a joint positioning and attitude solving method for

Research ArticleA Joint Positioning and Attitude Solving Method for Shearer andScraper Conveyor under Complex Conditions

Jiacheng Xie12 Zhaojian Yang12 XuewenWang12 ShupingWang12 and Qing Zhang12

1College of Mechanical Engineering Taiyuan University of Technology Taiyuan China2Shanxi Key Laboratory of Fully Mechanized Coal Mining Equipment Taiyuan China

Correspondence should be addressed to Zhaojian Yang yangzhaojiantyuteducn

Received 7 July 2017 Accepted 24 September 2017 Published 26 October 2017

Academic Editor Michael Defoort

Copyright copy 2017 Jiacheng Xie et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In a fully mechanized coal-mining face the positioning and attitude of the shearer and scraper conveyor are inaccurateTo overcome this problem a joint positioning and attitude solving method that considers the effect of an uneven floor isproposed In addition the real-time connection and coupling relationship between the two devices is analyzed Two typesof sensors namely the tilt sensor and strapdown inertial navigation system (SINS) are used to measure the shearer bodypitch angle and the scraper conveyor shape respectively To improve the accuracy two pieces of information are fused usingthe adaptive information fusion algorithm It is observed that using a marking strategy the shearer body pitch angle canbe reversely mapped to the real-time shape of the scraper conveyor Then a virtual-reality (VR) software that can visuallysimulate this entire operation process under different conditions is developed Finally experiments are conducted on a prototypeexperimental platform The positioning error is found to be less than 038 times the middle trough length moreover noaccumulated error is detected This method can monitor the operation of the shearer and scraper conveyor in a highly dynamicand precise manner and provide strong technical support for safe and efficient operation of a fully mechanized coal-miningface

1 Introduction

As a key equipment of a fully mechanized coal-miningface the shearer plays a pivotal role in the coal pro-duction process The positioning and attitude informa-tion of the shearer determines the state of the corre-sponding scraper conveyor [1ndash3] and the correspondinghydraulic supports [4] therefore monitoring and deter-mination of the shearerrsquos running information are of sig-nificance with regard to realizing automated operation ofthree machines [5 6] The scraper conveyor mainly com-pletes tasks such as transporting and shipping out cuttingcoal running orbit of shearer overall pushing to the coalwall side with other corresponding equipment and cou-pling with the floor in real time Therefore the real-timeshape of the scraper conveyor is the key link between theuneven floor and the shearer position and attitude informa-tion

To date a few attempts have been made to detect thechange in the topography and fluctuation range of the floorusing tilt sensors installed in the shearer body [7] Based onreal-time detection results obtained for pitch and roll anglesthe cutting height was compensated in the process of shearermemory cutting [7] However the shearer body pitch anglewas the connecting line of the two supporting sliding shoeswhose distance was four-to-six times the middle troughlength It was easy to neglect the variation in coal seambetween the two supporting sliding shoes therefore the floordescribed by the shearer body pitch angle was not reliableowing to the nonsensitivity character in the uneven floor[8]

Wu et al [9 10] obtained an accurate changing trend ofthe floor by installing tilt sensors in every middle troughThis improved the coupling degree of the scraper con-veyor and the uneven floor In general in the advancingdirection of the working face the height of the roof and

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 3793412 14 pageshttpsdoiorg10115520173793412

2 Mathematical Problems in Engineering

floor changed slowly Mutations will only appear whenencountering geological structures such as faults and foldsHowever with gradual changes in the roof and floor theaccumulation of circular errors led to inaccurate positioningand attitude calculation for the shearer [11 12] Xu [13]put forward a three-dimensional (3D) positioning theorythat adopted the strategy of integrating stability and move-ment On the premise of being in the same diagonal ofthe supporting points of the two supporting sliding shoesLiu and Chen [14] established a digital model of the coalroof and floor Su et al [15] established a mathematicalmodel of the profile cutting of the shearer Ge [16] proposeda 3D fine geological model that enabled the shearer toadapt to complex terrain structures such as faults and foldsBased on the real-time dynamic correction strategy Feng[17] obtained the floor curve using a shearer kinematicsmodel

However the above-mentioned studies were not uni-versal to every condition owing to the idealization of theassumed conditions and nonconsideration of the couplingrelationship between the scraper conveyor and shearer

Regarding the positioning of the shearer significantresearch progress has been made [18ndash22] This includes thedevelopment of some accurate fusion positioning methodssuch as SINS and encoders [23ndash25] wireless sensor networks[26ndash28] infrared cameras [29] and geographic informationsystems [30] which yielded remarkable results howeverthese methods are still in the theoretical research stage andare not yet used in industrial applications

To overcome this barrier Zhang et al [31] proposeda method to detect the layout inspection of the scraperconveyor on the basis of the running trajectory and precisepositioning of the shearerThismethod efficiently reproducedthe theoretical results However the shearer prototype wasdriven by four small wheels and the scraper conveyorprototype was relatively simple and could not reflect theconnection between the actual shearer and actual scraperconveyor efficiently Owing to the unique and complex char-acteristics of the underground environment it was difficult toconduct a physical experiment

In some laboratories because of the heavy equipmentof the fully mechanized mining system and inability tocreate real uneven-floor conditions it is difficult to verifythe correctness of the method Therefore a prototype of theshearer and scraper conveyor must be designed to simulatethe underground working conditions

In this paper to overcome the abovementioned problemsa joint positioning and attitude solving method for shearerand scraper conveyor is investigated under complex condi-tions

2 Theoretical Analysis

21 Related Concepts of Shearer and Scraper Conveyor Theentire coordination process of threemachines in a fullymech-anized coal-mining face is in accordance with the shearerlocation and relevant regulations As shown in Figure 1 theshearer walks on the flexible scraper conveyor and cuts thecoal

In the process of shearer running the coal plate comesinto contact with the left and right supporting sliding shoesin themiddle trough and the left and right walking wheels aremeshed with the pin rails of the middle trough

Therefore there are two meshing relationships namelythe coupling relationship between the walking wheels andshape of pin rails and that between the supporting slidingshoes and coal plate These two relationships directly affectthe shearer pitch angle therefore it is necessary to analyzethe coupling relationship between the two groups

The pin rails are divided into two categories the mid-dle pin rails and the connecting pin rails Each pin railconnects to the corresponding middle trough with two pinshafts The middle pin rails move with the correspondingmiddle trough and keep the same center position of thecorresponding middle trough Meanwhile the connectingpin rails change correspondingly according to the horizontalinclination angle

22 Overall Design and Layout of Sensors Some double-axistilt sensors are installed in each middle trough to obtainthe horizontal and vertical inclination angle of each middletrough in real time (Figure 2)

23 Overall Framework In this paper the connecting andcoupling relationship between the shearer and scraper con-veyor is developed under complex conditions using thesensors installed in the equipment The general method is asfollows (Figure 3)

(1) The horizontal and vertical inclination angles of eachmiddle trough are obtained using double-axis tiltsensors arranged on each middle trough thereforethe shape of the scraper conveyor can be determined

(2) The shapes of the coal plate and the pin rails can beobtained on the basis of the analytical results obtainedfor a middle trough structure

(3) By setting the left supporting sliding shoe as thepositioning point of the shearer when the shearer is ata position corresponding to a position in the scraperconveyor the contacting mode of the two supportingsliding shoes and the coal plate is assessed and the keypoint coordinate of the left supporting sliding shoe isobtained

(4) The key point coordinate of the right supportingsliding shoe is obtained using the exhaustionmethod

(5) The shearer body pitch angle is solved by connectingthe key points of the two supporting sliding shoes

(6) The key points of two walking wheels are determinedby the key point coordinates of the two supportingsliding shoes and the shearer body pitch angle isdetermined on the basis of the left and right walkingwheels and pin rails

(7) Taking the above-mentioned point as prior knowl-edge the actual real-time shearer body pitch angleobtained using tilt sensors and SINS is reversely

Mathematical Problems in Engineering 3

(1) (2) (3) (4)

(5)(6)(7)

