of revolute joints respectively can slide in order to obtain the assigned distance.

The length of the connecting bars can be varied screwing or unscrewing their ending part.

The inclination of the steering axis angle can be increased or decreased as well. Some test drivers carried out many tests with this prototype in different situations. Sometimes they tested limit manoeuvre in order to assess not only handling but also safety.

Figure 15 - Prototype built at the department. Revolute joints highlighted

6. Experimental results

The experimental tests yielded almost the same results that the simulations predicted.

The main handling and safety manoeuvres carried out were: obstacle avoidance, fast slalom, bump during turning manoeuvre and U turn manoeuvre, all these manoeuvres were performed with different four bar linkage configurations.

The table 1 summarizes the results obtained, reporting the driver judgements.

A vehicle with a positive h parameter turned out to be faster during the obstacle-avoidance manoeuvre than the ones with negative h values. Moreover, it was necessary to apply a lower torque to tilt the front frame during transient period. On the other hand the three wheeled vehicle was more stable with the i.r.c. under the road surface, but the test driver found it more difficult to roll the front frame during curve entrance.

All these results agree with computer simulation.

	h < 0, a = 0	h = 0, a = 0	h > 0, a = 0	h > 0, a > 0
Steering torque effort	++	+	-	+
Handling	--	+	++	+++
Rear frame hopping effect	++	++	+	--
Rear and front frame coupling effect	--	--	--	++
Vertical Revolute joint effect	++	+	-	-

Table 1 – Test driver judgements for different four bar linkage configurations

The “rear frame hopping effect” phenomenon rises when the driver applies a particular high frequency sinusoidal steering angle in order to make the rear frame to hop. This effect disappear almost completely when the rolling axis is inclined.

The test driver felt what we called “vertical revolute joint effect” as a negative effect. This happens when the rear frame and front frame seems to be linked by a vertical revolute joint during the turning manoeuvre. This behaviour disappears almost completely when the angle of the tilting axis is positive.

But with a positive tilting axis angle another undesired phenomenon rises. This fact consists of a sort of coupling between rear and front frame. Any perturbation that occurs on the rear frame propagates to the front frame and the driver feels this phenomenon quite disturbing.

6. Conclusions

A first series of studies were carried out on a three-wheeled vehicle having a tilting front frame. The vehicle was modelled by means of a 3D software and simulated with the aid of multi-body code. The influence of the four bar linkage, which connects the rear frame to the front frame, on the dynamic behaviour was deeply investigated.

The simulation results revealed the importance of the vertical position and inclination of the tilting axis on the load transfer between the rear wheels and on the steering torque that must be apply to do a curve.

The numerical results gave a contribution to the design and manufacturing of a working prototype that was tested in many different manoeuvres. A good agreement between simulation and experimental results was found.

The tests pointed out also some riding sensations that helped to understand the dynamic behaviour of this innovative vehicle.

Moreover, the prototype showed that it is possible to obtain substantial different vehicle performance simply varying the geometrical parameters of the four bar linkage, as predicted by the multi-body model.

Appendix 1

In Figure 16 are shown the main vehicle dimensions, used to carry out computer simulations.

Figure 16- Tricycle main dimensions

Table 2 represents the mass properties of the main elements of the tricycle used during computer simulations.

	Mass [kg]
Connecting bar	3.5
Front fork	12
Front frame	12
Rear left wheel	2.8
Rear right wheel	2.8
Front wheel	3
Rear frame	45
Tank	6
Man	70

Table 2 – Masses of model elements

In Table 3 the four bar linkage different geometrical configuration used for the computer simulations are shown.

Configuration N°	Four bar linkage geometrical parameter				i.r.c. position
	a [m]	b [m]	c [m]	a [°]	h [m]
Case 1	0.500	0.090	0.320	0	0.155
Case 2	0.440	0.160	0.320	0	0.003
Case 3	0.400	0.200	0.320	0	-0.150
Case 4	0.500	0.090	0.320	+5	0.155
Case 5	0.500	0.090	0.320	-5	0.155
Case 6	0.380	0.240	0.320	0	-0.390

Table 3 – Four bar linkage geometrical configurations used for simulation

Case 1 to 5 have the geometrical dimensions shown in Figure 16, while case 6 uses a different steering angle inclination (e = 27°) and a different offset (0.025m instead of 0.042m).

Appendix 2

List of symbols:

N_r Rear right tyre vertical force in static equilibrium

N_l Rear left tyre vertical force in static equilibrium

N N_r and N_l are equal in static equilibrium

F_r Rear right tyre lateral force during steady state curve

F_l Rear left tyre lateral force during steady state curve

F_c Centrifugal force during steady state curve

m×g rear frame weight

DN Load transfer between rear wheels during steady state curve

L Distance between the centre of the two rear wheels

f Front frame roll angle

e Steering axis inclination

a Four bar linkage revolute-joints axis inclination with respect to the rear frame

a Distance between the four bar linkage superior revolute-joints

b Distance between the four bar linkage inferior revolute-joints

c Connecting bars length

h i.r.c. vertical distance from road surface

z_cm Rear frame centre of mass vertical position

y_i.r.c. i.r.c. lateral position

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