Besselink 2004 Journal of Terramechanics

Journalof

www.elsevier.com/locate/jterra

TerramechanicsJournal of Terramechanics 41 (2004) 187–198

Development of a vehicle to study the tractiveperformance of integrated steering-drive systems

B.C. Besselink

Agricultural Machinery Research and Design Centre, University of South Australia,

Mawson Lakes, SA 5095, Australia

Available online 18 May 2004

Abstract

This paper describes a test-bed vehicle for studying the integration of the steering system of

a wheeled vehicle with the drive system. The vehicle was produced in order to determine

whether such an integrated system is practical; to investigate tractive performance compared

to other steering-drive systems; and to determine under which conditions such a system has

better performance. The integrated steering-drive system of the test-bed vehicle uses a com-

puter to co-ordinate the independently driven wheel speeds of the drive system (which is also

the primary steering system) with the steer angles of the non-driven steerable wheels to pro-

duce a beneficial secondary steering effect. The secondary steering system assists the primary

steering system when side forces act on the vehicle, while producing minimal conflict. This

concept can be applied to agricultural vehicles such as tractors, harvesters, mowers, sprayers

and self-propelled windrowers. The test-bed vehicle is able to be configured for the following

steering-drive systems types: open differential drive with steerable wheels, independent drive

wheels with castors, locked differential drive with steerable wheels and a computer integrated

steering-drive system. The capacity of the test-bed vehicle to be configured as described is a

significant advantage when measuring tractive performance, as the results obtained will be

more valid due to the vehicle parameters being the same.

� 2004 ISTVS. Published by Elsevier Ltd. All rights reserved.

Keywords: Tractive efficiency; Zero turn radius vehicle; Steer by wire; Computer control; Drive systems

1. Introduction

The two basic conventional two-wheel-drive configurations for wheeled vehicles

are independent drive and differential drive.

0022-4898/$20.00 � 2004 ISTVS. Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.jterra.2004.02.001

188 B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198

With an independent drive system, the left-drive wheel and right-drive wheel are

driven independently by means of a variable ratio transmission. Examples of

wheeled vehicles that use this system are garden tractors, ride-on mowers and self-

propelled windrowers. In these vehicles, the non-driven wheels must be castors:

otherwise, significant ground damage and handling problems occur when turning.

Compared to a vehicle with a differential, these vehicles have a high degree ofmanoeuvrability and traction. When both the left-drive wheel and right-drive wheel

are driven forward at the same speed, the vehicle moves straight ahead. On the other

hand, when both the left-drive wheel and right-drive wheel are driven at equal and

opposite speeds the vehicle rotates about the centre of the drive axle (a zero turn

radius (ZTR) vehicle). The independent drive means that if one drive wheel loses

traction, the other drive wheel is not affected and the vehicle is still able to move.

This contrasts with the behaviour of vehicle with an open differential.

However, when traversing steep slopes, the castors cannot exert a sideways force,so the end of the vehicle with the castors tends to move down the slope due to the

gravitational turning moment acting on the vehicle (where the centre of gravity is

substantially forward of the drive wheels). This presents a significant limitation in this

situation. In order to maintain the direction across the slope, a counteracting moment

must be provided by increasing the difference in drive speeds to produce a difference in

thrust between the two drive wheels. Thus, there is a decrease in tractive capability in

order to increase steering capability. This may lead to a loss of traction and control.

As well, on flat slippery terrain, castors also have a disadvantage: a sudden loss oftraction on one drive wheel will cause a sudden steering deviation. The castors

cannot contribute any steering effect to reduce or eliminate the deviation since they

cannot hold a side force.

The most common drive system for a two-wheel-drive vehicle is one that has a

differential. It is a relatively simple mechanical drive system that provides equal

torque to both drive wheels and produces minimal scuffing in turns. In this case,

the drive wheels cannot provide a steering effect, as they are not independent. The

vehicle is steered by changing the rolling direction of the non-driven wheels. Thebenefit when traversing slopes is that the non-driven wheels can hold a side force.