(1) (2) (3) (4)

(5)(6)(8)(7)

Shearer

Scraper conveyor

Figure 1 Related concepts of shearer and conveyor scraper (1) Left walking wheel (2) middle pin rails (3) connecting pin rails (4) rightwalking wheel (5) right supporting sliding shoe (6) coal plate (7) left supporting sliding shoe (8) middle rough

mapped to the shape of the scraper conveyor in theactual operation process thus the shearerrsquos walkingdistance and position relative to the scraper conveyorcan be obtained

24 Positioning and Attitude Solving Method for Shearer andScraper Conveyor

241 Positioning and Attitude Solving Method for ShearerThe shearer attitude described by the several key pointsshown in Figure 2 can be obtained using sensors installed inthe shearer bodyWhen a vertical inclination angle exists thecoordinates of these key points can be easily calculated byconverting and correcting all angles

242 Positioning and Attitude Solving Method for ScraperConveyor Suppose that the length of the middle trough is119871119885119861119862 and the horizontal and vertical inclination angles of themiddle trough 119899 are 120572119899 and 120573119899 respectively

A piecewise function of the middle troughs in the 119883119884plane (Figure 4) can be expressed as follows1198911 (119909) = 119909 tan1205721 0 le 119909 le 11990911198912 (119909) = 1198911 (1199091) + (119909 minus 1199091) tan1205722 1199091 lt 119909 le 1199092119891119899minus1 (119909) = 119891119899minus2 (119909119899minus2) + (119909 minus 119909119899minus2) tan120572119899minus1119909119899minus2 lt 119909 le 119909119899minus1119891119899 (119909) = 119891119899minus1 (119909119899minus1) + (119909 minus 119909119899minus1) tan120572119899119909119899minus1 lt 119909 le 119909119899

(1)

where 119909119894 is the boundary point of the middle trough 119894 in the119883 coordinateBy setting the key point 1198741 which is located at the 119901

position of the middle trough 119896 119904119871119885119861119862 = 119896 sdot sdot sdot 119901 where 119904 isthe shearer walking length relative to the scraper conveyor


(1) (2) (3) (4) (5) (6)

(7)(8)(9)(10)(11)(12)

Figure 2 Connection relationship between the shearer and scraper conveyor and sensor arrangement (1)Hinge point of the left arm and body(characteristic point E1) (2) tilt sensors installed in the shearer body (3) SINS device (4) key point of the left walking wheel (characteristicpoint D1) (5) key point of the right walking wheel (characteristic point D2) (6) hinge point of the right arm and body (characteristic pointE2) (7) key point of the right supporting sliding shoe (characteristic point O2) (8) coal plate (9) middle pin rails (10) connecting pin rails(11) key point of the left supporting sliding shoe (characteristic point O1) (12) double-axis tilt sensor installed in every middle trough

The horizontal and vertical inclination angles of each middle trough

The shape of the coal plate The shape of the pin rails

The shape of the scraper conveyor

Full contact (a) semicontact(b) suspending (c)

Right supportingsliding shoe

Left supporting sliding shoe

Right walking wheel

Left walking wheel

Trend of shearer body pitch angle incurrent shape of scraper conveyor

characteristic point O2


characteristic point D2


Reversely mapped to theshape of scraper conveyor

The shearerrsquos real-time walking lengthand position relative to the scraperconveyor

Actual real-time shearer body pitch angle

Marking strategy

Tilt sensors SINS

Adaptive weighted fusion algorithm

VR simulation software

Figure 3 Research process

119896 is the serial number of the middle trough and 119901 is theposition of the middle trough 119896 (119909119896 119910119896) and (119909119901 119910119901) can becalculated Here (119909119896 119910119896) is the coordinate of hinge joint 119896 ofthe scraper conveyor and (119909119901 119910119901) is the coordinate offset of

the 119901 position of scraper conveyor 119896 relative to the point (119909119896119910119896)Therefore if the running distance is 119904 the coordinates can

be expressed as follows


The shape of coal plateThe shape of scraper conveyor

The shape of pin rails

y

O 1

h

2

nminus1

x

n

Figure 4 Shape of a scraper conveyor

119909119904 = 119909119896 + 119909119901 = 119871119885119861119862 119896sum119894=1

cos120572119894 + 119871119885119861119862 lowast 119901 lowast cos120572119896+1119910119904 = 119910119896 + 119910119901 = 119871119885119861119862 119896sum

119894=1

sin120572119894 + 119871119885119861119862 lowast 119901 lowast sin120572119896+1(2)

25 Analysis of Coupling Positioning and Attitude Relationshipbetween the Shearer and Scraper Conveyor

251 Coupling Relationship between Supporting Sliding Shoesand Coal Plate

(1) Contacting Modes of Supporting Sliding Shoes and CoalPlates The shearer body pitch angle reflects the fluctuationdegree between the left and the right supporting sliding shoesBased on a theoretical analysis we obtained three contactingmodes between the supporting sliding shoes and coal plateas shown in Figure 5

(a) Full contact the base line of the supporting slidingshoe is parallel to the coal plate

(b) Semicontact the supporting sliding shoe is at theintersection position of the two adjacent middletroughs and can only come into contact with onemiddle trough

(c) Suspending the supporting sliding shoe is at theintersection position of the two adjacent middletroughs and cannot come into full contact with anyof the two middle troughs

The determination rule of the contacting mode is shownin Table 1

Points119860 119861 and119874 are the left right andmiddle points ofthe base line of the supporting sliding shoes respectively NaNb and No are the serial numbers of the middle trough thatpoints 119860 119861 and 119862 belong to respectively and FloatHA[119894] isthe horizontal inclination angle of the middle trough 119894(2) Analysis of the Contacting Mode between the SupportSliding Shoes and Coal Plate There are three contactingmodes between the supporting sliding shoes and the coalplate Taking the semicontact case which is themost complexcondition as an example the shearer attitude and positionparameters can be obtained using the followingmethodThismethod is known as the suspending solving algorithm andits parameters are shown in Figure 6 where 119883119860 119883119861 1205791 and1205792 are unknown parameters and 119871119867 and 120576 are structuralparameters Among them Na = 119901 and Nb = 119901 + 1

According to the relationship we can list the followingequations

119883119861 minus 119883119860 = (2119871119867 cos 120576) lowast cos (1205791 + 120572119901)1198831198741 minus 119883119860 = 119871119867 cos (120576 + 1205791 + 120572119901)(119883119861 minus 119883119862) cos120572119901+1sin 1205791 = 2119871119867 cos 120576

sin (120587 minus (120572119901+1 minus 120572119901))1198721 = minus2 lowast 119871119867 lowast cos (120576) lowast sin (120572119901) + 119871119867 lowast sin (120576 + 120572119901) minus 119862 lowast cos (120572119901+1)119883119862 minus 11988311987411198722 = 2 lowast 119871119867 lowast cos (120576) lowast cos (120572119901) minus 119871119867 lowast sin (120576 + 120572119901)119883119862 minus 11988311987411198723 = 2 lowast 119871119867 lowast cos (120576)sin (120572119901+1 minus 120572119901)120574 = arcsin( 1198722radic11987212 +11987222)

(3)


Table 1 Determination rule of the contacting mode

Mode Meaning Condition Calculation angle

0 Full contact the supporting sliding shoe isfully located in a middle trough

(1) Na = Nb(2) Na = Nb and FloatHA[Na] = FloatHA[Nb] Na

10 Semicontact in the range of the middletrough Na

(1) Na = Nb and Na = No1 FloatHA[Na] gtFloatHA[Nb] Na

11 Semicontact in the range of the middletrough Nb

(1) Na = Nb and Nb = No1 FloatHA[Na] gtFloatHA[Nb] Nb

2 Suspending (1) Na = Nb and FloatHA[Na] lt FloatHA[Nb] Suspending solvingalgorithm

(a) (b) (c)

Figure 5 Contacting model between the supporting sliding shoes and coal plate

where11987211198722 and1198723 are the three middle variables and 120574is the middle angle

