A Data-acquisition System to Monitor Performance of Fully Mounted Implements

A Data-acquisition System to Monitor Performance of Fully Mounted Implements

J. agric. Engng Res. (2000) 75, 167}175 doi:10.1006/jaer.1999.0496, available online at http://www.idealibrary.com on A Data-acquisition System to Mo...

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J. agric. Engng Res. (2000) 75, 167}175 doi:10.1006/jaer.1999.0496, available online at http://www.idealibrary.com on

A Data-acquisition System to Monitor Performance of Fully Mounted Implements Abdulrahman Al-Janobi Agricultural Engineering Department, College of Agriculture, King Saud University, Riyadh, Saudi Arabia; e-mail: [email protected] (Received 4 December 1998; accepted in revised form 14 October 1999)

A data-acquisition system was developed for a three-point linkage-implement force and depth transducer to measure draught and implement depth for mounted implements of categories II and III. The transducer was equipped with an extended octagonal ring transducer in each of the lower link and a tension/compression load cell in the top link. A rotary position transducer attached to the rockshaft was used to measure the implement depth and the angular position of the linkage. The data-acquisition system and the transducers were installed on the Massey Ferguson 3090 tractor and tested in the "eld with a mounted-type chisel plough to determine the capability of the system. The resultant force was determined at implement depths of 7, 12 and 15 cm with coe$cient of variations 3)18, 1)55 and 1)49%, respectively. Testing demonstrated that the data-acquisition system was capable to provide reliable results with acceptable accuracy. ( 2000 Silsoe Research Institute

1. Introduction Performance data from various tractors and implements are essential for farm machinery management and manufacturers alike. Proper selection of tractor and implement for a particular farm situation can be determined from these performance parameters. These data can also be used to evaluate various farm machinery systems to determine the relative merits of each system. As "eld machines contribute a major portion of the total cost of crop production systems, proper selection and matching of farm machinery is essential to reduce signi"cantly the cost of ownership and farm machinery use. Also, e$cient operation of tractors and implements is a main concern for farmers because of the rising costs of fuel and other operating costs. One major parameter needed for the formation of a performance database is the draught force. The availability of draught requirement data of tillage implements is an important factor in selecting suitable tillage implements for a particular farm situation. Farm managers and consultants use draught and power requirement data of tillage implements in speci"c soil types to determine correctly the proper size of tractor required. Therefore, by using accurate draught data, the operating costs of both tractors and implements can be minimized. Farmers mostly depend on past experience for selecting tractors 0021-8634/00/020167#09 $35.00/0

and implements for various farming operations. This previous experience may be of little e!ect in selecting newly available implements. Therefore, prediction of implement draught requirement on di!erent soil types and conditions is important for tractor selection and implement matching. Many studies have been conducted to measure draught and power requirements of tillage implements under various soil conditions. Grisso et al. (1994) reviewed the work reported by di!erent researchers in measuring draught and power requirements of the most common tillage implements. Several methods have been developed to measure the draught forces on tractors. Researchers proposed and built many systems for draught measurements, most using mounted strain gauges or strain gauge load cells. The dynamometers measuring the draught of tillage implements can be classi"ed into two main groups (Chaplin et al., 1987). The "rst group consists of those in which the transducers are mounted on a frame between the implement and the tractor, whereas the second group consists of integral systems in which the dynamometer arms are modi"ed to accommodate the transducers. The frame type has been designed and built in many shapes with adjustments suitable for use on a wide range of tractors and implements (Chaplin et al., 1987; Barker et al., 1981; Reid et al., 1985; Garner & Dodd, 1985; Thomson & Shinners, 1989). Some designs also permit the free use