The steering behaviour of a vehicle with a differential is more stable under changing

tire-surface conditions than a vehicle with independent drive wheels. With a differ-

ential, although total thrust is reduced when the traction conditions are different for

each drive wheel, the driving torques will be equal; and if the rolling resistances are

equal, the thrusts will be equal. Hence, there is no turning moment induced under

these different conditions.

However, when one wheel has lower traction, a vehicle using a differential hasdisadvantages. Differences in traction characteristics may come about from different

tire-surface characteristics or weight distribution. Since a differential delivers equal

torque, the wheel with better traction characteristics can only deliver the same

amount of torque as the wheel with the lower traction. To overcome this problem,

various forms of differential locking or drive shaft braking techniques are used.

These result in poor handling. For example, locking the differential enables the

steering effect from wheel speeds, and the equal wheel speeds create a tendency to

B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198 189

move the vehicle straight ahead. The application of a braking effect to a drive wheel

produces energy losses. Generally, manoeuvrability is reduced and handling is

impaired. As well, vehicles in an agricultural context require traction control on an

ongoing basis since the drive wheels of an agricultural vehicle usually operate with

high longitudinal slip. Whereas with road vehicles, traction control is only required

for a small percentage of the time.A wheeled vehicle having the tractive advantages of two independent drive wheels

but having steerable non-driven wheels has greater design possibilities with respect to

weight distribution, space considerations, and wheel sizes. It should also have

improved tractive ability, mobility and safety on slopes and slippery surfaces.

The aim of the author�s current research is to integrate the steering and drive

systems of a wheeled vehicle having two independently driven wheels. The steering

and drive systems are to be integrated using a computer with an appropriate algo-

rithm. Another objective of the research is to investigate the performance of such avehicle, particularly in turning and especially on slopes and slippery terrain, and to

compare it with conventional systems.

Contrary to conventional two-wheel-drive vehicles, the two-wheel-drive vehicle

developed will have a steering system at one end from wheel direction (steerable

wheels) and at the other end from wheel speeds (independent drive wheels).

The purpose of this paper is to describe the design of the test vehicle and control

system hardware being used for this research.

2. Background

Besselink and Spark [4] have described a computer controlled steering-drive

system for four-wheeled vehicles having two independently driven wheels. The

steering-drive system is proposed to be achieved by replacing the two castors of the

conventional system with two steerable non-driven wheels. These are positively

turned to steer angles appropriate to the radius of curvature produced by the wheelspeeds of the two independently driven wheels. A microprocessor is used to deter-

mine the appropriate steer angles. The microprocessor uses an algorithm based on

the mathematical relationship between the wheel speeds of the two independently

driven rear wheels and the Ackerman steer angles of the two front steerable wheels.

Sensors are used to determine the speed and direction of the two driven rear wheels

and the microprocessor controls the actuators that turn the non-driven wheels to the

appropriate steer angles.

Further mathematical relationships have been developed for vehicles having morethan two driving wheels and more than four wheels [3,5,6].

The paper by Spark and Besselink [4] presents the mathematical relationships and

some analysis of the motion of the vehicle. However, the analysis for the develop-

ment of a practical computer algorithm was not presented. The presence of the in-

verse tangent function in the mathematical expressions presented some problems

with instability for a steerable wheel as Blair and Spark [2] highlighted (but did not

solve). The other references do not disclose a computer algorithm either.


Besselink [1] presented an analysis of the motion of a vehicle with two indepen-

dently driven rear wheels and described a computer algorithm which solves the in-

stability problem and which emulates and improves upon the motion of a zero turn

radius vehicle with two drive wheels.

3. Theory

3.1. Steering effects

The radius of the turning circle of a wheeled vehicle is a result of either or both of

the following two steering effects:

• the radius of curvature produced by the independent wheel speeds of the left drive

wheels and the right drive wheels; and/or• the radius of curvature produced by the rolling direction of thewheels of the vehicle.

