GB2332051A

GB2332051A - Camera position detecting apparatus for trolley eg for a container crane

Info

Publication number: GB2332051A
Application number: GB9905128A
Authority: GB
Inventors: Hiromitsu Hoshina; Toshiyuki Fujii
Original assignee: Mitsubishi Heavy Industries Ltd
Current assignee: Mitsubishi Heavy Industries Ltd
Priority date: 1996-11-06
Filing date: 1997-10-31
Publication date: 1999-06-09
Anticipated expiration: 2017-10-31
Also published as: GB2332051B; GB9905128D0

Abstract

A trolley position detecting apparatus, eg for a container crane movable on rails 3, comprises a camera 12 installed on a girder 6 supporting a trolley 8 having a suspended load, a clinometer 13 attached to the camera, and a target 14 on the crane. A constant value # 0 relating to the horizontal position of a girder reference point O1 is measured in advance by using the outputs # cg and # kg from the camera and the clinometer which are related to the direction of the target # cg and the vertical inclination # kg . Then the outputs # cg and # kg of the camera and clinometer are measured continuously and the horizontal displacement # g is determined from these, the constant value # 0 , and the known position of the trolley camera 10 relative to the rail centre C. Swing of the load is controlled using a further camera 10 and a target 11 on the load.

Description

2332051 TROLLEY CAMERA POSITION DETECTING APPARATUS The present invention

relates to a position detecting apparatus for a trolley camera on a trolley for a container crane, for example, and can be applied to all machines for carrying a cargo lifted by a wire rope, such as a transfer crane, overhead crane, and the like.

Conventionally, a container crane etc. are used when cargoes piled on the ground are loaded on a ship alongside a pier or cargoes on a ship are unloaded and piled on the ground. In such cargo handling work, the cargo is controlled so that the swing of cargo is decreased, and the lifted cargo is landed accurately at a target position by using a landing control device, described later.

With the conventional landing control device, a cargo is hung with a lifting wire via a hoisting accessory, the crane is run to the target position along the rails in this state, the trolley is moved to the target position along the girder, the swing amount of lifted cargo is subsequently detected by a sensor (the swing amount is detected as an inclination angle with respect to the vertical line by photographing a target on the hoisting accessory with a camera installed on the trolley), and the movement of the trolley is controlled based on this detection value, by which the swing of lifted cargo is made as small as possible, and the lifted cargo is landed at the time when the swing amount becomes within an allowable value.

1 For the above-mentioned landing control device for hoisting accessory, the trolley on the girder is first stopped correctly at a predetermined position, the swing amount of the hoisting accessory is then detected by a swing sensor, and swing stopping control is carried out based on this detection value, by which the cargo is landed at the target position. The position of the trolley camera on the trolley at this time is successively detected by detecting the travel amount from the reference point provided on the girder by using an encoder (not shown).

However, if the deflection of the support leg or girder is changed, or a shift occurs between the crane wheel and the rail because of the movement of trolley on the girder or the change of the weight of lifted cargo, a shift of reference point on the girder is produced by the resultant horizontal travel amount, which produces a measurement error, so that the detection accuracy of the trolley position or trolley camera position is worsened. As a result, the landing accuracy is also decreased.

The present invention was made in view of such a situation, and accordingly an object thereof is to provide a trolley camera position detecting apparatus in which the position of a hoisting accessory is detected accurately, whereby the accuracy of landing position control can be increased.

2 i 1 To solve the problem with the above-described prior art, the present invention provides a crane installation comprising a crane which runs along a rail, the crane including at least one support leg, a girder mounted on the leg, a trolley movable along the girder, the detecting comprising (a) a trolley camera installed on the trolley; (b) a leg target which moves with the crane at a predetermined horizontal distance from the centre of the said rail; (c) a girder camera installed at a predetermined position on the girder for measuring an inclination angle 0,cl between the camera centreline and the leg target; (d) a clinometer installed to the girder camera to measure an inclination angle Okg of the clinometer with respect to the vertical line; (e) a measuring instrument for measuring a horizontal travel amount Yo of the trolley with respect to a reference point on the girder, where said reference point is located a horizontal distance 6g from the centre of said rail; (f) means for calculating a constant value 6, installation further comprising apparatus for the position of the trolley, said apparatus relating to the horizontal travel amount where 6. = 890 - H90)Cgo - Okgo) where H.. is a height f rom, the leg target to the girder camera, and Ocgop 6k90, and 6g, are the initial values of the measured values Ocgy Okg, and Yo; and (g) calculation means for calculating from the measured inclination angles Ocg and Okg during cargo 3 handling operation, a changing horizontal displacement amount 6g of the reference point on the girder with respect to the rail centre where 6g = 6,, + Hg(Ocq - ekg) by using the measured values Ocg and ok. and the constant value b., and for correcting the position Yo of the trolley camera by using the horizontal displacement amount 6. to give the position of the trolley camera with the rail centre as reference.