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of the power take-o! (p.t.o.) shaft. The integral systems accommodate the force transducers in the tractor links itself by preserving the original geometry and is usually designed to measure the forces in the longitudinal and the vertical planes (Bandy et al., 1985). These are designed for use on one particular tractor only and proved to be a simple system to incorporate. An accurate knowledge of the geometry of the linkage is required for the force-sensing elements in the links to measure the resultant draught force on the tractor. These dynamometers do not interfere with the p.t.o. shaft and present no problems with those implements, which project forward in front of the lower links. The integral systems have used load-sensing elements on or between the tractor and the implement to measure the forces. Some of the designs measured all the forces acting between the implement and the tractor by using a three point dynamometer suspension system (Chaplin et al., 1987; Barker et al., 1981), whereas other designs measured only the longitudinal and vertical forces and neglected the side forces as being small (Reid et al., 1985; Garner & Dodd, 1985; Thomson & Shinners, 1989). The system developed by Reece (1961) was considered as the most basic system, only measuring the horizontal force for a free linkage system. A datalogger can be used to scan and record data from the transducers in an instrumentation system. Also it can provide the excitation for the transducers without the need of an external power supply. Many data acquisition systems to record data from the transducers using datalogger and microcomputers have been reported in literature. In order to record the data from the strain gauges or load cells, suitable data-acquisition systems have been designed and built for "eld use. A datalogger has been used to excite and record the output signals from the strain gauge load cells in the force dynamometer (Chaplin et al., 1987; Thomson & Shinners, 1989). The data were then transferred from the datalogger memory to magnetic tape for transfer to a microcomputer for further processing. Microcomputer-based data-acquisition systems have also been developed for use on the instrumented tractor (McLaughlin et al., 1993; Clark & Adsit, 1985; Lackas et al., 1991). Mounting such dataacquisition systems inside the tractor cab allowed greater versatility in the sampling rate, signal conditioning, and data storage and processing. However, on-board computers require much more space than dataloggers and need su$cient capacity inverters for operating them. Also they are more susceptible to the e!ects of adverse environments. With the implementation of laptop computer-based data-acquisition systems, the problem of taking more space and the necessity of inverters are greatly solved. Also the overall weight of the instrumentation system is considerably reduced.

The objective of this work was to develop a dataacquisition system capable of measuring and recording the performance parameters of a three point linkageimplement force and depth transducer. Speci"cally, the vertical and the horizontal forces on mounted implements of categories II and III and the angular position of the linkage must be measured to determine the resultant force at di!erent measured implement depths.

2. Three-point linkage-implement force and depth transducer A three-point linkage-implement force and depth transducer was developed for a Massey Ferguson (MF) 3090 tractor as a tool for monitoring tractor performance. The details concerning the design and other aspects of the transducer can be found in Al-Janobi and Al-Suhaibani (1996). It was designed for use with mounted implements of categories II and III, measuring forces in the longitudinal and vertical planes. The lower links of the three-point linkage dynamometer were modi"ed to accommodate the sensing elements by preserving the original geometry and the use of the p.t.o. shaft was not restricted. A tension/compression load cell of maximum rated load of 100 kN was used in the centre portion of the standard top link. The extended octagonal ring transducer (EORT) design proposed by Godwin (1975) was used for instrumenting the lower links. This design has been widely used by researchers in the study of farm machinery with good results. Bandy et al. (1985) also successfully used this design in the bottom links of a three point linkage dynamometer. The EORT measures simultaneously a vertical load of up to 30 kN and a horizontal load of up to 60 kN at the ball end of the lower link. Mounted implements of categories II and III can be easily attached by the use of interchangeable steel bushes at the ball ends. These instrumented lower links can also be used on other tractors by providing additional pads at the lower links of the tractor. An RS rotary position transducer functioning as a potential divider was used to measure the implement depth and the angular position of the three point linkage dynamometer. This transducer with its hollow rotor coupled to a small D pro"le shaft attached to the rockshaft operates on the movement of the three point linkage dynamometer.

2.1. ¹hree point linkage forces Once the three-point linkage-implement force and depth transducer measures the forces on the three links and the rockshaft angle (angular position of the linkage),

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the three point linkage mechanism consists mainly of ties and pin joints to make the force calculation simpler. The values of the tie lengths in Fig. 1 were obtained from the tractor test report, (OECD, 1987). The relative position of all the pin joints with respect to the rear wheel axis can be calculated by using the rockshaft angle and the known tie lengths. The system can be modelled in two dimensions to represent the forces in the original geometric con"guration between the tractor and the implement. The force resolution procedure used in Bandy et al. (1985) was adapted in deriving the equations for the forces in the X> plane. They are given in Appendix A.