However, for a conventional four-wheeled vehicle in a turn, when both of these

steering effects are operating there is conflict between them. An extreme example of

this conflict occurs with a skid-steer vehicle, such as a four-wheeled skid loader. The

wheels of the vehicle are always directed straight ahead and hence would produce an

infinite radius of curvature if acting alone. However, this steering effect conflicts with

the dominant effect: the radius of curvature resulting from the different independent

wheel speeds selected by the operator. The actual turn radius will be a compromisebetween the two radii of curvature. The conflict results in extreme scuffing, ground

damage, tire wear, fuel wastage and, in some cases, reduced manoeuvrability.

The traditionalmethod toavoid this conflict is todisableone steering effect.Zero turn

radius vehicles donot haveany steering conflict because the non-drivenwheels aremade

inoperative as steerable wheels by turning them into castors. The steering is solely from

the independent drive wheel speeds. With a conventional motor vehicle, the steering

effect of the drive wheel speeds is eliminated by the inclusion of a differential, which

removes their independence. As a result, there is no conflict between the two systems.

3.2. Integrated steering-drive systems

For a two-wheel-drive vehicle of typical configuration with equal front and rear

tracks, the mathematical relationship between the speeds of the drive wheels and the

steer angles for the steerable wheels is detailed as follows (Spark and Besselink [4]):

/L ¼ tan�1 bt

1

�� xR

xL

��; ð1Þ

/R ¼ tan�1 bt

xL

xR

�� 1

��; ð2Þ

where b is the wheel base of the vehicle; t, the track of the vehicle when front and reartracks are equal;xL andxR are the rotationalwheel speeds of the rear left and rear right

drive wheels of the primary steering system respectively;/L and/R are the steer angles

of the front left and front rightwheels of the secondary steering system respectively. It is


assumed that the drive wheels have equal wheel diameters. An understanding of the

terms used may be obtained from Fig. 1 (which is for unequal track).

Fig. 1 depicts a vehicle with a primary steering system using two independently

driven wheels and a secondary steering system using the wheel direction of the front

non-driven wheels. tB is the track of the rear wheels; tF is the track of the front

wheels; R is the radius of the turning circle of the vehicle. Clockwise rotations areregarded as positive and have a positive radius of curvature.

The following equations for the general case, where the track of the front wheels is

different to the track of the rear wheels, were developed by Besselink [1]. The un-

derlying assumptions in all these equations is that there are no slip angles on any

wheels and that longitudinal slip is the same on each drive wheel.

For the front left steerable wheel,

/L ¼ tan�1 2bðxL � xRÞxLðtB þ tFÞ þ xRðtB � tFÞ

� �: ð3Þ

Similarly, for the front right steerable wheel,

/R ¼ tan�1 2bðxL � xRÞxLðtB � tFÞ þ xRðtB þ tFÞ

� �: ð4Þ

We can see that if tB ¼ tF, the equations simplify to the equations developed by

Spark and Besselink [4].

For a vehicle using two independently driven wheels and only one steerable wheel

at the front, we have the case where tF ¼ 0. Hence, the equation for the steer angle is

as follows:

/ ¼ tan�1 2bðxL � xRÞtBðxL þ xRÞ

� �; ð5Þ

Fig. 1. Geometry of a 2WD2WS vehicle with unequal track.


where / is the steer angle of a lone non-driven wheel. This relationship is used as the

basis for the computer algorithm of the test-bed vehicle described later.

3.3. Measures of performance

Drawbar performance is the most important performance indicator for off-roadvehicles that are designed to pull or push various types of working machinery, e.g.,

tractors. The main measures are as follows.

Drawbar pull, Fd, is the force available at the drawbar, and is equal to the dif-

ference between the driving force, F , developed by the wheels and the resultant re-

sisting force,P

R, acting on the vehicle:

Fd ¼ F �X

R: ð6Þ

Drawbar power, Pd, is the product of drawbar pull and vehicle speed and rep-

resents the potential productivity of a vehicle. It is defined by the following:

Pd ¼ FdV ; ð7Þ
where V is the actual forward speed.
Tractive efficiency (or drawbar efficiency) is usually defined as the ratio of the

output power of a tractive device to its input power. The equation for tractive effi-

ciency may be expressed as follows:

gd ¼PdPW

; ð8Þ

where PW is the power inputted to the driven wheels.

