three point hitch

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Research Paper: PMPower and Machinery

Three-point hitch-mechanism instrumentation for tillage

power optimization

H. Bentahera,, E. Hamzab, G. Kantchevc, A. Maalejc, W. Arnoldd

aOlive-tree Institute, P.O. Box 1087, Sfax-3000, TunisiabNational Agronomic Institute of Tunis, Tunisiac

National Engineering School of Sfax, PBW, Sfax-3000, TunisiadFraunhofer-Institute for Non-Destructive Testing (IZFP), Campus E3.1, University, D-66123 Saarbrucken, Germany

a r t i c l e i n f o

Article history:

Received 29 December 2006

Received in revised form

28 November 2007

Accepted 29 January 2008

Available online 17 March 2008

In order to study tillage power optimization, a tillage-force measuring system has been

built with transducers in the three-point hitch mechanism, and then has been calibrated

and tested in the field. The uniqueness of this system is its ability to measure the three

orthogonal components of the tillage force despite using only three force sensors; this was

possible by using a three-dimensional analysis of the tractor linkage mechanism.

A dynamic calculus program was developed to take into consideration the changes of

the three-point hitch-mechanism geometry during the tillage operation. The calibration

results showed a linear relation between the applied and the measured forces. The

preliminary field tests proved the stability of the system results. The developed system can

readily be applied in studies to minimize tillage energy consumption.&2008 IAgrE. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Due to the rapid increase of energy cost, power optimization

is a common objective for many engineering devices. Tillage

is the biggest power consumer in an agricultural production

system, and hence the evaluation of tillage effort is a field of

great interest.

Researchers have proposed and built many systems to

measure the force and power requirements of tillage imple-ments. These systems can be classified into three types based

on the location of the force transducers. For the first type,

sensors are mounted on the tillage tool (Girma, 1989;Formato

et al., 2005). These systems give a precise idea about strain

distribution on the implement that helps in their design

optimization. However, they are expensive because each

tested tool has to be equipped with sensors. Moreover, the

transducers installation required some changes to imple-

ment global geometry which could modify the soiltool

interaction and the tool weight. The second category of

systems has separate frames in which transducers are

mounted. These frames are introduced between the tractor

and the implement. Because these systems are interchange-

able between different tractors and tools and are easy to

manufacture, the majority of researchers have investigated

such devices (Reece, 1961;Barker et al., 1981;Reid et al., 1985;

Clark and Adsit, 1985;ODogherty, 1986;Chaplin et al., 1987;

Thomson and Shinners, 1989; Palmer, 1992; Godwin et al.,1993; Hammada, 1998; Al-Jalil et al., 2001; Kasisira and du

Plessis, 2006). However, this approach presents many incon-

veniences: first, it requires a heavy frame to fix the

transducers which causes a change of the total weight and

requires a backward displacement of the implement. Second,

fixing the transducers and the frame to the tractor necessi-

tates many extra elements at the articulations that are a

source of error in the measurements. For these reasons, the

second type of system does not reflect real work conditions.

ARTICLE IN PRESS

1537-5110/$ - see front matter & 2008 IAgrE. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.biosystemseng.2008.01.008

Corresponding author. Tel.: +216 74 241589; fax: +21674 241033.E-mail address:[email protected] (H. Bentaher).

B I O S Y S T E M S E N G I N E E R I N G 1 0 0 ( 2 0 0 8 ) 2 4 3 0
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The third type consists of installation of transducers in the

three-point hitch system of the tractor. Despite the fact that

this category preserves the real conditions of field work (e.g.

tool-tractor position), little research has been focused on it.

The efficiency of these systems is highly related to the

position of the sensors. On the one hand, some researchers

mounted the transducers on the top and the two lower links

(Bandy et al., 1985; Upadhyaya et al., 1985; Al-Janobi, 2000;

Bentaher et al., 2003). The load of the lower links is complex.

It entails tension, compression and flexure which prevent the

installation of force sensors. As a result, with such systems it

is not possible to measure the lateral effort generated by

asymmetrical implements. On the other hand, the installa-

tion of force transducers on the top and the two lift links

seems to be the best solution. To the best of our knowledge,

the only work that has been done on this type of system is by

McLaughlin et al. (1993). In that work, the three-point hitch

system was instrumented by five force sensors. A transfor-

mation matrix was derived to transform the force of these

transducers into orthogonal components of the tillage force.