Solution

1205791 = 1205872 minus 120574119883119860 = 1198831198741 minus 119871119867 cos (1205791 + 120572119901 + 120573)119883119861 = 1198831198741 + 2119871119867 cos120573 lowast cos (1205791 + 120572119901)

minus 119871119867 cos (1205791 + 120572119901 + 120573) (4)

So 1198841198741 can be expressed as follows

1198841198741= 119891 (119883119860) + 119871119867 sin (1205791 + 120572119901 + 120573) 1198731198741 = 119901119891 (119883119860) + 119871119867 sin (1205791 + 120572119901+1 + 120573) 1198731198741 = 119901 + 1

(5)

where for 1198731198741 the number of middle troughs it belongs tomust be determined

(3) Shearer Body Pitch Angle After determining the conditionof the left supporting sliding shoe the condition of the rightsupporting sliding shoe must be assessed

A p

LH

C

2

1p+1

B

O1

Figure 6 Analysis under semicontact condition

Point 1198742 coordinates can be solved by the followingformula 1198831198742 = 1198831198741 + 119871119895119904 cos1205721198951199041198841198742 = 1198841198741 + 119871119895119904 sin120572119895119904 (6)

where120572119895119904 is the shearer body pitch angle and119871119895119904 is the shearerbody length (the connection length between point 1198631 andpoint1198632)

There are nine possible conditions under which thecontacting mode of the two supporting sliding shoes isconsidered simultaneously


Output

Stop

Yes

No

Yes

No

s k p

s + 001k

S lt S1

(b) suspending (c)

(b) suspending (c)

js

XO1 XO2 + 01 mm

O1 state full contact (a) semicontact


YO1

XO2 = XO1 + Ljs minus Ljs lowast 02

XO2 YO2

YO2

minus01 ＧＧ lt LO1O2 minus Ljs lt 01 ＧＧ

LO1O2

Figure 7 Flow chart of the solving method

Owing to the difficulty in calculating the condition ofthe right sliding shoe using a direct method the indirectcalculation method is used as shown in Figure 7

In Figure 7 1198781 is the limit position of the shearer walkingon the scraper conveyor

When the 1198831198741 coordinate increases the distance to 08times the length of the shearer body the 1198831198742 coordinatecan be analyzed and the contacting mode can be assessedThereby the corresponding algorithm was used to solve theproblem

Based on the condition of the distance and the shearerbody length the1198831198742 coordinates were assessed by comparingthe 1198831198741 coordinates If an error exists in a small range thesolution would be correct If an error does not fall withinthis range the unit operation length would be increased tothe1198831198742 coordinates and assessment would continue until thecondition was satisfied and the correct 1198742 point coordinatescould be solved

Therefore the shearer body pitch angle could be calcu-lated as follows

120572119895119904 = tan 1198841198742 minus 11988411987411198831198742 minus 1198831198741 (7)

According to the shape of the scraper conveyor the leftand right supporting sliding shoes must rotate around points1198741 and 1198742 respectively thus they affect the shearer bodypitch angle

252 Coupling Relationship between Guide Sliding Shoes andthe Shape of Pin Rails

(1) Analysis of the Shape of Pin Rails Due to a small changein the vertical inclination angle the connecting pin rails arebent along the shape of the two adjacent middle troughs andtheir pitch angle is half the sum of the horizontal inclinationangles of the two adjacent middle troughs

The horizontal inclination angle of the middle pin rails isgiven as follows 120579119872119894 = 120572119894 (8)

The horizontal inclination angle of the connecting pinrails is given as follows

120579119873119894 = (120572119894 + 120572119894+1)2 (9)

The curvilinear equation of the pin rails can be expressedaccording to the coordinate of each axle hole therefore theequation of the pin rails can be expressed as follows1198921 (119909) = 119884119872119883119875 (1) + (119909 minus 119883119872119883119875 (1)) lowast tan 1205791198721119883119872119883119875 (1) le 119909 le 119883119873119883119875 (1)1198922 (119909) = 119884119873119883119875 (1) + (119909 minus 119883119873119883119875 (1)) lowast tan 1205791198731119883119873119883119875 (1) lt 119909 le 119883119872119883119875 (2)


1198922119894minus1 (119909) = 119884119872119883119875 (119894) + (119909 minus 119883119872119883119875 (119894)) lowast tan 120579119872119894119883119872119883119875 (119894) le 119909 le 119883119873119883119875 (119894)1198922119894 (119909) = 119884119873119883119875 (119894) + (119909 minus 119883119873119883119875 (119894)) lowast tan119873119894119883119873119883119875 (119894) lt 119909 le 119883119872119883119875 (119894 + 1)

(10)

where (119883119872119883119875(119894) 119884119872119883119875(119894)) and (119883119873119883119875(119894) 119884119873119883119875(119894)) are thecoordinates of the left and right axle holes of middle trough 119894respectively

(2) Coordinate Analysis of Walking Wheels Coupled with thecurve of the pin rails points1198631 and1198632 can be calculated onthe basis of points 1198741 and 1198742 The shearer body pitch angleis verified and the vertical inclination angle is adjusted untilthe shearer body pitch angle is equal to the value calculated inSection 241 In contrast the vertical inclination angle mustbe compensated

26 Fusion Strategy of Positioning and Attitude Based on theInformation Fusion Strategy

261 Information Fusion Strategy The SINS and tilt sensorsare used to measure two variables the shearer body pitchangle and the horizontal and vertical inclination angles ofevery middle trough

At different temperatures and in different environmentselectromagnetic interference easily affects the sensors bycausing noise and error this means that the drifting phe-nomenon of original data could possibly occur in a single sen-sor and that the true operation state of shearer and conveyormay not be accurately displayedThus the information fusionalgorithm was used to improve the two variables using twosensors

The theoretical values were obtained using the simulationresult and the information fusion value of the middle troughobtained by two sensors and the shearer body pitch angleswere corrected and fused with the information fusion algo-rithm in real time

Therefore the multisensor information fusion algorithmwhich uses multiple data collected from multiple sensors atdifferent times marks the actual state of two devices

The premise of the adaptive algorithm is the batchalgorithm so it is necessary to explain it

The batch estimation algorithm and adaptive weightedfusion algorithm are used for calculation

(1) Batch Estimation Algorithm 119901 measurement datum[1205741 1205742 120574119901] collected by one sensor at regular intervals isdivided into two groups

(1) When119901 is odd the two groups are [1205741 1205742 120574(119901+1)2]and [120574(119901+1)2 120574(119901+1)2+1 120574119901]

(2) When 119901 is even the two groups are [1205741 1205742 1205741199012]and [1205741199012+1 1205741199012+2 120574119901]

Taking the second case as an example we analyzed thefollowing

The arithmeticmean 1205741 and themean square deviation 1205901of the first set measurements are

1205741 = 11199012 1199012sum119894=1

1205741198941205901 = radic 11199012 minus 1 1199012sum

119894=1

(120574119894 minus 1205741)(11)

The arithmeticmean 1205741 and themean square deviation 1205901of the second set measurements are

1205742 = 11199012 119901sum119894=1199012+1

1205741198941205902 = radic 11199012 minus 1 119901sum

119894=1199012+1

(120574119894 minus 1205741)(12)

The batch estimation 120574 and variance 1205902119894 of the singlesensor could be calculated using the following formula

120574 = 120590221205741 + 12059012120574212059012 + 120590221205902 = 12059012 ∙ 1205902212059012 + 12059022

(13)

The angles calculated by the above algorithms weretaken as the accurate results using which the next step wascalculated and analyzed

Prior knowledge of the tilt sensor and SINS was notrequired and the adaptive weighted fusion algorithm couldbe obtained using the value of the batch estimation angleWorking independently every angle measured by the tiltsensor or SINS is interfered with by factors such as noise andvibration therefore the angle value calculated by the optimalangle is random and could be expressed as follows120574119898 minus (119906119898 120590119898) (14)

where 119906119898 is the expected value and 120590119898 is the varianceMutually independent of each other theweighting factors

of the tilt sensor11988211198822 119882119898 and 1205741 1205742 120574119898 are usedto perform information fusion therefore 120574 the value ofintegration needs to satisfy the following relations