3. Data-acquisition system 3.1. Equipment

Fig. 1. End view of the geometry of the three point linkage dynamometer

the process of computing the resultant force is fairly straightforward. Figure 1 shows the side view of the three point linkage dynamometer geometry with respect to the rear wheel of the tractor. The dynamometer assumes that

The block diagram of the data-acquisition system developed to install on the MF 3090 tractor is shown in Fig. 2. The main part of the data-acquisition system was a Campbell Scienti"c CR7 datalogger mounted on a platform to the left of the tractor operator. The datalogger, with a wide range of instructions for scanning and sampling signals, was used to scan and record the output signals from the transducers in the system. The EORTs and the top link load cell were connected to the datalogger

Fig. 2. Block diagram of data acquisition system; EORT, extended octagonal ring transducer

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through the strain gauge ampli"er units, whereas the rotary position transducer was directly connected to it. The activity unit was used to provide excitation to both the datalogger and transducers with input supply from the tractor 12 V battery and also it was used to indicate the activity performed during "eld tests. The design and set-up of the strain gauge ampli"er and activity units are presented in Al-Suhaibani and Al-Janobi (1996). The personal computer located at the base station was used for developing datalogger programs and data analysis. The cassette tape recorder was used for loading program from the personal computer to the datalogger and for data storage during the "eld tests. The PC201 serial I/O card in the personal computer helped to transfer the sampled data stored in the cassette tape to the storage of the personal computer for further analysis. Communication could also be made between the PC201 serial I/O card and the control module of the datalogger with an optically isolated RS232 interface SC32A. This equipment was used to transfer the program to the datalogger and to view the required performance parameters on the personal computer console by a sample run of the test program. This helped to judge the validity of the program and hence to test the proper functioning of the dataacquisition system prior to moving the tractor from the base station for "eld tests.

3.2. Software and data collection A performance test program was documented for the datalogger to scan and sample the transducers every 1 s. A #ow chart of the data collection and storage routine is illustrated in Fig. 3. The program was transferred from the computer to the on-board datalogger and tested for its validity prior to the "eld test. The push button switch on the activity unit was used to start and stop execution of the program during the "eld test. During log on, the datalogger sampled data from the transducers in the system. These data were converted into the engineering units using the calibration constants and coe$cients and stored in the "nal storage bu!er of the datalogger. During this time, when the storage bu!er was full the stored data from it was automatically downloaded to the cassette tape. At the end of each test run, the push button switch was pressed to hold logging and the rest of the data in the storage bu!er was manually downloaded to the cassette tape. This procedure was repeated for a number of test runs until a set of data was collected. The data for each run were identi"ed by a number ranging from 1 to 6 provided by the datalogger. This number was generated corresponding to the voltage fed to the datalogger by positioning the rotary switch mechanism on a voltage divider circuit in

Fig. 3. Flowchart for the data collection and storage routine

the activity unit. At the end of the "eld test, the data stored in the cassette tape were transferred to the personal computer for "nal processing.

3.3. Calibration The EORTs and the top link load cell in the dynamometer were calibrated for known loads against a standard load cell of 100 kN in a specially designed and built calibration rig. The rotary position transducer was calibrated for known vertical positions of the ball end of the lower link and angular displacement of the three point linkage dynamometer. The constants and coe$cients from this calibration were used for measuring the implement depth and the angular position of the three point linkage dynamometer during the "eld test. The angular

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Table 1 Basic characteristics of the transducers in the system Sensitivity, mV/N V

Cross sensitivity, mV/N V

Hysteresis, %

Linearity, R2

¸eft EOR¹* Force coincident left Force perpendicular left

0)007524 0)032213

0)000604 0)000176

0)39 0)28

0)99 0)99

Right EOR¹* Force coincident right Force perpendicular right

0)007019 0)032635

0)000699 0)000092

0)26 0)25

0)99 0)99

¹op link transducer

0)007022

*

0)32

0)99

Rotary position transducer

9)104s

*

0)23

0)99

Transducer

* Extended octagonal ring transducer. smV/deg V; R2, coe$cient of determination.

position measurement was used for calculating the three point linkage forces. The details of the calibration procedure are given in Al-Suhaibani et al. (1994). Also, some basic characteristics of the transducers in the system had been evaluated. The numerical values of these parameters are presented in Table 1. They were well with in the accepted limits.

4. System performance To evaluate the data-acquisition system's capability to monitor the performance of the three-point linkage-implement force and depth transducer, "eld tests were conducted. Prior to the "eld tests, initial checkout and testing of the data-acquisition system were performed at the base station.