Generally, all the traditional performance measures are for vehicles travelling in a

straight-line and on level ground. Performance characteristics in turns will be mea-

sured in this project; and due to the presence of slip angles, the component of tire

force in the direction of motion needs to be considered in these expressions. How-

ever, it is not possible to investigate these considerations in this paper.

3.4. Test-bed vehicle

The requirements of the test-bed vehicle were as follows:

• to provide a practical example of a computer integrated steering-drive system;

• to allow instrumentation of the vehicle for measuring tractive performance;

• to be capable of being instrumented to assist in the validation of the computer

models developed in the project; and

• to provide comparisons between different conventional vehicle configurations.

The basis of the test-bed vehicle is a John Deere Z-Trak 757 (Fig. 2). This is a zeroturn radius (ZTR) lawn mower. Although it is a ride-on mower, at 25 hp, it has a

power rating near to that of a small tractor but with the benefit of a hydrostatic drive

system. Being a hydraulically driven vehicle, it is capable of being converted to a

vehicle with different drive configurations by changing the arrangement of the hy-

draulic lines. Thus, the tractive efficiency of different drive configurations may be

Fig. 2. John Deere Z-Trak 757.


compared directly on the same vehicle. As well, when modified to include a drawbar,

it should be able to handle moderate to high drawbar loads.Since the computer-integrated concept can be extended from a three-wheeled

vehicle to a four-wheeled vehicle, the three-wheeled vehicle design was selected over a

four-wheeled vehicle. It eliminates problems resulting from uneven load distribution

when the terrain is uneven. A suspension system was considered, but this would

make the vehicle too complex without entirely removing the weight distribution

problem. It also provides a close emulation of a tractor-type vehicle since the usual

trunnion mounted front axle of a tractor has a stability that is similar to a three-

wheeled vehicle. Hence, the two castors were removed and replaced with a frontwheel module with a single wheel.

3.5. Front wheel module

The front wheel module had to have a wheel which was steerable: in some cases,

manually and in other cases automatically by the computer (depending on the

configuration chosen). Therefore, a 12 V 130 W electric motor was connected to the

vertical axis of the front wheel via a chain and two sprockets. Using this arrangementinstead of linkages allows the possibility of an infinite number of turns. The position

sensor for feedback to the computer is described in a later section.

The front wheel module was made to be configurable as a conventional castor, as

well as a steerable wheel. Thus, the original zero turn radius configuration could also

be compared with the other configurations (see Fig. 3).

In order to obtain the characteristics for a specific tire of a steerable wheel for use in

computer models, the front wheel module can be detached and mounted with a dyna-

mometer on a rolling trolley device with guides. This device allows side force and rollingresistance to be measured for different vertical loads, tire pressures and slip angles.

Fig. 3. Steerable wheel and castor configuration of front wheel module.


The module is also adapted for the mounting of a specially designed dynamom-

eter for the measurement of forces along any of the three axes. Spacers are used when

the dynamometer is not present.

3.6. Control system

The control system consists of the following:

• a computer,

• a data acquisition card,

• relays and electronics, and

• control sensors.

The program for the control of the steering-drive system is loaded in a notebook

computer that is interfaced with the control sensors via a data acquisition card(National Instruments DAQCard-1200). The data acquisition card has 24 digital

inputs/outputs, eight analog inputs, two analog outputs and three counter/timers.

One counter may be used to generate a pulse output.

The steering motor on the front wheel module is switched on and off by a set of

relays triggered from the digital outputs of the data acquisition card.