120574 = 119898sum119894=1

119882119894120574119894119898sum119894=1

119882119894119894 = 1(15)

The optimal weighting factor corresponding to the mini-mum total variance is obtained using the following formula

119882119894 = 11205901198942sum119911119894=1 (11205901198942) (16)


Table 2 The shearer body pitch angle measured by tilt sensors and SINS (units degrees)

TypeValue

Group 1 Group 21 2 3 4 5 6 7 8 9 10

SINS 1352 1361 1363 1367 1353 1349 1352 1367 1369 1363Tilt sensor 1369 1370 1390 1384 1384 1369 1371 1382 1386 1387

Table 3 Measured values for the SINS and tilt sensor and fusion values (units degrees)

Tilt sensor SINS

Group 1 Mean value 13794 13592Mean square deviation 00088 00042


Batch estimation algorithm Fusion value 13792 13594Variance 558119890 minus 5 139119890 minus 5

Adaptive weighted fusion algorithm Fusion value 13664Weighting factor 0354 0646

The acquisition frequency of the sensor is determined tobe 50ms Owing to the shearer haulage speed being generallywithin the range of 6ndash8mmin the walking length is small at05 s Therefore the 10 sets of data collected on the tilt sensorand SINS (Table 2) were used infusion and batch fusionrespectively then the accurate shearer position relative to thescraper conveyor by the adaptive weighted fusion could beobtained In this paper the fusion values obtained using theadaptive weighted fusion algorithm are shown in Table 3

In this way a series of data is calculated as shown inTable 4

262 ReverseMappingMethod Based on Prior Knowledge Byconsidering this result obtained by the simulation as priorknowledge the fusion value of the shearer body pitch angleobtained using two sensors in real time corresponds to thereverse shape of the scraper conveyor In particular somekey inflection positions must be corrected in order to bedetermined according to the measured value

As shown in Figure 8 the theoretical curve is first dividedinto some blocks corresponding to several stages including119860 119861 119872 and boundary points marked as 1198861015840 1198871015840 1198981015840

From prior experience in the actual operation of theshearer some points such as 1198861015840 1198871015840 1198981015840 are used to correctand verify the theoretical points in real time including points119886 119887 119898 Thus every interval can be determined thenthe shearer position is reversely mapped to the shape of thescraper conveyor

27 Planning Software Based on Unity3d

271 VR Simulation Software The models were obtainedusing the UG software and could access the Unity3d softwarethrough model repairing and conversion The virtual scene

The position of scraper conveyora middle trough length

Measurement curveTheoretical curve

b

c

d

e

f g

hj k l

m

A B C D E F G H I J K L M N

minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6

ii

a

ab

c

d

e

f

g

ℎ(j)(k) l

m

Figure 8 Reverse mapping method

was arranged according to specific rules By integrating all thealgorithms this software could conduct various simulationsunder different conditions A visual GUI was responsible forsetting some simulation parameters which included bodylength and structural parameters The real-time processingdatum could be output to an XML file which was easy toanalyze as shown in Figure 9

The shape of the scraper conveyor could be estimatedusing the input parameters of every middle trough Tocoordinate the virtual shape of the scraper conveyor thewalking position and the attitude of the shearer were cal-culated backstage in real time The shearer position wascalculated according to the virtual shearer haulage speedwhich was decided by an increment and the shearer positionwas reversely mapped to the shape of the scraper conveyor


Table 4 The measured value of SINS and the tilt sensor and thefusion value (units degrees)

Number SINS Tilt sensor Fusion value(1) 136 1379 13664(2) 132 1331 13233(3) 143 1421 14273(4) 129 1291 12903(5) 124 1331 12673(6) 59 612 5966(7) 83 807 8231(8) 42 401 4143(9) 57 533 5589(10) 44 46 446(11) 03 083 0459(12) 13 146 1348(13) 83 874 8432(14) 12 129 1227(15) minus07 038 minus0376(16) 0 02 006(17) minus56 minus563 minus5609(18) 13 056 1078(19) 55 528 5434(20) 02 007 0161(21) 06 008 0444(22) 04 016 0328(23) minus82 minus88 minus838(24) 07 015 0535(25) minus1 minus142 minus1126(26) minus08 minus121 minus0923(27) minus18 minus146 minus1698(28) minus02 minus073 minus0359(29) 01 minus032 minus0026(30) minus09 minus13 minus102(31) minus13 minus145 minus1345(32) minus22 minus26 minus232(33) minus66 minus708 minus6744(34) minus12 minus107 minus1161(35) minus84 minus872 minus8496

3 Experiments and Results

31 Test Prototype Three machines in our laboratory wereselected as the research objects The type of the scraperconveyor was SGZ764630 The type of the shearer wasMGTY250600 and its body length was 5327mm

Therefore a prototype shearer and scraper conveyorwhose sizes were 133 of the size of the original equip-ment were designed and manufactured This enabled moreconvenient and faster experimentation (Figure 10) Using the

scraper conveyor prototype we were able to achieve thefollowing (1) variable shapes of the scraper conveyor couldbe formed (2) in a different connection state of the middletroughs the curve formed by the pin rails directly influencedthe running trajectory of the shearer (3) in a differentconnection state of the middle troughs the contacting modebetween the support sliding shoe and the coal plate could besimulated (4) a tilt sensorwas installed in themiddle positionof every middle trough to mark the horizontal and verticalinclination angles in real time

Using the shearer prototype we could achieve the follow-ing (1) the shearer body length could be changed (2) coupledwith the coal plate the supporting sliding shoes could self-adapt (3) two walking wheels were perfectly replaced by twotires which could simulate the movement of the shearer (4)a SINS device and a double-axis tilt sensor were installed inthe position of the left supporting sliding shoe

32 Static Experiment The shape of the scraper conveyorprototype was placed as in Figure 10(a) and tilt sensors wereinstalled on every middle trough Each middle trough wasmarkedwith five key points which divided themiddle troughinto five parts on an average

The shearer position is successively decided at every keypoint belonging to the five key points of each middle troughSeries values of the shearer body pitch angle were read andrecorded at every key point

The datum of every middle trough tilt angle measuredby the tilt sensors and SINS was imported to the Unity3dsimulation software and two simulation curves were outputThe two theoretical curves of the shearer body pitch anglemeasured by the Unity3d simulation software and the twoactual curves of the shearer body pitch angle measured by thetwo sensors are shown in Figure 11

As we can see from Figure 11 the variation trend of theshearer body pitch angle is basically the same as that observedin the theoretical analysis in addition the maximum differ-ence is 053∘Thepositioning error of the shearerwas less than038 times the middle trough length

33 Dynamic Experiment The static experiment cannotdetermine the properties and measurement accuracy of thesensors in the actual process of dynamic operationThereforeit was necessary to conduct a dynamic experiment in orderto study the dynamic operation properties of the two types ofsensors under the condition in which the shearer prototypecould operate along with the shape of the scraper conveyorprototype automatically

After pressing the operation button the shearer startedrunning and the shearer body pitch angle in the runningprocess was recorded using two types of sensors in real time

After selecting the shearer body length as 5327mm thetest was conducted five times The comparison results of themeasurement values obtained using the two types of sensorsand the theoretical values obtained using the VR software areshown in Figures 12 and 13

The analysis showed that the tilt sensor was more fluc-tuant in the process of shearer dynamic operation and thatit was easily disturbed by environmental noise Moreover


Table 5 Comparison of experimental results of shearer positioning (units a middle trough length)

Theoretical value Shearer body pitch anglemeasured by the tilt sensors

Shearer body pitch anglemeasured by SINS

Shearer body pitch anglemeasured according to the

fusion valueTheoretical value measured by the tilt sensors 073 059 042Theoretical value measured by SINS 067 049 045Theoretical value measured according to thefusion value 053 047 038