The invention also provides trolley camera position detecting apparatus for detecting the position of a trolley which is movable along a girder mounted on a support leg of a crane, which crane runs along a rail, the apparatus comprising trolley camera for installation on the trolley, leg target for fixedly mounting on said crane, girder camera for installation on the girder at a fixed position for measuring an inclination angle Ocg between the camera centreline and the leg target, a clinometer installed on, or for installation on, the girder camera to measure an inclination angle 0,g of the clinometer with respect to a vertical line, a measuring instrument for measuring a horizontal travel amount Yo of the trolley with respect to a reference point on the girder, where said reference point is located a horizontal distance 6. from the centre of said rail, and calculation means for receiving (a) a measured horizontal distance Yg of the leg target apart from the centre of the rail; 4 i i i (b) a constant value 6. relating to the horizontal travel amount, where = bgo - Hg(OcgO OkgA where H. is a measured height f rom. the leg target to the girder camera and OcgO, OkgO, and 6,0 are the initial values of the measured values 0,,gr ok., and Yo prior to a cargo handling operation, and (c) the inclination angles 0,,g and ok. as measured during a cargo handling operation, said calculation means being arranged to calculate a changing horizontal displacement amount 5. of the reference point on the girder with respect to the rail centre as 8g = 8, + H9(6cg - Okg) by using the measured values Ocg and Okg and the constant value b., and to correct the position Yo of the trolley camera by using the horizontal displacement amount 6. to give the position of the trolley camera with the rail centre as reference.

The invention also provides a method of determining the horizontal displacement of a trolley which travels along a girder of a crane relative to a rail upon which the crane runs, the trolley being provided with means for measuring its displacement Yo along the girder, the method comprising providing a camera on the girder, an inclinometer on the camera, a target located on the crane at a predetermined horizontal location relative to the rail and at a predetermined height Hg relative to the camera, the camera being adapted to provide an output indicative of the angle Oc subtended by the target C] relative to the centre line of the camera, and the inclinometer being adapted to provide an output indicative of the angle Okg 0 f the inclinometer relative to a true vertical line, the method comprising an initial determination of a value = 690 - Hg ( OcgO Okgo where Ocgo and ok,,,:, are initially measured values of 0,, and Okg JI and 890 is an initially determined value of displacement Yo of the trolley along the girder, and thereafter using the measured values Ocg and ok. to provide a value 69 = 6. + Hq ( 6C9 - Okg for correcting the measured displacement Yo relative to the rail.

Furthermore, the invention provides a method of determining the horizontal displacement 6g of a girder of a crane relative to a rail upon which the crane runs, the method comprising providing a camera on the girder, an inclinometer on the camera, and a target located on the crane at a predetermined horizontal location relative to the rail and at a predetermined height H. relative to the camera, the camera being adapted to provide an output indicative of the angle E)cg subtended by the target relative to the centre line of the camera, and the inclinometer being adapted to provide an output indicative of the angle 3kg of the inclinometer relative to a true vertical line, the method comprising an initial determination of a value 60 = Hg(OcgO - Okgo) 6 1 where 0... and ok.. are initially measured values, and thereafter using the measured values Oc and 0,g to provide,g the value 8g = (5, + Hg ((3cg - Okg) With the trolley camera position detecting apparatus in accordance with the present invention, the inclination angle Ocg between the camera centreline and the leg target at the lower part of a leg is measured by the girder camera, the inclination angle 0,g of the clinometer with respect to the vertical line is measured by the clinometer on the girder, the horizontal travel amount 6. due to the inclination of crane leg on the rails is measured by a transit (measuring instrument) etc., the constant value relating to the horizontal travel amount 6, = 69o - Hg(OcgO - Okg.) is calculated by using the initial values, the inclination angles Ocg and 0,, are measured every moment during cargo handling operation (during control), the horizontal travel amount of the reference point on the girder 6. = 80 + H g(OCg - ok.) is calculated by using these measured values Ocg and ok, and the constant value b., and the position (distance) 8 is corrected by using 6. thus calculated.