4.1. Field tests The "eld tests were performed in King Saud University's Agricultural Research and Experimental Farm at Dirab, where the soil was sandy loam consisting of 79% sand, 11% silt and 10% clay. The average cone index and moisture content, dry basis (d.b.) of the soil for a range of depths between 7 and 15 cm were 630 kPa and 10)2%, respectively. A 210 cm wide mounted-type chisel plough (Massey Ferguson}Denmark, Model MF 38, Serial no. L4078) with 13 shanks arranged on two tool bars was used for the "eld tests. The shanks were spaced 35)5 cm apart in each tool bar. The shank stem angle was 553, whereas the width of each shank was 7 cm.

A tractor speed of 2 km/h and implement depths of 7, 12 and 15 cm were selected for "eld tests. During the "eld tests, the tractor was operated in a suitable gear to attain the target speed. In order to obtain the implement depths during "eld operation, corresponding depths were preset in the base station. After conducting the "eld test for the "rst implement depth, the tractor was taken back to the base station for presetting the next implement depth. It was necessary because the presetting of implement depth needed changing the positions of both the top link and lift link of the three point linkage dynamometer. Wooden blocks of heights 7, 12 and 15 cm were used to preset the implement depths. For the "rst depth setting, the chisel plough was mounted on the instrumented tractor and then the three point linkage height lever in the tractor cab was operated to keep the plough resting on the #oor. The tractor, together with the implement, was pivoted such that the four wheels of the tractor were exactly on the top centre of four wooden blocks of same height (7 cm). The three point linkage height lever was operated to lower the implement to touch the #oor. The plough was levelled by adjusting the top link and lift link together. Then a chalk marking was provided against the present position of the three point linkage height lever to indicate the "rst depth. The top link and lift link lengths and mast height to be used in the force calculation were also measured. For the other each depth, prior to the "eld test, the same procedure was repeated and corresponding markings were provided against the three point linkage height lever to indicate the depths. Also the top link and lift link lengths and mast height were measured for each depth. Three test areas, each of 60 m long by 5 m wide were used for the "eld tests. These areas were in a single row

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and spaced with a practice area of 15 m by 5 m to achieve the same operating speed and the desired implement depth before entering the test area. Also the practice area between the test areas was helpful for the operator to control the data acquisition. Due to insu$cient area available in the experimental "eld, the test areas for the selected implement depths could not be randomized. To begin the "eld tests, the three point linkage height lever was operated to lower the implement corresponding to the "rst implement depth (7 cm). Then the tractor was accelerated to the required operating speed with a known gear range before entering the "rst test area. The data acquisition was activated by pressing the push button switch on the activity unit as the tractor passed the #ag marking the beginning of the "rst test area. Data acquisition continued until the end of the test area and it was stopped by pressing the push button switch again as the tractor passed the #ag showing the end of the test area. After "nishing the "eld test for the "rst implement depth, the tractor was taken back to the base station for the next depth setting. Depth setting was made as described above and the tractor was again driven straight towards the second test area with the same gear range and operating speed. While the tractor approaching the

test area, the implement was lowered corresponding to the implement depth, 12 cm before entering the test area. For the data acquisition, the same procedure was repeated as in the "rst test area. After presetting the implement depth at the base station, data acquisition was also performed in the third test area with the implement depth, 15 cm and the same operating speed. Data collected for the three implement depths were identi"ed by numbers 1}3 from the six positions of the microswitch on the activity unit.

4.2. Results and discussion All the sampled data from the three runs, one in each test area, were pooled in an Excel spread sheet to obtain a statistical description for the parameters: implement depth, tractor speed, horizontal, vertical, and resultant forces, and resultant angle (Table 2). Implement depth data were obtained from the rotary position transducer using its calibration constant and coe$cient, whereas tractor speed data were obtained from the optical shaft encoder coupled to the rear wheel of the tractor. The details of calibration of the shaft encoder and the speed

Table 2 Statistical description of some measured and calculated parameters of a mounted chisel plough Speed, km/h

Horizontal force, kN

Vertical force, kN

Resultant force, kN

Resultant angle, deg.