No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical

Scraper conveyor1325

1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

left supporting sliding shoe

right supporting sliding shoe

left drum height

right drum height

left rocker rotation angle

right rocker rotation angle

m

Shearer

Figure 9 Interface of the Unity3d simulation software under complex conditions

owing to the interdesign of filtered characteristic the SINSshowed good seismic performance

The variation trend of the shearer body pitch angle wasbasically the same as that observed in the theoretical analysisHowever the deviations between the two sensors and thetheoretical values were greater than those obtained in thestatic test Positioning correction caused by the numericallymeasured value may lead to a location error Therefore itwas necessary to predict and correct the result in real timeusing the adaptive information fusion algorithm The curvesobtained after processing are shown in Figure 14

According to the analysis result obtained using the twosensors the shearerrsquos position relative to the shape of thescraper conveyor can be reversely inferred After processingwith the adaptive fusion algorithm the position of the shearercould meet the high level of positioning accuracy under the

static condition which was 038 times the middle troughlength that could be reached (Table 5)

34 Experiments under Different Body Lengths At differentshearer body lengths the variation trends of the shearer bodypitch angle were studied The shearer body lengths were setas 4500 4900 5327 5800 and 6300mm which refer to aseries of specialized shearer Under these five conditions allthe experimental results were consistent with the theoreticalcurves (Figure 15) and two conclusions were drawn

(1) A shorter shearer body length corresponded to a morebackward shearer to the shape of the scraper conveyor andwas more sensitive to terrain changes a longer shearer bodylength corresponded to an earlier adaptation of the shearerto terrain changes and the shearer being more insensitive toterrain changes


(a)

(b)

(c)

(d)(e)

Figure 10 (a) Shape of the scraper conveyor (b) the two sensors installed in the shearer body (c) the supporting sliding shoe (d) the walkingwheel (e) the shearer prototype

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6


Measurement curve using SINS

Measurement curve using tilt sensorsTheoretical curve using SINS

Theoretical curve using tilt sensors

minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

Figure 11 Results of the static test


0 5 10 15 20 25 30The position of scraper conveyora middle trough length

Theoretical curve using SINSMeasurement curve using SINS

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees

Figure 12 Comparison of the results obtained using SINS with thetheoretical results


Measurement curve using tilt sensorsTheoretical curve using tilt sensors

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees

Figure 13 Comparison of the results obtained using the tilt sensorswith the measurement results

(2) The longer the shearer body length the smaller therelative change in the pitching angle under the same shape ofthe scraper conveyor

4 Conclusions

In this study a joint positioning and attitude solving methodwas proposed and investigated for shearer and scraper con-veyor under complex conditions The following conclusionswere drawn

(1) This method can provide more precise dynamicmonitoring for the operation of shearer and scraper conveyorBy obtaining the shape of the scraper conveyor in real timethe shearer can be used in advance to predict and regulate theoperating attitude in the current cycle

(2) Based on this method the cutting trajectory of thefront and rear drums can be calculated in real time providingstrong support for the memory cutting method in a fullymechanized coal-mining automation face

(3) No error accumulated Hence this positioningmethod of the shearer could integrate existing positioningmethods including the SINS positioning method infraredpositioning method walking shaft encoder positioningmethod and UWB wireless sensor positioning method



Theoretical fusion curveMeasurement curve using tilt sensors

Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees

Figure 14 Theoretical values and fusion values of the two sensormeasurements

116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees

Figure 15 Variation trend of the shearer body pitch angle underdifferent shearer body lengths

These methods realize a more precise positioning for theshearer in actual composite conditions

(4)This method provides support for the 3D coordinatedpositioning of fully mechanized coal-mining equipment

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by Shanxi Postgraduate EducationInnovation Project under Grant 2017BY046 Shanxi Schol-arship Council of China under Grant 2016-043 Programfor the Outstanding Innovative Teams of Higher LearningInstitutions of Shanxi under Grant 2014 and Natural ScienceFund of Shanxi Province under Grant 201601D011050


References

[1] P Przystalka and A Katunin ldquoA concept of automatic tuningof longwall scraper conveyor modelrdquo in Proceedings of theFederated Conference on Computer Science and InformationSystems (FedCSIS rsquo16) pp 11ndash14 Gdansk Poland September2016

[2] K Cenacewicz and A Katunin ldquoModeling and simulationof longwall scraper conveyor considering operational faultsrdquoStudia Geotechnica et Mechanica vol 38 no 2 pp 15ndash27 2016

[3] O Stoicuta and T Pana ldquoModeling and simulation of the coalflow control system for the longwall scraper conveyorrdquo Annalsof the University of Craiova Electrical Engineering Series vol 40pp 101ndash108 2016

[4] A Stentz M Ollis S Scheding et al ldquoPosition measurementfor automated mining machineryrdquo in Proceedings of the Inter-national Conference on Field and Service Robotics pp 299ndash304Agapito Associates Pittsburgh Pa USA August 1999

[5] S K Michael and D W Hainsworth ldquoOutcomes of the land-mark long-wall automation project with reference to groundcontrol issuesrdquo in Proceedings of the 24th International Con-ference on Ground Control in Mining pp 66ndash73 AgapitoAssociates Morgantown WVa USA 2005

[6] G A Einicke J C Ralston C Hargrave D C Reid and DW Hainsworth ldquoLongwall mining automation an applicationof minimum-variance smoothingrdquo IEEE Control Systems Mag-azine vol 28 no 6 pp 28ndash37 2008

[7] C S Liu ldquoMathematic principle for memory cutting on drumshearerrdquo Journal of Heilongjiang Institute of Sciences and Tech-nology vol 20 pp 85ndash90 2010

[8] L Yin J Y Liang Z C Zhu et al ldquoSimulation analysis of coalfloor undulation based on long wall working facerdquo Coal MineMachinery vol 31 pp 75ndash77 2010

[9] P LWu andN PNiu ldquoResearch and analysis of the relationshipbetween the angle of scraper and the working facerdquo ElectronicsWorld vol 16 pp 98-99 2012

[10] W F Jiang S B Li J F Niu et al ldquoA scraper conveyorattitude control system and control method based on wirelessthree-dimensional gyroscope technologyrdquo China Parent CN102431784 A 2012

[11] Y L Suo ldquoMechanism and control of the floor undulation of theslicing fully mechanized facesrdquo Journal of XianMining Institutevol 19 pp 101ndash104 1999

[12] R G Zhang and D W Si ldquoAnalysis on angle of tilt andoffset angle influencing on characteristic of scraper conveyorrdquoZhongzhou Coal vol 12-13 2005

[13] Z P Xu Study on the key technologies of self-adaptive cuttingfor shearer [Dissertation] China University of Mining andTechnology Xuzhou China 2011

[14] C S Liu and J G Chen ldquoMathematicmodel of memory cuttingfor coal shearer based on single demo kniferdquo Coal Sciences andTechnology vol 39 pp 71ndash73 2011

[15] X L Su Z S Lian and C Y Zhang ldquoResearch on mathematicmodel of memory cutting for coal shearer based on doubledemo kniferdquo Coal Mine Machinery vol 35 pp 55ndash57 2014

[16] Z L Ge Study on shearer self-adaptive control based on itsabsolute position and attitude [Dissertation] China Universityof Mining and Technology Xuzhou China 2015

[17] S Feng Study on the key technologies of relative position fusionand correction system between shearer and hydraulic support[Dissertation] China University of Mining and TechnologyXuzhou China 2015

[18] B Sofman J A Bagnell A Stentz et al Terrain classificationfrom aerial data to support ground vehicle navigation [Disserta-tion] Carnegie Mellon University Pittsburgh Pa USA 2006

[19] Y Hai L I Wei C M Luo et al ldquoExperimental studyon position and attitude technique for shearer using SINSmeasurementrdquo Journal of China Coal Society vol 39 pp 2550ndash2556 2014

[20] D C Reid DW Hainsworth J C Ralston et al ldquoShearer guid-ance a major advance in longwall miningrdquo in Field and ServiceRobotics vol 28 pp 469ndash476 Springer Berlin Germany 2006