As described above, the trolley camera position detecting apparatus in accordance with the present invention is configured so that the girder camera is installed to the girder, the clinometer is installed to the girder camera, the constant value relating to the 7 horizontal travel amount of girder reference point is calculated in advance by using the output values thereof, and on the other hand, the horizontal travel amount is calculated by using the output values of the girder camera and clinometer measured every moment and the constant value, and the position of the trolley camera with the rail centre being the reference is corrected by using this horizontal travel amount. Therefore, the position of hoisting accessory can be detected accurately, whereby the accuracy of landing position control of hoisting accessory can be increased.

In addition, the invention provides a method of determining the horizontal displacement of a trolley which travels along a girder of a crane relative to a rail upon which the crane runs, the trolley being provided with means for measuring its displacement Y. along the girder, the method comprising providing a camera on the girder with its centre vertically below a point at a distance Y, from a reference point 01; an inclinometer on the camera; and a target located on the crane at a predetermined horizontal distance Y9 relative to the rail and at a predetermined height Hg relative to the camera; wherein the camera is adapted to provide an output indicative of the angle 0,, subtended by the target relative to the centre line of the camera, and the inclinometer is adapted to provide an output indicative of the angle Okg of a reference direction of the inclinometer relative to a true vertical line; 8 1 1 the method further comprising an initial determination of a value Oy. being the misalignment between the centre line of the camera and the reference direction of the inclinometer, followed by a determination of the value = H90yg - Yg + Y, and thereafter using the measured values 0,, and 0,, to 10 provide a value 89 = 60 + Hc3(6cg - Okg) for correcting the measured displacement Yo relative to the rail.

The invention further provides a method of determining the horizontal displacement 6. of a girder of a crane relative to a rail upon which the crane runs, the method comprising providing a camera on the girder with its centre vertically below a point at a distance Yc from a reference point 01; an inclinometer on the camera; and a target located on the crane at a predetermined horizontal distance Y9 relative to the rail and at a predetermined height Hg relative to the camera; wherein the camera is adapted to provide an output indicative of the angle Qg subtended by the target relative to the centre line of the camera, and the inclinometer is adapted to provide an output indicative -30 of the angle Okg of the inclinometer relative to a true vertical line; 9 the method further comprising an initial determination of a value Oyg being the misalignment between the centre line of the camera and the reference direction of the inclinometer, followed by a determination of the value 6,) = H90Y9 - Yg + Y, and thereafter using the measured values Ocg and 0,, to 10 provide the value 6g = 6, + Hg(Ocg - Okg) For a better understanding of the invention, an 15 exemplary embodiment thereof will now be described in more detail with reference to the accompanying drawings, in which:

FIG. 1 is a schematic position detecting apparatus; FIG. 2 is a schematic view showing the whole of a container crane equipped with the trolley camera position detecting apparatus of Figure 1; FIG. 3 is a schematic view showing a storage unit and an arithmetic unit provided in relation to the trolley camera position detecting apparatus of Figure 1; and view of a trolley camera FIG. 4 is a flowchart showing a work procedure for detecting the position of the trolley camera of Figures 1 and 2.

1 As shown in FIGS. 1 and 2, a container crane 1, which is a machine for loading cargoes (containers) 2 piled on the ground G onto a ship S alongside a pier or unloading cargoes 2 on the ship S onto the ground G, has a support leg 5 which is erected so as to be capable of running on a pair of rails 3 laid on the ground G via wheels 4, a girder 6 which is provided on top of the support leg 5 and extends horizontally perpendicular to the support leg 5, and a trolley 8 which is installed on the girder 6 so as to move while hanging a hoisting accessory 7.

With such a container crane 1, a cargo 2 is lifted with a lifting wire 9 attached to the trolley 8 via the hoisting accessory 7, and in this state the trolley 8 is moved along the girder 6 or the support leg 5 is run along the rails 3 by driving the wheels 4 at the lower part of the support leg 5. Thereby, the lifted cargo 2 is carried to a predetermined position and landed at that position for loading/unloading.