3.7. Control sensors

The computer program compares the appropriate steer angle for the front wheel

to the current steer angle. The current steer angle is measured with an angular po-

sition sensor. This is a Hewlett Packard HEDS-5701#E10 optical encoder rated at

200 pulses per turn; but since it also has quadrature encoding, further electronics

produces 800 pulses per turn. This encoder is an incremental encoder and not an

absolute encoder, and so some further electronics (which includes an up/down

counter) produces an absolute encoder for the time it is powered on. The use of an

encoder allows an infinite number of turns to be made by the steerable wheel, as well


as allowing a complete rotation to be measured. Potentiometers generally do not

cover 360�, and if capable of infinite rotation have a discontinuity between the ends.

The drive wheel rotational speeds are measured for inputting into the control

program by optical encoders (Allen-Bradley Bulletin 845T Optical Incremental

Encoder 360 pulses per turn) mounted on each drive wheel. The pulses from the two

encoders are used to gate two counters on the data acquisition card: one counter foreach drive wheel. The third counter is used to the generate the set frequency of pulses

which are gated by the encoders. Hence, the drive wheel rotational speeds are in-

versely proportional to the counts. This system is able to produce estimations of

speed more rapidly than by counting the pulses outputted by the encoders.

The above sensors are required for a basic control system. Further sensors are

required for a more sophisticated system.

3.8. Performance measurement sensors

Various sensors are required in order to determine tractive performance. The

power input and power output are required for efficiency measurement. For power

input, the input torque to the wheels and rotational speed need to be measured.

In conventional tractor experiments, torque load cells are used (and rotational

velocity measured) on an input shaft. These are not be able to be applied in the test-

bed vehicle as it is hydraulically driven. Since the rotational speed of each of the

drive wheels is already required for the computerised steering-drive control system, itis advantageous to measure the torque at each drive wheel as well. With the test-bed

vehicle, this is conducted by measuring the pressure drop across each hydraulic drive

motor using pressure sensors. The pressure drop across a motor is a function of

torque and rotational speed. With a set of calibration curves, the torque can be

determined from the measured pressure drop and the rotational speed. One pressure

sensor (Measurement Specialties Inc. MSP-600-350) is on the inlet and the other on

the outlet of each motor. The pressure sensors input data to the data acquisition card

via the analog inputs. Since the torque input is measured for each drive wheel, anextra benefit, in terms of analysis, is that the torque distribution between the drive

wheels is able to be determined.

For output power, the drawbar pull and velocity at the drawbar hitch is required

for drawbar efficiency. In a straight line, the velocity at the drawbar hitch is the

vehicle velocity. For turning, the velocity of the hitch needs to be determined either

directly or by deduction. Drawbar pull is measured with a load cell. When turning,

the draw angle also needs to be known and this is measured using a potentiometer

connected to an analog input of the data acquisition card.When the instrumentation is set up for tractive (drawbar) efficiency, other com-

mon measures of performance, such as drawbar power, can also be calculated.

3.9. Dynamometer

A dynamometer was designed and constructed for mounting on the front wheel

module (see Fig. 4). It consists of a S-type load cell sandwiched between two 10 mm

Fig. 4. The dynamometer designed for measuring forces on the front wheel.


plates with five small roller bearings and guides. It has overall dimensions of 200

mm� 200 mm� 70 mm.

The dynamometer or a number of dynamometers can be mounted in the front

wheel module to measure force in the vertical axis (vertical load), lateral horizontal

axis (side force) and longitudinal horizontal axis (rolling resistance). The amplified

load cell output is inputted via an analog input of the data acquisition card to the

computer. The forces on the front wheel are not necessary for standard tractive

efficiency measurement. However, the forces are needed to validate computer sim-ulations developed in the project for each of the steering-drive systems.

3.10. Comparison of configurations

An aim of the research is to compare the tractive performance of the computer

integrated steering-drive system with conventional steering-drive systems. In order to

compare like with like (experimentally, rather than with computer simulations), it

was desirable to have a test-bed vehicle that was able to adapt to different steering-drive configurations. Hence, factors such as track, wheelbase, tire type, vehicle

weight, weight distribution, and power would be the same for each configuration.