Since the establishment of this matrix was based on a two-

dimensional kinematic study (Bandy et al., 1985), the in-

formation concerning the lateral tillage force was lost.

In the present work, a three-dimensional kinematic study was

developed to establish the transformation matrix. We instru-

mented a tractor with three force sensors (on the top and the two

lift links) and an angular transducer for the hitch rock shaft

(Fig. 1). A dynamic program, taking into consideration the

changes of the three-point hitch-system geometry, was estab-

lished to calculate the tillage effort. The developed system is able

to measure the three orthogonal components of the tillage force.

2. Materials and methods

2.1. Theoretical considerations

In the majority of the published work, researchers considered

the three-point hitch mechanism as a planar system. This

system was modelled in two dimensions to represent the forces

in the original geometrical configuration between the tractor

and the implement (Bandy et al, 1985; Al-Janobi, 2000). This two-

dimensional approximation, which causes the loss of the lateral

force, can be accepted for the studies of symmetric implements.

In order to evaluate the longitudinal, vertical and lateral

forces of a non-symmetric tillage tool, a three-dimensional

study of the tractor linkage mechanism is needed. The

mechanism consists of seven articulated beams. During field

work, this system is isostatic with one degree of freedom. The

angular position of the rockshaft is sufficient to determine the

exact geometry of this system.

To make the force calculation simpler, the three-point hitch

system is modelled by ties and pin joints. The coordinates of

each joint are calculated in a Cartesian coordinate system (X0,

Y0,Z0) with I0, the centre of the rear wheel, as the point of origin(Fig. 2). The calculus equations of all the pin-joint positions are

developed. The position of the tillage application point G in

reference to this coordinate system is given by the equations:

xG xDIHzKzD

IK HG

xDxKIK

(1)

zG zD HGzKzD

IK IH

xDxKIK

(2)

For a definition of the variables in these equations, see

Fig. 2. An Excel calculus program (CP1) was developed to

determine these coordinates. The inputs of this program are:

tractor characteristics: Cartesian coordinates of O, O0

, B, B0

,E, and the distances: AA0, L1, L01and L3;

ARTICLE IN PRESS

Fig. 1 Instrumented three-point hitch mechanism.

Nomenclature

AtoKandO positions of pin joints of the three-point hitch-

mechanism as defined inFig. 2

Cg gravity centre of the tillage tool chassis

G tillage application point

g gravitational accelerationl0 centre of the rear wheel

L1 length of the lower link

L01 distance between the joint of the lower link (tractor

side) and the pivot connection of the lift rod

L2 length of the lift rod

L3 length of the lift arm

L4 length of the upper link

m tillage tool masslRij reaction force in the point i at the direction j for

the left side of the hitch mechanismrRij reaction force in the point i at the direction j for

the right side of the hitch mechanismWx, Wy, Wz orthogonal components of the tillage force at

the pointG

Xi, Yiand Zi Cartesian coordinates of the point i

XG, YG, ZG Cartesian coordinates of the pointG

f rock shaft angular position

B I O S Y S T E M S E N G I N E E R I N G 1 0 0 ( 2 0 0 8 ) 2 4 3 0 25


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adjustable lengths: L2and L4; tool triangular chassis characteristics: distances DD0, IK, IH

and HG;

rock shaft angular position f which is the variableparameter during the field work.