On the other hand, a trolley camera 10 for measuring the swing amount of the hoisting accessory 7 is provided above the trolley 8 of the container crane 1 as shown in FIGS. 1 and 2. This trolley camera 10 is used for photographing a target 11 provided on the upper surface of the hoisting accessory 7 and detecting the swing amount by processing the image. When this detected value is sent to an arithmetic unit (not shown), a manipulated variable is calculated by the arithmetic unit, and the trolley 8 is controlled by the resultant 11 manipulated variable, whereby the cargo 2 is landed after the swing of the cargo 2 is decreased.

is The position of the trolley 8 on the girder 6 or the position of the trolley camera 10 is detected by an encoder (not shown) by taking a distance from a reference point 01 set on the girder 6 to a camera centreline D as a horizontal travel amount Y,. In the present invention, the position (distance) of the trolley camera 10 is corrected by detecting a horizontal travel amount 6g of the reference point 01 with a rail centre C being a reference, which is caused by a change of the inclination of the support leg 5, a shift between the rail 3 and the wheel 4, and the like.

Also, a girder camera 12 for photographing a later described leg target is installed so as to depend from the girder 6. This girder camera 12 is located at a position Y,, distant from the reference point 01. At the side of the girder camera 12, a clinometer 13 for measuring the inclination angle protrudes horizontally. At the lower part of the support leg 5 located under the girder camera 12 by a height Hg. a leg target (for example, a laser target) 14 protruding horizontally is provided. This leg target 14 is located at a position Y. distant from the rail centre C.

The symbols in FIG. 1 denote the following:

Y.: distance from the reference point on the girder to the trolley camera centreline Yg: distance from the rail centre to the leg target 12 1 Y,: distance from the reference point 0, to the girder camera a: intersection point of the vertical line passing through the rail centre and the girder hg: horizontal travel amount from the rail centre to the reference point on the girder Hg: height from the leg target to the girder camera ok.: clinometer output value (rad) of the girder camera 0,,.: output value (rad) of the girder camera 0.9:: ( Okg - Ocg) - Oyg(rad) Oy.: angular difference (rad) between the girder camera centreline and the clinometer 6: true trolley camera distance A constant value 80 and the measured value of height Hg are sent and stored in a storage unit 15 and then sent to an arithmetic unit 16 as shown in FIG. 3. Also, the measured value of distance Y, and the output values 0,,g and ()kg are sent to the arithmetic unit 16. The true distance & of the trolley camera 10 is calculated based on these values sent to the arithmetic unit 16.

For the trolley camera position detecting apparatus of this embodiment, the true position (distance) 6 of the trolley camera 10 is detected by the work procedure shown in FIG. 4.

First, the inclination angle 0.g between the camera centreline E and the leg target 14 is measured, and the inclination angle (installation angle) ok. with respect to the vertical line is measured by using the clinometer 13.

13 In FIG.

H 9 E).g = ye - Y 9 9 ().g Okg - 6C9) (3Y9 (1) (2) Multiplying both sides of Eq. (2) by Hg, HgO,,c) = Hg(okg - Ocg) - HqOyg (3) From Eqs. (1) and (3), 6g = Hg(Ocg - (3kg) + H90Y9 - Y9 + Y,:

(4) Here, 0 Y9 is constant because it is the angular misalignment between the centreline E of the girder camera 12 and the reference direction of the clinometer 13, Yg is constant because it is the distance between the rail centre C of the rail 3 and the leg target 14, and Y,, is also constant because it is the distance between the reference point 01 and the camera centreline E of the girder camera 12.

Therefore, Eq. (4) indicates that the horizontal travel amount 69 can be calculated by the output 0,,g of the girder camera 12 and the output (3kg of the clinometer 13.

If the amount (constant value: H.0y. - Yg + Yj independent of the change of horizontal travel amount is taken as 80, the horizontal travel amount can be expressed as 6g = 6. + Hg (Ocg - Okg) (5) 14 i Thus, by substituting the respective initial values E)rgof Okg., and 6,,, of the aforesaid Ocg, Okg, and b., measured under the same lifted cargo condition into Eq. (5), the constant value 6, can be calculated as 6. = 6go H9(0cgO - ekgo) (6) Thereupon, the output O,g of the girder camera 12 and the output Okg of the clinometer 13 are measured every moment during cargo handling operation (during control), the horizontal travel amount bg of the reference point 0, is successively calculated by substituting these measured values and the initial value 8, into Eq. (5), the true distance 6 (6 = Y, + 8,,) of the trolley camera 10 is calculated by the arithmetic unit 16 using the calculated value 8. and the distance Y., and the position of the trolley camera 10 is corrected. If the position is corrected in such a manner, the accuracy of the landing position control of the hoisting accessory 7 can be enhanced.