The front wheel module (as described already) is one element of the adaptable

steering-drive configuration concept used in this research (note that the castor option

produces a slightly varying wheel base in turns). The other element is the adaptable

hydraulic circuit that was fitted.

An hydraulically driven vehicle was chosen because of its potential for re-con-

figuration compared to a mechanically driven vehicle. The original drive system ofthe test-bed vehicle is an independent drive system with one variable displacement

hydraulic pump matched with one fixed displacement hydraulic motor for each drive

wheel.

Fig. 5 shows the three different hydraulic circuits that can be configured with two

pumps and two motors: independent, open differential and locked differential (1:1

speed ratio) drive systems. These are the three configurations of interest. This allows

Fig. 5. Independent drive, open differential and locked differential hydraulic configurations obtained using

the hydraulic circuit designed for the project.


the comparison of following steering-drive systems: open differential drive with

wheel direction steering, independent drive with wheel speed steering (and castor),

locked differential drive with wheel direction steering, and the computer integratedsteering-drive system.

The original hydraulic pipes were removed and replaced with an arrangement of

hoses and valves that can be configured to these three drive systems relatively easily.

Opening two valves switches the circuit from independent drive to differential drive.

To obtain the locked differential drive two short hoses are disconnected, and a longer

hose installed between the outlet of one motor and the inlet of the other. For the

locked differential configuration, it was considered that a system with valves was too

complex and not necessary.The John Deere Z-Trak 757 as it appears after modification is shown in Fig. 6.

Fig. 6. John Deere Z-Trak 757 after modification.


4. Conclusion

The test-bed vehicle outlined in this paper demonstrates the feasibility of an im-

proved wheeled vehicle that uses a computer integrated steering-drive system and

that has two independent drive wheels and steerable non-driven wheels. This vehicle

has all the tractive advantages of two independent drive wheels with none of thedisadvantages. The secondary steering system assists the primary steering system

(from the drive wheel speeds) when side forces act on the vehicle, while producing

minimal conflict.

As it is hydraulically driven, the test-bed vehicle can be instrumented in a unique

way to measure the parameters required for tractive performance, in particular,

tractive efficiency. This is achieved by utilizing the outputs of the sensors of the

control system and providing additional measurement sensors.

The capacity of the test-bed vehicle to be configured to emulate a range ofsteering-drive systems provides a significant advantage when measuring tractive

performance, due the vehicle parameters being the same. Hence, since like is com-

pared with like, the performance comparisons are more valid than if different ve-

hicles using these steering-drive systems were compared.

The major advantage of a vehicle using a computer integrated steering-drive

system, as described, is the improved ability to traverse steep slopes and the ability to

have larger non-driven wheels. The latter allows improved load carrying capacity.

The presence of a steering system at each end of the vehicle allows greater variationof load distribution while maintaining the same level of steering capability.

References

[1] Besselink BC. Computer controlled steering system for vehicles having two independently driven

wheels. Comput Electron Agricult 2003;39:209–26.

[2] Blair DB, Spark IJ. Computer controlled integrated steering/drive system for vehicles. In: ASME

Computers in Engineering Conference, California, USA, 1996.

[3] Lu J, Spark IJ, Vains GG, Spriggs KR. Computer integrated steering/drive systems with steering wheel

control. In: Proceedings of I.E. Aust. Conference on Control Engineering, Sydney, Australia, 1997. p.

236–41.

[4] Spark IJ, Besselink BC. Zero turn radius vehicle incorporating computer-controlled �intelligentcastors�. In: ASME Computers in Engineering Conference, Minneapolis, USA, 1994. p. 825–27.

[5] Spark IJ, Ibrahim MY. Integrated mechatronics solution to maximise tractability and efficiency of

wheeled vehicles. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics,

Como, Italy, 2001.

[6] Spark IJ, Ibrahim MY, Spriggs KR. Maximising the tractive effort, drive efficiency and manoeuvra-

bility of wheeled mobile robots. In: Proceedings of International Conference on Robotics, Vision and

Parallel Processing for Industrial Automation, Ipoh, Malaysia, 1996. pp. 843–51.

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