Preset implement depth, 7 cm Mean 6)94 Min. 6)52 Max. 7)40 Std. deviation 0)22 CV*, % 3)18 CNUs, % 13

2)66 2)32 2)89 0)13 4)97 22

3)61 3)17 4)17 0)24 6)65 28

2)65 2)43 2)88 0)10 3)68 17

4)48 4)04 4)92 0)21 4)64 20

36)31 31)45 39)68 1)97 5)42 23

Preset implement depth, 12 cm Mean 11)23 Min. 10)83 Max. 11)55 Std. deviation 0)17 CV*, % 1)55 CNUs, % 6

2)59 2)32 2)75 0)13 4)97 17

7)04 6)20 7)99 0)52 7)41 25

3)19 2)88 3)73 0)20 6)21 27

7)74 6)95 8)67 0)50 6)42 22

24)47 20)99 29)19 1)87 7)66 34

Preset implement depth, 15 cm Mean 14)22 Min. 13)58 Max. 14)69 Std. deviation 0)21 CV*, % 1)49 CNUs, % 8

2)59 2)32 2)89 0)15 5)62 22

11)22 10)25 12)75 0)77 6)90 22

3)48 3)06 3)98 0)21 6)01 26

11)75 10)72 13)26 0)77 6)54 22

17)30 14)33 19)31 1)11 6)43 29

Description

Depth, cm

* Coe$cient of variation. s Coe$cient of non-uniformity of readings,

max!min ]100. mean

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measurement are found in Al-Suhaibani et al. (1994). The other parameters were calculated using the force equations (Appendix A). The detailed discussion of the experiments and results concerning the performance of tractor}implement combination or any other related task is beyond the scope of this article. However, some measured and calculated parameters for a mounted chisel plough are presented in a table and in "gures to illustrate the capability of the data-acquisition system to monitor the "eld performance of the three-point linkage-implement force and depth transducer. Table 2 shows that the values of the coe$cient of variation for all the parameters were within the normal range of 10% about the mean (ASAE, 1994). These variations could be expected under "eld conditions. Thus, the data-acquisition system appeared to introduce no signi"cant adverse e!ects on the signals. The mean values of the three actual implement depths were very close to the preset depth values. The small di!erence was due to the bouncing of the tractor during the "eld tests. The mean tractor speed in all the three test areas were almost very close to each other. The mean value of horizontal force (draught) increased with increase in implement depth as expected and the values were in agreement with the draught data presented in the ASAE Standards (1994). The vertical force, almost dependent on the weight of the implement, was expected to give uniform mean values for all the three implement depths. The variation of the values could be due to the bouncing of the tractor during "eld operation that in

Fig. 5. Plot of the measured and calculated parameters versus time

Fig. 4. Positions of resultant force vectors for the three implement depths; , depth of 7 cm; , depth of 12 cm; , depth of 15 cm

turn could have a!ected the reading of the corresponding force-sensing elements of the EORTs. The mean values of the resultant force (total pull) and resultant angle varied in accordance with the implement depth. The resultant force positions corresponding to the three implement depths are shown in Fig. 4. With an increase in implement depth, the mean values of the

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resultant force increased and the resultant angle decreased correspondingly. This variation would be expected, implying that the horizontal force (draught) increased with increase in implement depth and vertical force remained almost constant. The variation in resultant force and resultant angle corresponding to the di!erent values of implement depth a!ect the coe$cient of traction C . It is more clear from the following relation T for the C . T H C " (1) T = where: H is the horizontal force (R cos h) in kN; = is the dynamic vertical load on the tractor rear wheel in kN; R is the resultant force in kN; and h is the resultant angle in deg. As C is one of the major parameters that describes the T tractor performance, so any change of C would a!ect T the performance of the tractor. The measured and calculated parameters from all the sampled data for the three implement depths were also presented in Fig. 5. This re#ects the variation of the sampled data collected from the three test areas for the di!erent implement depths. This variation for each parameter was within the normal range of variability and any one would expect this under "eld conditions. As illustrated, the system was capable of sensing rather small changes in any tractor parameter. 5. Conclusions A data-acquisition system was developed to monitor the performance of a three-point linkage-implement force and depth transducer for use in "eld operations. The system was tested in the "eld and its performance was found to be excellent. The consistent measurements showed the ability and accuracy of the data-acquisition system in "eld operations. Draught data obtained for a mounted chisel plough agreed with published data in a similar soil. The data-acquisition system together with the three-point linkage-implement force and depth transducer yielded an e!ective means of measuring the draught of mounted implements of categories II and III. However, further "eld tests under di!erent soil types and environments for the implements should be conducted to evaluate the performance of the system.