The above is a description of one embodiment of the present invention. The present invention is not limited to the above-described embodiment, and various modifications and changes can be made within the scope of the appended claims.

For example, the initial value b., of the horizontal travel amount of the reference point on the girder with respect to the rail centre C in the above-described embodiment can be measured by measuring means such as a transit provided in the vicinity of the base of the support leg 5. Also, if the angular difference Oy. between the camera and the clinometer can be measured by some method, the constant value 6. can be determined directly together with other measured distances H,, YgI and Yc.

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Claims

1. A crane installation comprising a crane which runs along a rail, the crane including at least one support leg, a girder mounted on the leg, a trolley movable along the girder, the installation further comprising apparatus for detecting the position of the trolley, said apparatus comprising (a) a trolley camera installed on the trolley; (b) a leg target which moves with the crane at a predetermined horizontal distance from the centre of the said rail; (C) a girder camera installed at a predetermined position on the girder for measuring an inclination angle Ocg between the camera centreline and the leg target; (d) a clinometer installed to the girder camera to measure an inclination angle 0,g of the clinometer with respect to the vertical line; (e) a measuring instrument f or measuring a horizontal travel amount Yo of the trolley with respect to a reference point on the girder, where said reference point is located a horizontal distance 8g from the centre of said rail; (f) means for calculating a constant value 6, relating to the horizontal travel amount where 6,) = 890 - Hg(OcgO - (kgo) where H,, is a height from the leg target to the girder camera, and 6c90, okgo, and 6.. are the initial values of the measured values Ocgy (3kg, and Yo; and (g) calculation means for calculating from the measured inclination angles Ocg and ok, during cargo handling operation, a changing horizontal displacement amount 6g of the reference point on the girder with respect to the rail centre where 59 = 6, + Hg(OCg - Okg) by using the measured values 0.,g and ok. and the constant value b., and for correcting the position Yo of the trolley camera by using the horizontal amount 6g to give the position of the trolley camera with the rail centre as reference.

disDlacement

2. A crane installation according to claim 1 wherein the line joining the girder camera and the leg target subtends at most a small angle 0.. to the vertical such that sin 0.. " 0,, q.

3. A crane installation according to claim 1 or claim 2, wherein the calculation means comprises an arithmetic unit for receiving the constant value 6. relating to the horizontal travel amount, the measured value of height Hg, the measured value of a distance Y. from the reference point on the girder to the trolley camera centreline and the measured values of inclination angles 0,,g and Okg.

4. A crane installation according to claim 3, wherein the constant value h. relating to the horizontal travel amount and the measured value of height Hg are stored before being sent to the arithmetic unit.

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5. A crane installation substantially as hereinbefore described with reference to the accompanying drawings.

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6. Trolley camera position detecting apparatus for detecting the position of a trolley which is movable along a girder mounted on a support leg of a crane, which crane runs along a rail, the apparatus comprising a trolley camera for installation on the trolley, a leg target for fixedly mounting on said crane, a girder camera for installation on the girder at a fixed position for measuring an inclination angle 0c9 between the camera centreline and the leg target, a clinometer installed on, or for installation on, the girder camera to measure an inclination angle okg Of the clinometer with respect to a vertical line, a measuring instrument for measuring a horizontal travel amount Yo of the trolley with respect to a reference point on the girder, where said reference point is located a horizontal distance 6. from the centre of said rail, and calculation means for receiving (a) a measured horizontal distance Yg of the leg target apart from the centre of the rail; (b) a constant value 8. relating to the horizontal travel amount, where = 8go - Hg(Oc90 - OkgA where H. is a measured height from the leg target to the girder camera and OcgO, okgo, and 8g. are the initial values of the measured values 0..r okgr and Yo prior to a cargo handling operation, and 19 (C) the inclination angles 0,:, and 0,g as measured during a cargo handling operation, said calculation means being arranged to calculate a changing horizontal displacement amount 6. of the reference point on the girder with respect to the rail centre as 69 = 6, + H9fficg - Okg) by using the measured values 0,,g and 6.g and the constant value b., and to correct the position Yo of the trolley camera by using the horizontal displacement amount 6g to give the position of the trolley camera with the rail centre as reference.