[21] J Ralston D Reid C Hargrave and D Hainsworth ldquoSensingfor advancingmining automation capability A review of under-ground automation technology developmentrdquo InternationalJournal ofMining Science and Technology vol 24 no 3 pp 305ndash310 2014

[22] MDunnD Reid and J Ralston ldquoControl of automatedminingmachinery using aided inertial navigationrdquo in Machine VisionandMechatronics in Practice pp 1ndash9 Springer Berlin Germany2015

[23] D C ReidM T Dunn P B Reid and J C Ralston ldquoA practicalinertial navigation solution for continuous miner automationrdquoin Proceedings of the 12th Coal Operatorsrsquo Conference Universityof Wollongong the Australasian Institute of Mining and Met-allurgy pp 114ndash119 The Australasian Institute of Mining andMetallurgy Wollongong Australia 2012

[24] S Hao S Wang R Malekian B Zhang W Liu and Z LildquoA geometry surveying model and instrument of a scraperconveyor in unmanned longwallmining facesrdquo IEEEAccess vol5 pp 4095ndash4103 2017

[25] A Li S Q Hao S B Wang et al ldquoExperimental study onshearer positioning method based on SINS and Encoderrdquo CoalScience and Technology vol 44 pp 95ndash100 2016

[26] B H Ying W Li C M Luo et al ldquoExperimental study oncombinative positioning system for shearerrdquo Chinese Journal ofSensors and Actuators pp 260ndash264 2015

[27] Q Fan W Li J Hui et al ldquoIntegrated positioning for coalmining machinery in enclosed underground mine based onSINSWSNrdquo The Scientific World Journal vol 2014 Article ID460415 12 pages 2014

[28] V Henriques and R Malekian ldquoMine safety system usingwireless sensor networkrdquo IEEEAccess vol 4 pp 3511ndash3521 2016

[29] J C Ralston ldquoAutomated longwall shearer horizon controlusing thermal infrared-based seam trackingrdquo in Proceedings ofthe IEEE International Conference on Automation Science andEngineering vol 8 pp 20ndash25 August 2012

[30] S R Ge Z S Su A Li et al ldquoStudy and application ofpositioning and orientiation of shearer based on geographicinformation systemrdquo Journal of China Coal Society vol 40 pp2503ndash2508 2015

[31] Z Zhang S B Wang B Y Zhang et al ldquoShape detection ofscraper conveyor based on shearer trajectoryrdquo Journal of ChinaCoal Society vol 40 pp 2514ndash2521 2015

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Journal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


floor changed slowly Mutations will only appear whenencountering geological structures such as faults and foldsHowever with gradual changes in the roof and floor theaccumulation of circular errors led to inaccurate positioningand attitude calculation for the shearer [11 12] Xu [13]put forward a three-dimensional (3D) positioning theorythat adopted the strategy of integrating stability and move-ment On the premise of being in the same diagonal ofthe supporting points of the two supporting sliding shoesLiu and Chen [14] established a digital model of the coalroof and floor Su et al [15] established a mathematicalmodel of the profile cutting of the shearer Ge [16] proposeda 3D fine geological model that enabled the shearer toadapt to complex terrain structures such as faults and foldsBased on the real-time dynamic correction strategy Feng[17] obtained the floor curve using a shearer kinematicsmodel

However the above-mentioned studies were not uni-versal to every condition owing to the idealization of theassumed conditions and nonconsideration of the couplingrelationship between the scraper conveyor and shearer

Regarding the positioning of the shearer significantresearch progress has been made [18ndash22] This includes thedevelopment of some accurate fusion positioning methodssuch as SINS and encoders [23ndash25] wireless sensor networks[26ndash28] infrared cameras [29] and geographic informationsystems [30] which yielded remarkable results howeverthese methods are still in the theoretical research stage andare not yet used in industrial applications

To overcome this barrier Zhang et al [31] proposeda method to detect the layout inspection of the scraperconveyor on the basis of the running trajectory and precisepositioning of the shearerThismethod efficiently reproducedthe theoretical results However the shearer prototype wasdriven by four small wheels and the scraper conveyorprototype was relatively simple and could not reflect theconnection between the actual shearer and actual scraperconveyor efficiently Owing to the unique and complex char-acteristics of the underground environment it was difficult toconduct a physical experiment

In some laboratories because of the heavy equipmentof the fully mechanized mining system and inability tocreate real uneven-floor conditions it is difficult to verifythe correctness of the method Therefore a prototype of theshearer and scraper conveyor must be designed to simulatethe underground working conditions

In this paper to overcome the abovementioned problemsa joint positioning and attitude solving method for shearerand scraper conveyor is investigated under complex condi-tions

2 Theoretical Analysis

21 Related Concepts of Shearer and Scraper Conveyor Theentire coordination process of threemachines in a fullymech-anized coal-mining face is in accordance with the shearerlocation and relevant regulations As shown in Figure 1 theshearer walks on the flexible scraper conveyor and cuts thecoal

In the process of shearer running the coal plate comesinto contact with the left and right supporting sliding shoesin themiddle trough and the left and right walking wheels aremeshed with the pin rails of the middle trough

Therefore there are two meshing relationships namelythe coupling relationship between the walking wheels andshape of pin rails and that between the supporting slidingshoes and coal plate These two relationships directly affectthe shearer pitch angle therefore it is necessary to analyzethe coupling relationship between the two groups

The pin rails are divided into two categories the mid-dle pin rails and the connecting pin rails Each pin railconnects to the corresponding middle trough with two pinshafts The middle pin rails move with the correspondingmiddle trough and keep the same center position of thecorresponding middle trough Meanwhile the connectingpin rails change correspondingly according to the horizontalinclination angle

22 Overall Design and Layout of Sensors Some double-axistilt sensors are installed in each middle trough to obtainthe horizontal and vertical inclination angle of each middletrough in real time (Figure 2)

23 Overall Framework In this paper the connecting andcoupling relationship between the shearer and scraper con-veyor is developed under complex conditions using thesensors installed in the equipment The general method is asfollows (Figure 3)

(1) The horizontal and vertical inclination angles of eachmiddle trough are obtained using double-axis tiltsensors arranged on each middle trough thereforethe shape of the scraper conveyor can be determined

(2) The shapes of the coal plate and the pin rails can beobtained on the basis of the analytical results obtainedfor a middle trough structure

(3) By setting the left supporting sliding shoe as thepositioning point of the shearer when the shearer is ata position corresponding to a position in the scraperconveyor the contacting mode of the two supportingsliding shoes and the coal plate is assessed and the keypoint coordinate of the left supporting sliding shoe isobtained

(4) The key point coordinate of the right supportingsliding shoe is obtained using the exhaustionmethod

(5) The shearer body pitch angle is solved by connectingthe key points of the two supporting sliding shoes

(6) The key points of two walking wheels are determinedby the key point coordinates of the two supportingsliding shoes and the shearer body pitch angle isdetermined on the basis of the left and right walkingwheels and pin rails

(7) Taking the above-mentioned point as prior knowl-edge the actual real-time shearer body pitch angleobtained using tilt sensors and SINS is reversely


(1) (2) (3) (4)

(5)(6)(7)

(1) (2) (3) (4)

(5)(6)(8)(7)

Shearer

Scraper conveyor







(1)




(1) (2) (3) (4) (5) (6)

(7)(8)(9)(10)(11)(12)








Right walking wheel

Left walking wheel









Marking strategy

Tilt sensors SINS










y

O 1

h

2

nminus1

x

n


119909119904 = 119909119896 + 119909119901 = 119871119885119861119862 119896sum119894=1


119894=1













(3)











(a) (b) (c)



Solution


minus 119871119867 cos (1205791 + 120572119901 + 120573) (4)


1198841198741= 119891 (119883119860) + 119871119867 sin (1205791 + 120572119901 + 120573) 1198731198741 = 119901119891 (119883119860) + 119871119867 sin (1205791 + 120572119901+1 + 120573) 1198731198741 = 119901 + 1