The tractor characteristics are measured and compared to

the Organization for Economic Cooperation and Development

(OECD) restricted code test report (CEMAGREF, 1995). The

equilibrium of the left lower link arm gives the following

system of equations:

lRDxl RBx

l RCx 0

lRDyl RBy

l RCy 0

lRDzl RBz

lRCz 0

lRCzyC yB lRCyzCzB l RDzyD yB lRDyzD zB 0

lRCxzC zB l RCzxCxB

l RDxzD zB l RDzxDxB 0

lRCyxCxB l RCxyC yB

l RDyxDxB l RDxyD yB 0

lRCxxA xC

lRCy

yAyC

lRCzzAzC

lRCL2

(3)

Here,Rijis the reaction force at the point i at the direction j,

xi,yiandzi, are the Cartesian coordinates of the point i andl

indicates the left side of the three-point hitch mechanism. The

equilibrium of the right lower link arm gave a similar system of

equations (r for the right side). From the equilibrium of the

tillage tool chassis (Fig. 3), this system of equations is derived:Wx l RDx r RDxRK

xKxEL4

Wy l RDy r RDy

Wz l RDz r RDz RKzKzE

L4mg

yDrRDz l RDz WyzGzD mgyCg

zKzDxKxE xKxDzKzE RKL4

WxzGzD WzxG xD mgxCg xI

Wy r RDx

lRDxxGxD

yD

8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

(4)

Here, Wx, Wy and Wz are the orthogonal components of the

tillage force at the pointG,mis the tillage tool mass andgis the

gravitational acceleration. The last two of these equations arederived knowing the direction of the reactions in the two lift

ARTICLE IN PRESS

A1

O1

K

Z0 A2

O2E

B2B1

I0

D1 Wy

Wz

D2

Y0 I0

Z0

O

3A

EX0

B

1

C

2Z

K

45

H

X

Wz W

WxGD

Y0

I0 X0

EA2

B2C2 D2

Y

IKA1

B1

O1

C1 D1

X Wy

Wx

W

G

Line of attack

Fig. 2 Rear view (a), side view (b) and upper view (c) of the three-point hitch mechanism showing lower link 1 and its length

L1 BD; L01:the distance BC; lift rod 2 and its length L2 AC; lift arm 3 and its length L3 OA; upper link 4 and its length

L4 EK; tool triangle chassis 5; longitudinal component of tillage force Wx; lateral component of tillage force Wy; vertical

component of tillage force Wz.

Z0

I0

X0

B CRD D

mg

CgI

2

I

E

O

A 4

3

1

Rk K

5

W

Fig. 3 Force diagram of the three-point hitch mechanism,

Cgand mg are, respectively, the gravity centre and the

weight of the tool chassis,Wis the tillage force and Riis the

reaction force in the pointi.



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links and the top link: they are bi-articulated beams, and so

their reactions are parallel to the beam directions.

The solutions of these equations give the three orthogonal

components of the tillage force:

xi, yi and zi, are the Cartesian coordinates of the point i.

These equations show that the voltage responses of three

force transducers located in the two lift rods and the upperlink are sufficient to identify the tillage force. A second Excel

calculus sheet (CP2) was developed to evaluate the three

orthogonal components of the tillage effort. The inputs of this

program are the outputs of the first program (CP1) and the

responses of these transducers. The flow chart of the two

calculus programs is shown inFig. 4.

2.2. Instrumentation

The three-point hitch mechanism of a Massey Ferguson 6120

tractor was instrumented to evaluate the orthogonal compo-

nents of tillage implements without changing the dimensions

of the mechanism. Two HBM-U2B force transducers with a

range of 200 kN were incorporated into the two lift links. Four

simple thread shells were designed and manufactured to

make the assemblage of these transducers possible. A third

load cell with the same capacity and a lower weight was

designed and constructed for the top link (Fig. 1). The

incorporation of this transducer does not change the weight

of the top link much (less than 5%). More detailed information

concerning the design of this sensor and its calibration has

been presented by Bentaher et al. (2006). A rotary position

transducer functioning as a potential divider was mounted on

the rockshaft to monitor its movement. This transducer was

used to measure the angular position of the hitch mechanism

and to calculate the implement depth.

2.3. Data-acquisition system

The three load cells and the rotary position transducer wereconnected to four differential channels of the 21X Campbell

scientific data logger. This data logger was connected to the

RS232 port of a notebook via an optically isolated interface

SC32A. The whole acquisition system was mounted on a

platform behind the drivers seat. This system worked either

on its own batteries or on the 12 V power supply of the tractor.