7. Trolley position detecting apparatus substantially as hereinbefore described with reference to the accompanying drawings.

8. A method of determining the horizontal displacement of a trolley which travels along a girder of a crane relative to a rail upon which the crane runs, the trolley being provided with means f or measuring its displacement Yo along the girder, the method comprising providing a camera on the girder; an inclinometer on the camera; and a target located on the crane at a predetermined horizontal location relative to the rail and at a predetermined height H. relative to the camera; wherein the camera is adapted to provide an output indicative of the angle Ocg subtended by the target relative to the centre line of the camera, and the inclinometer is adapted to provide an output indicative of the angle 0,,, of the inclinometer relative to a true vertical line; the method further comprising an initial determination of a value 6, = bgo - Hg(OcgO - OkgA where 0.g. and Okg,, are initially measured values of 0,,, and Okg F and 890 is an initially determined value of displacement Yo of the trolley along the girder, and thereafter using the measured values Ocg and 0,, to provide '10 a value 6g = 6, + Hg(Ocq - Okg) for correcting the measured displacement Yo relative to the rail.

9. A method of determining the horizontal displacement 6ci of a girder of a crane relative to a rail upon which the crane runs, the method comprising providing a camera on the girder; an inclinometer on the camera; and a target located on the crane at a predetermined horizontal location relative to the rail and at a predetermined height Hg relative to the camera; wherein the camera is adapted to provide an output indicative of the angle Ocg subtended by the target relative to the centre line of the camera, and the inclinometer is adapted to provide an output indicative of the angle Okg of the inclinometer relative to a true vertical line; the method further comprising an initial determination of a value = H9(0cgO - ekgo) where 6c and 0 are initially measured values, and go kgo thereafter using the measured values 6, and okg to provide the value 6g = 6, + Hg (Ocg - Okg)

10. A method of determining the horizontal displacement of a trolley which travels along a girder of a crane relative to a rail upon which the crane runs, the trolley being provided with means for measuring its displacement Y. along the girder, the method comprising providing a camera on the girder with its centre vertically below a point at a distance Yc from a reference point 01; an inclinometer on the camera; and a target located on the crane at a predetermined horizontal distance Y. relative to the rail and at a predetermined height H. relative to the camera; wherein the camera is adapted to provide an output indicative of the angle Ocg subtended by the target relative to the centre line of the camera, and the inclinometer is adapted to provide an output indicative of the angle 0k. Of a reference direction of the inclinometer relative to a true vertical line; the method further comprising an initial determination of a value 0Y. being the misalignment between the centre line of the camera and the reference direction of the inclinometer, followed by a determination of the value = H90Y9 - Yg + Yo and thereafter using the measured values 0o. and 0,, to provide a value 22 1 8g = 8,> + Hg(Ocg Okg) f or correcting the measured displacement Yo relative to the rail.

11. A method of determining the horizontal displacement hg of a girder of a crane relative to a rail upon which the crane runs, the method comprising providing a camera on the girder with its centre vertically below a point at a distance Yc from a reference point 0,; an inclinometer on the camera; and a target located on the crane at a predetermined horizontal distance Y9 relative to the rail and at a predetermined height Hg relative to the camera; wherein the camera is adapted to provide an output indicative of the angle Ocg subtended by the target relative to the centre line of the camera, andthe inclinometer is adapted to provide an output indicative of the angle Okg of the inclinometer relative to a true vertical line; the method further comprising an initial determination of a value Oyg being the misalignment between the centre line of the camera and the reference direction of the inclinometer, followed by a determination of the value = HgOyg - Yg + Yc and thereafter using the measured values Ocg and ok. to provide the value 6g = 60 + H9(0c9 - Okg) 23

12. A method of determining the horizontal displacement of a trolley which travels along a girder of a crane relative to a rail upon which the crane runs substantially as hereinbefore described with reference to the accompanying drawings.

13. A method of determining the horizontal displacement of a girder of a crane relative to a rail upon which the crane runs substantially as hereinbefore described with reference to the accompanying drawings.

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