(5)



A p

LH

C

2

1p+1

B

O1






Output

Stop

Yes

No

Yes

No

s k p

s + 001k

S lt S1

(b) suspending (c)

(b) suspending (c)

js

XO1 XO2 + 01 mm



YO1


XO2 YO2

YO2


LO1O2







120572119895119904 = tan 1198841198742 minus 11988411987411198831198742 minus 1198831198741 (7)






120579119873119894 = (120572119894 + 120572119894+1)2 (9)




(10)















1205741 = 11199012 1199012sum119894=1

1205741198941205901 = radic 11199012 minus 1 1199012sum

119894=1

(120574119894 minus 1205741)(11)


1205742 = 11199012 119901sum119894=1199012+1

1205741198941205902 = radic 11199012 minus 1 119901sum

119894=1199012+1

(120574119894 minus 1205741)(12)


120574 = 120590221205741 + 12059012120574212059012 + 120590221205902 = 12059012 ∙ 1205902212059012 + 12059022

(13)





120574 = 119898sum119894=1

119882119894120574119894119898sum119894=1

119882119894119894 = 1(15)


119882119894 = 11205901198942sum119911119894=1 (11205901198942) (16)



TypeValue

Group 1 Group 21 2 3 4 5 6 7 8 9 10

SINS 1352 1361 1363 1367 1353 1349 1352 1367 1369 1363Tilt sensor 1369 1370 1390 1384 1384 1369 1371 1382 1386 1387


Tilt sensor SINS














b

c

d

e

f g

hj k l

m


minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6

ii

a

ab

c

d

e

f

g

ℎ(j)(k) l

m


























No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical


1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees



left drum height

right drum height



m

Shearer









(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





(1) (2) (3) (4)

(5)(6)(7)

(1) (2) (3) (4)

(5)(6)(8)(7)

Shearer

Scraper conveyor







(1)




(1) (2) (3) (4) (5) (6)

(7)(8)(9)(10)(11)(12)








Right walking wheel

Left walking wheel









Marking strategy

Tilt sensors SINS










y

O 1

h

2

nminus1

x

n


119909119904 = 119909119896 + 119909119901 = 119871119885119861119862 119896sum119894=1


119894=1













(3)











(a) (b) (c)



Solution


minus 119871119867 cos (1205791 + 120572119901 + 120573) (4)


1198841198741= 119891 (119883119860) + 119871119867 sin (1205791 + 120572119901 + 120573) 1198731198741 = 119901119891 (119883119860) + 119871119867 sin (1205791 + 120572119901+1 + 120573) 1198731198741 = 119901 + 1

(5)



A p

LH

C

2

1p+1

B

O1






Output

Stop

Yes

No

Yes

No

s k p

s + 001k

S lt S1

(b) suspending (c)

(b) suspending (c)

js

XO1 XO2 + 01 mm



YO1


XO2 YO2

YO2


LO1O2







120572119895119904 = tan 1198841198742 minus 11988411987411198831198742 minus 1198831198741 (7)






120579119873119894 = (120572119894 + 120572119894+1)2 (9)




(10)















1205741 = 11199012 1199012sum119894=1

1205741198941205901 = radic 11199012 minus 1 1199012sum

119894=1

(120574119894 minus 1205741)(11)


1205742 = 11199012 119901sum119894=1199012+1

1205741198941205902 = radic 11199012 minus 1 119901sum

119894=1199012+1

(120574119894 minus 1205741)(12)


120574 = 120590221205741 + 12059012120574212059012 + 120590221205902 = 12059012 ∙ 1205902212059012 + 12059022

(13)





120574 = 119898sum119894=1

119882119894120574119894119898sum119894=1

119882119894119894 = 1(15)


119882119894 = 11205901198942sum119911119894=1 (11205901198942) (16)



TypeValue

Group 1 Group 21 2 3 4 5 6 7 8 9 10

SINS 1352 1361 1363 1367 1353 1349 1352 1367 1369 1363Tilt sensor 1369 1370 1390 1384 1384 1369 1371 1382 1386 1387


Tilt sensor SINS














b

c

d

e

f g

hj k l

m


minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6

ii

a

ab

c

d

e

f

g

ℎ(j)(k) l

m


























No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical


1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees



left drum height

right drum height



m

Shearer









(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





(1) (2) (3) (4) (5) (6)

(7)(8)(9)(10)(11)(12)








Right walking wheel

Left walking wheel









Marking strategy

Tilt sensors SINS










y

O 1

h

2

nminus1

x

n


119909119904 = 119909119896 + 119909119901 = 119871119885119861119862 119896sum119894=1


119894=1













(3)











(a) (b) (c)



Solution


minus 119871119867 cos (1205791 + 120572119901 + 120573) (4)


1198841198741= 119891 (119883119860) + 119871119867 sin (1205791 + 120572119901 + 120573) 1198731198741 = 119901119891 (119883119860) + 119871119867 sin (1205791 + 120572119901+1 + 120573) 1198731198741 = 119901 + 1

(5)



A p

LH

C

2

1p+1

B

O1






Output

Stop

Yes

No

Yes

No

s k p

s + 001k

S lt S1

(b) suspending (c)

(b) suspending (c)

js

XO1 XO2 + 01 mm



YO1


XO2 YO2

YO2


LO1O2







120572119895119904 = tan 1198841198742 minus 11988411987411198831198742 minus 1198831198741 (7)






120579119873119894 = (120572119894 + 120572119894+1)2 (9)




(10)















1205741 = 11199012 1199012sum119894=1

1205741198941205901 = radic 11199012 minus 1 1199012sum

119894=1

(120574119894 minus 1205741)(11)


1205742 = 11199012 119901sum119894=1199012+1

1205741198941205902 = radic 11199012 minus 1 119901sum

119894=1199012+1

(120574119894 minus 1205741)(12)


120574 = 120590221205741 + 12059012120574212059012 + 120590221205902 = 12059012 ∙ 1205902212059012 + 12059022

(13)





120574 = 119898sum119894=1

119882119894120574119894119898sum119894=1

119882119894119894 = 1(15)


119882119894 = 11205901198942sum119911119894=1 (11205901198942) (16)



TypeValue

Group 1 Group 21 2 3 4 5 6 7 8 9 10

SINS 1352 1361 1363 1367 1353 1349 1352 1367 1369 1363Tilt sensor 1369 1370 1390 1384 1384 1369 1371 1382 1386 1387


Tilt sensor SINS














b

c

d

e

f g

hj k l

m


minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6

ii

a

ab

c

d

e

f

g

ℎ(j)(k) l

m


























No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical


1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees



left drum height

right drum height



m

Shearer









(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







y

O 1

h

2

nminus1

x

n


119909119904 = 119909119896 + 119909119901 = 119871119885119861119862 119896sum119894=1


119894=1













(3)











(a) (b) (c)



Solution


minus 119871119867 cos (1205791 + 120572119901 + 120573) (4)


1198841198741= 119891 (119883119860) + 119871119867 sin (1205791 + 120572119901 + 120573) 1198731198741 = 119901119891 (119883119860) + 119871119867 sin (1205791 + 120572119901+1 + 120573) 1198731198741 = 119901 + 1

(5)



A p

LH

C

2

1p+1

B

O1






Output

Stop

Yes

No

Yes

No

s k p

s + 001k

S lt S1

(b) suspending (c)

(b) suspending (c)

js

XO1 XO2 + 01 mm



YO1


XO2 YO2

YO2


LO1O2







120572119895119904 = tan 1198841198742 minus 11988411987411198831198742 minus 1198831198741 (7)






120579119873119894 = (120572119894 + 120572119894+1)2 (9)




(10)















1205741 = 11199012 1199012sum119894=1

1205741198941205901 = radic 11199012 minus 1 1199012sum

119894=1

(120574119894 minus 1205741)(11)


1205742 = 11199012 119901sum119894=1199012+1

1205741198941205902 = radic 11199012 minus 1 119901sum

119894=1199012+1

(120574119894 minus 1205741)(12)