The data logger was used to excite the transducers and to

sample and record their responses. The notebook was used

to control the in-field sampling, to collect the stored data and

to calculate the tillage effort using the developed calculus

programs CP1 and CP2. The software (PC208) was used to

prepare the data logger program and to run and test its

validity and the proper functioning of the acquisition system.The sampling frequency used for the preliminary tests was

1 Hz and the excitation voltage for the transducers was

500mV.

2.4. Calibration

The instrumented three-point hitch-mechanism was cali-

brated using a separate HBM-U9B force transducer with a

ARTICLE IN PRESS

Chassis dist.: D1D2,

IK, IH and HG

Input :

Coord. of O1,

O2, B1, B2, E

Distance: A1A2,

L1, L1, L3

Adj. length:

L2 and L4

Cartesian

Coord. of:

A1, A2,

C1, C2,

D1, D2,k,

and G

CP1

Angular position

(t)

CP2

Transducer

voltages

V1, V2and V3

Chassis Charact. : m

and XCg, YCg, ZCg

Tillage

components

Wx, Wyand Wz

Fig. 4 Flow diagram of the calculus programs; AA 0 is the distance between the two liftarm joints; L1 is the distance between

the joints of the lower link; L0

1 is the distance from the lower link joint to the lift rod joint; L2 is the lift rod length; and L3 isthe lift arm length.

Wx xKxExD xBzKzD xG xKxDxBzKzE xK xExGxDzDzB

xDxBzG zD xG xDzDzB

RKL4

xCxBzAzC xAxCzCzB

xD xBzGzD xGxDzDzB

xD xG

L2lRC

r RCh i

xD xBxGxCg

xD xBzG zD xGxDzDzBmg (5)

Wy xCxBzAzC xA xCzCzB

xDxBzGzD xGxDzDzB

yDL2

lRCr RC

h i

xBxDyCgxD xBzGzD xGxDzDzB

mg (6)

Wz xKxEzK zGzDzB xD xKzK zEzDzB xDxBzKzEzGzD

xDxBzGzD xGxDzDzB

RKL4

xCxBzAzC xAxCzC zB

xDxBzGzD xGxDzD zB

zD zG

L2lRC

r RCh i

xDxBzGzD xCgxDzDzB

xD xBzGzD xGxDzD zB

mg (7)



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capacity of 20 kN. The simulated effort was applied and varied

with a chain-hoist attached to a fixed point from one side,

and to the force transducer from the other side. This

transducer was fixed to the force application point (G) of the

triangular chassis with a cable. The tractor was placed on a

horizontal plane verified by an engineers spirit level. The

applied forces, given by the sheared cable, were located in the

horizontal and vertical planes; their modules were controlled

by an HBM-MVD 2510 control-panel measuring-amplifier.

Three principal forces, related to the orthogonal directions,

were applied: longitudinal (Wx), lateral (Wy) and vertical (Wz)

effort. The applied forces were increased stepwise and at

each value, the signals of the three sensors were logged for a

period of 1 min. The results of the calibration are presented in

Figs. 57.

3. Results and discussions

The calibration was done in the three directions in order to

prove that the developed instrumentation was able to detect

the three orthogonal components of the tillage force. The

results (Figs. 57) showed thatWxand Wzwere proportional to

the reaction force of the two lift links and the top link.

However, the lateral force Wy was proportional to the

difference between the reactions of the two lift links and

was independent of the top lift reaction.The calibration results showed a linear relation between

the applied force and the responses of the three force sensors.

The output of the calculus program CP2 (Wy) and its standard

deviation are displayed versus the applied force in Fig. 8and

similar curves are obtained for Wx and Wz. The measured

data fall very close to a straight line with a unit slope. The

least square fit with an R2 of 0.995 indicates that the force was

underestimated by approximately 0.5%.

The longitudinal measured force showed an error of 13%

for the lowest force (900N). This can be explained by the

sensitivity of the developed system. In fact, the use of trans-

ducers with a high capacity (200kN) represents a limitation in

the measurement of small forces (McLaughlin et al., 1993).

However, for higher forces, the maximal error was 0.82%. For

the lateral force, the highest error between the applied and

the measured forces was 7.6%. The error of the vertical force

was less than 2.8%.