References Al-Janobi A; Al-Suhabani S A (1996). Performance of a three point linkage-implement depth transducer. Misr Journal of Agricultural Engineering, 13(3), 545}557 Al-Suhabani S A; Al-Janobi A (1996). An instrumentation system for measuring "eld performance of agricultural tractors. Misr Journal of Agricultural Engineering, 13(3), 516}528 Al-Suhaibani S A; Bedri A A; Babeir A S; Kilgour J (1994). Mobile instrumentation package for monitoring tractor performance. Agricultural Engineering Research Bulletin No. 40, King Saud University, Riyadh, p. 26 ASAE (1994). Agricultural machinery management data. Standards, 41st Edition, D497 Bandy S M; Babacz W A; Grogan J; Searcy S W; Stout B A (1985). Monitoring tractor performance with a three point hitch dynamometer and an onboard microcomputer. ASAE Paper No 85}1078 Barker G L; Smith L A; Colwick R F (1981). Three point hitch dynamometer for directional force measurement. ASAE Paper No. 81}1044 Chaplin J; Lueders M; Zhao Y (1987). Three point hitch dynamometer design and calibration. Applied Engineering in Agriculture, 3(1), 10}13 Clark R L; Adsit A H (1985). Microcomputer based instrumentation system to measure tractor "eld performance. Transactions of the ASAE, 28(2), 393}396 Garner T H; Dodd R B (1985). Application of a three point hitch dynamometer. ASAE Paper No. 85}107 Godwin R J (1975). An extended octagonal ring transducer for use in tillage studies. Journal of Agricultural Engineering Research, 20, 347}352 Grisso R D; Yasin M; Kocher M F (1994). Tillage implement forces operating in silty clay loam. ASAE Paper No. 94}1532 Lackas G M; Grisso R D; Yasin M; Bashford L L (1991). Portable data acquisition system for measuring energy requirements of soil-engaging implements. Computers and Electronics in Agriculture, 5, 285}296 McLaughlin N B; Heslop L C; Buckley D J; St. Amour G R; Compton B A; Jones A M; Van Bodegom P (1993). A general purpose tractor instrumentation and data logging system. Transactions of the ASAE, 36(2), 265}273 OECD (1987). OECD Test of an Agricultural Tractor (Restricted Code). Test Report No 6055, CEMAGREF Division MTAN, BP121-92164 ANTONY CEDEX Reece A R (1961). A three point linkage dynamometer. Journal of Agricultural Engineering Research, 6(1), 45}50 Reid J T; Carter L M; Clark R L (1985). Draft measurements with a three point hitch dynamometer. Transactions of the ASAE, 28(1), 89}93 Thomson N P; Shinners K J (1989). A portable instrumentation system for measuring draft and speed. Applied Engineering in Agriculture, 5(2), 133}137

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Appendix A S "(F #F ) cos a#(F #F ) sin a#F cos b x cl cr pr pl tl S "(F #F ) cos a!(F #F ) sin a!F sin b y pr pl cr cl tl

(A.1)

R"JS2#S2 x y S h"tan~1 y S x b!f#A sin c a"tan~1 !cos~1 a!e#A cos c

(A.3)

(a#A cos c!e)2#(b#A sin c!f )2#D2!¸2 ] 2 D J(a#A cos c!e)2#(b#A sin c!f )2 b"cos~1

(A.2)

(A.4)

(A.5)

2 S J(e#B cos a!c)2#(d!f#B in a)2 d!f#B sin a e!c#B cos a

A, B, ¸, S D M

S2#(e#B cos a!c)2#(d!f#B sin a)2!M2

!tan~1

where: a, b c, d e, f

(A.6)

F Fcl Fcr Fpl Fpr Stl Sx Ry h a b c

horizontal and vertical distances from the rear wheel axis to the pivot points of rockshaft, top link, and lower links, m lengths of rockshaft arm, lower links, lift link, and top link, m distance between lower link and lift link pivot points on lower link, m vertical distance between top link and lower link hitch points (mast height), m force coincident to the lower left link, kN force coincident to the lower right link, kN force perpendicular to the lower left link, kN force perpendicular to the lower right link, kN top link force, kN total horizontal forces (draught), kN total vertical forces, kN resultant force (pull), kN resultant angle (angle of pull), deg lower link angle, deg top link angle, deg rockshaft angle, deg