120574 = 120590221205741 + 12059012120574212059012 + 120590221205902 = 12059012 ∙ 1205902212059012 + 12059022

(13)





120574 = 119898sum119894=1

119882119894120574119894119898sum119894=1

119882119894119894 = 1(15)


119882119894 = 11205901198942sum119911119894=1 (11205901198942) (16)



TypeValue

Group 1 Group 21 2 3 4 5 6 7 8 9 10

SINS 1352 1361 1363 1367 1353 1349 1352 1367 1369 1363Tilt sensor 1369 1370 1390 1384 1384 1369 1371 1382 1386 1387


Tilt sensor SINS














b

c

d

e

f g

hj k l

m


minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6

ii

a

ab

c

d

e

f

g

ℎ(j)(k) l

m


























No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical


1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees



left drum height

right drum height



m

Shearer









(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of














(a) (b) (c)



Solution


minus 119871119867 cos (1205791 + 120572119901 + 120573) (4)


1198841198741= 119891 (119883119860) + 119871119867 sin (1205791 + 120572119901 + 120573) 1198731198741 = 119901119891 (119883119860) + 119871119867 sin (1205791 + 120572119901+1 + 120573) 1198731198741 = 119901 + 1

(5)



A p

LH

C

2

1p+1

B

O1






Output

Stop

Yes

No

Yes

No

s k p

s + 001k

S lt S1

(b) suspending (c)

(b) suspending (c)

js

XO1 XO2 + 01 mm



YO1


XO2 YO2

YO2


LO1O2







120572119895119904 = tan 1198841198742 minus 11988411987411198831198742 minus 1198831198741 (7)






120579119873119894 = (120572119894 + 120572119894+1)2 (9)




(10)















1205741 = 11199012 1199012sum119894=1

1205741198941205901 = radic 11199012 minus 1 1199012sum

119894=1

(120574119894 minus 1205741)(11)


1205742 = 11199012 119901sum119894=1199012+1

1205741198941205902 = radic 11199012 minus 1 119901sum

119894=1199012+1

(120574119894 minus 1205741)(12)


120574 = 120590221205741 + 12059012120574212059012 + 120590221205902 = 12059012 ∙ 1205902212059012 + 12059022

(13)





120574 = 119898sum119894=1

119882119894120574119894119898sum119894=1

119882119894119894 = 1(15)


119882119894 = 11205901198942sum119911119894=1 (11205901198942) (16)



TypeValue

Group 1 Group 21 2 3 4 5 6 7 8 9 10

SINS 1352 1361 1363 1367 1353 1349 1352 1367 1369 1363Tilt sensor 1369 1370 1390 1384 1384 1369 1371 1382 1386 1387


Tilt sensor SINS














b

c

d

e

f g

hj k l

m


minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6

ii

a

ab

c

d

e

f

g

ℎ(j)(k) l

m


























No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical


1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees



left drum height

right drum height



m

Shearer









(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Output

Stop

Yes

No

Yes

No

s k p

s + 001k

S lt S1

(b) suspending (c)

(b) suspending (c)

js

XO1 XO2 + 01 mm



YO1


XO2 YO2

YO2


LO1O2







120572119895119904 = tan 1198841198742 minus 11988411987411198831198742 minus 1198831198741 (7)






120579119873119894 = (120572119894 + 120572119894+1)2 (9)




(10)















1205741 = 11199012 1199012sum119894=1

1205741198941205901 = radic 11199012 minus 1 1199012sum

119894=1

(120574119894 minus 1205741)(11)


1205742 = 11199012 119901sum119894=1199012+1

1205741198941205902 = radic 11199012 minus 1 119901sum

119894=1199012+1

(120574119894 minus 1205741)(12)


120574 = 120590221205741 + 12059012120574212059012 + 120590221205902 = 12059012 ∙ 1205902212059012 + 12059022

(13)





120574 = 119898sum119894=1

119882119894120574119894119898sum119894=1

119882119894119894 = 1(15)


119882119894 = 11205901198942sum119911119894=1 (11205901198942) (16)



TypeValue

Group 1 Group 21 2 3 4 5 6 7 8 9 10

SINS 1352 1361 1363 1367 1353 1349 1352 1367 1369 1363Tilt sensor 1369 1370 1390 1384 1384 1369 1371 1382 1386 1387


Tilt sensor SINS














b

c

d

e

f g

hj k l

m


minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6

ii

a

ab

c

d

e

f

g

ℎ(j)(k) l

m


























No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical


1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees



left drum height

right drum height



m

Shearer









(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






(10)















1205741 = 11199012 1199012sum119894=1

1205741198941205901 = radic 11199012 minus 1 1199012sum

119894=1

(120574119894 minus 1205741)(11)


1205742 = 11199012 119901sum119894=1199012+1

1205741198941205902 = radic 11199012 minus 1 119901sum

119894=1199012+1

(120574119894 minus 1205741)(12)


120574 = 120590221205741 + 12059012120574212059012 + 120590221205902 = 12059012 ∙ 1205902212059012 + 12059022

(13)





120574 = 119898sum119894=1

119882119894120574119894119898sum119894=1

119882119894119894 = 1(15)


119882119894 = 11205901198942sum119911119894=1 (11205901198942) (16)



TypeValue

Group 1 Group 21 2 3 4 5 6 7 8 9 10

SINS 1352 1361 1363 1367 1353 1349 1352 1367 1369 1363Tilt sensor 1369 1370 1390 1384 1384 1369 1371 1382 1386 1387


Tilt sensor SINS














b

c

d

e

f g

hj k l

m


minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6

ii

a

ab

c

d

e

f

g

ℎ(j)(k) l

m


























No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical


1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees



left drum height

right drum height



m

Shearer









(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






TypeValue

Group 1 Group 21 2 3 4 5 6 7 8 9 10

SINS 1352 1361 1363 1367 1353 1349 1352 1367 1369 1363Tilt sensor 1369 1370 1390 1384 1384 1369 1371 1382 1386 1387


Tilt sensor SINS














b

c

d

e

f g

hj k l

m


minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees

11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6

ii

a

ab

c

d

e

f

g

ℎ(j)(k) l

m


























No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical


1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees



left drum height

right drum height



m

Shearer









(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of


























No1

No10

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degreesdegrees

No5

No6

No9

No8

No7

No4

No3

No2

No20

No19

No18

No17

No16

No15

No14

No13

No12

No11

Vertical


1800

1118

1680

1579

1564

1248

1314

1392

1759

1563

1618

1608

1610

1822

1196

1178

1131

1610

1033

0

73499

5

08999

139558

0

full contact

semi contact

200021

0961

minus1095

2627

confirm

confirm

walking length

No p

k

body pitch angle

body roll angle

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees



left drum height

right drum height



m

Shearer









(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





(a)

(b)

(c)

(d)(e)


11

82

63

44

2 55

86

67

48

2 99

810

611

412

2 1313

814

615

416

2 1717

818

619

420

2 2121

822

623

424

2 2525

826

627

428

2 2929

830

6





minus10

minus5

0

5

10

15

Shea

rer b

ody

pitc

h an

gle

degr

ees





minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees




minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees



4 Conclusions








Actual fusion curve

minus7

minus2

3

8

13

Shea

rer b

ody

pitc

h an

gle

degr

ees


116

6667

196

6666

276

6666

356

6665

436

6664

516

6663

596

6665

676

6668

756

6671

836

6674

916

6678

996

6681

107

6668

115

6669

123

6669

131

6669

139

667

147

667

155

667

163

667

171

6671

179

6671

187

6671

195

6672

203

6672

211

6672

219

6671

227

667

235

6669

243

6668

251

6666

259

6665

267

6664

275

6663

283

6662

291

666

299

6659

307

6658


4500 mm4900 mm

5327 mm5800 mm6300 mm

minus8

minus3

2

7

12

17

Shea

rer b

ody

pitc

h an

gle

degr

ees






Acknowledgments



References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




a joint positioning and attitude solving method for

Documents