In the design of this system we preserved the geometry of

the hitch mechanism and the position of the tillage tool to the

tractor because it will be used for two purposes. The first one

is to study the stability of the tractor and its characteristic

curves (power supply/fuel consumption) for different speeds.

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-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0

Sensorresponse,mV

Time, s

Left Link

Right Link

Top Link

50 100 150 200 250

Fig. 5 Sensors response to longitudinal applied force (Wx).

-0.1

-0.05

0

0.05

0.1

0.15

0

Sensorr

esponse,mV

Time, s

Left Link

Right Link

Top Link

100 200 300 400 500

Fig. 6 Sensors response to lateral applied force (Wy)

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0

Sensorresponse,mV

Time, s

Left LinkRight Link

Top Link

100 200 300 400

Fig. 7 Sensors response to vertical applied force (Wz)

0

1000

2000

3000

4000

5000

6000

0

Measuredforce,N

Applied force, N

1000 2000 3000 4000 5000 6000

Slope = 0.968

R2= 0.995

Fig. 8 Lateral measured force (Wy) versus applied force(solid curve is 1:1 line).



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In fact, the change of the tool position gives unreal results

concerning the tractor reactions which are not directly

transposable. The second purpose is to measure the power

demand of different tillage tools in relation to the type of soil,

its mechanical characteristics and the work parameters

(depth and speed). These kinds of results are very useful for

the evaluation of different tillage tools, the decision in the

choice of the tool (e.g. according to the tractor power,

availability on the farm, to calculate the number of plough

shares) as well as the design of new tools adapted to the type

of soil.

The developed system gives us reliable results directly

exploitable for research and for manufacturers in order to

optimize power consumption.

The field tests were conducted at the Tunisian agriculture

institute farm (361480N, 101100E), where the soil was silty

consisting of 63.69% silt, 36.16% sand and 0.15% clay. The

mean water content (dry basis) and the cone index for the

upper horizon (020 cm) were 14% and 2.2 MPa, respectively.

A 50.8cm (2000) locally manufactured mouldboard with one

ploughshare was used for the tests. The tractor speed used for

these tests was 1kmh1 with a slip less than 2%. A tillage

depth of 20cm was chosen. The registered data are repre-

sented inFig. 9. This figure shows good stability of the three

orthogonal components of the tillage force. The means of the

horizontal, lateral and vertical forces generated by the tested

mouldboard are, respectively, 4105 N,40N and 295N. The

negative values indicate that the forces are in the opposite

direction to the Cartesian coordinate system. The obtained

data are in agreement with those given by several researchers

working on a similar type of soil (McLaughlin et al., 1993;Al-Janobi, 2000;Al-Jalil et al., 2001).

4. Conclusion

Instrumentation of the three-point hitch mechanism allowed

the force generated by tillage implements to be measured

using just three force transducers. The system was calibrated

and tested in the field and the results showed its capability to

measure the three orthogonal components of the tillage force.

The three-dimensional study of the hitch mechanism of the

tractor demonstrates that the technique allows the difference

in the reaction of the two lift arms to be measured whenusing non-symmetric tools like mouldboards. Their differ-

ence is proportional to the lateral component of the tillage

force. The developed calculus programs gave this system

flexibility in the interpretation of the logged data in relation to

the tool penetration in the soil.

The three components of the tillage force have been measured

using a system that allows the natural positions of tool and

tractor to be retained. This will allow the energy consumption of

different tillage tools to be measured during natural operation, so

that steps can be taken to optimize their design. More investiga-

tions would be needed to study the influence of work parameters

such as tillage speed, tillage depth and soil type on the measured

forces to achieve this optimization.

Acknowledgements

The authors would like to thank the Agence Universitaire de

la Francophonie for the financial support of the researchersmobility between the laboratories: IZFP in the Saarland

University LASEM in the Engineering school of Sfax and

LAPOAF in Olive-tree institute of Tunisia.

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ARTICLE IN PRESS

-1000

0

1000

2000

3000

4000

5000

0 5 10

Time, s

Wx

Wy

WzForce,N

15 20 25

Fig. 9 Measured data of the forces Wx,Wy, and Wzacting on the ploughshare of a 50.8cm (2000) mouldboard.



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