GB2425263A

GB2425263A - Modified measuring and/or training apparatus

Info

Publication number: GB2425263A
Application number: GB0607630A
Authority: GB
Inventors: Shaun Brian Womersley
Original assignee: DAVID WOMERSLEY; JOANNE WOMERSLEY
Current assignee: DAVID WOMERSLEY; JOANNE WOMERSLEY
Priority date: 2005-04-19
Filing date: 2006-04-18
Publication date: 2006-10-25
Also published as: GB0607630D0

Abstract

Measuring and/or training apparatus for determining one or more parameters of a golf club consists of means for measuring a golfers physical characteristics at address position to determine at least one parameter of a golf club to suit the golfer. The apparatus also consists of a training device to facilitate the golfer adopting a correct address position with his eyes correctly aligned over the ball when putting and also for facilitating the golfer to train and adjust his golf swing not only when putting but also when using other clubs.

Description

"Modified Measuring Jpj Training Apparatus" This invention relates to

measuring and/or training apparatus and more particularly, but not exclusively, to apparatus for providing measurements from a golfers physical characteristics to determine one or more of the parameters for a golf club so as to be able to match the club to the golfers optimum body position and/or training a golfer to effect a correct address position, strike and swing through a golf ball.

When a golfer is choosing a set of golf clubs, it is usual for the supplier of the golf clubs to ask the golfer to select his favourite club which is often a five or six iron and the supplier will provide the golfer with two or three different sizes of that particular club to select the one which he feels is most suitable. This usually only gives one parameter such as the length of the shaft of that particular club and once this has been determined the other clubs of the set to be supplied are selected by : * utilising a rule of thumb formula developed from *:*. 20 experience to determine their size. It will be appreciated this is an inaccurate method of matching a set of clubs to the golfer's physical characteristics and position at address.

The object of the present invention is to provide a measuring and/or training apparatus to more accurately match a golf club to the requirements of a golfer than the (2) above rule of thumb method and training the golfer to adopt an improved address position or strike or swing through the ball.

According to one aspect of the invention, measuring and/or training apparatus for determining one or more parameters of a golf club by measuring a golfers physical characteristics at address position comprises a base member on which a golfer can stand in his normal address position whilst gripping a golf club or a simulated golf club and measuring means for determining at least one parameter of a golf club.

Preferably, the simulated golf club is connected to the base plate by a universal joint.

Preferably, also, the base plate is in the form of a mat having markings thereon to enable the golfer to align S...

himself correctly with reference to the simulated golf club at address position.

The simulated golf club has, preferably, a removable : * grip portion to allow various shapes and sizes of grip to S...

*:*. 20 be mounted thereon to meet the golfers preference.

Preferably, the simulated golf club is of a variable length so that a shaft length which is suitable for the golfer can be determined.

Preferably, also, the length of the golf club is measured by measuring means which gives a read out on a control unit of the length of the simulated golf club. (3)

Additional measuring means is, preferably, provided for measuring the lie angle of the simulated golf club and providing a read out on the control unit of said lie angle.

Preferably, further measuring means is provided for measuring the lean angle of the simulated golf club and providing a read out on the control unit of said lean angle.

Preferably, also, the additional and/or further measuring means comprise television cameras to provide views of the simulated golf club when the golfer has positioned it at address position.

The simulated golf club is, preferably, provided with a removable head so that different shapes and sizes of head can be mounted thereon to meet the golfers S...

preference.

According to another aspect of the invention, measuring and/or training apparatus for a golfer comprises : * * a ground engaging base having ball positioning means on or adjacent to which a golfer can stand at an address position and alignment means interposed between the ball position and the golfers eyes to facilitate correct positioning of the golfer at the address position.

Preferably, the ball positioning means comprises an arm mounted on the base for pivotal movement about an axis extending Perpendicularly to the plane of the base whose (4) free end has a location means for locating a golf ball therein and which is capable of movement from a ball locating position to an out of use position so that the ball can be struck by a golf club.

Preferably, also, the alignment means comprises a ruler mounted in an elevated position on the base and extending through the centre of the positioned ball along the line which the ball is to be struck by a putter towards a remote measuring means.

The ruler is, preferably, disposed in an upright orientation relative to the plane of the base to give a two dimensional view showing one side face or the other side face of the ruler to the golfer unless his sightline is directly above the centre of the ball when addressing * *.

the ball with a putter.

The alignment means may also comprise a laser device providing a line on which the ball is to be struck by a putter to a point indicated by the laser on the remote : ** measuring means. * S..

*:*. 20 Alternatively, the alignment means may comprise an arm pivotally mounted on the base for movement about an axis perpendicular to the plane of the base and having a target at its free end to be interposed between the golfers eyes and the ball to facilitate correct positioning of the golfer at the address position when using irons or woods.

Preferably, the arm is of adjustable length and (5) preferably, also, the free end including the target thereon is of adjustable pitch angle.

A posture maintaining adjustable length spindle is, preferably, mounted on the base and extends upwardly to contact a suitable part of the golfer at address position and through the swing of the golfer.

According to a further aspect of the invention, measuring and/or training apparatus for facilitating the correct positioning of a golfer at the address position when using a putter comprises a positioning or training device for ensuring the golfers eyes are vertically above the golf ball, said device being disposed at the normal ball position adjacent to a putters face and comprising two vertically spaced-apart inter-connected parts which * S. are circular in plan view. S...

Preferably, the lower part has a larger diameter than the upper part.

Alternatively, the upper and the lower parts have the : * * same diameter. S...

. 20 Preferably, the upper and lower parts have a sphere of the same diameter interposed therebetween and the sphere may comprise a golf ball.

Preferably, also, the upper part is a solid cylinder having a depth which allows the sides of the cylinder to be discerned by a golfer when the golfers eyes are not vertically aligned above the centre of the cylinder. (6)

Sections of the curved sides of the solid cylinder are, preferably, provided in different colours or visual finishes or markings to facilitate the golfers eye alignment vertically above the centre of the cylinder.

Preferably, the upper and lower parts are formed of discs and the discs and the central sphere have the same diameter to allow the apparatus to be disposed with the axis connecting the centres of the upper and lower parts and the sphere horizontally to enable the apparatus to be struck with a putter to roll the apparatus along the ground.

Preferred embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings of which:- * *5 Figure 1 is a diagrammatic perspective view of a S...

measuring and/or training apparatus for providing measurements to determine parameters of a golf club, Figure 2 is a perspective view of part of the :., apparatus shown in Figure 1 to a larger scale, Figure 3 is a diagrammatic perspective view of an alternative measuring and/or training apparatus, Figure 4 is a front view of the apparatus shown in Figure 3, Figure 5 is a side view of the apparatus shown in Figure 3, Figure 6 is a plan view of the apparatus shown in (7) Figure 3, Figure 7 is a view from underneath of the apparatus shown in Figure 3, Figure 8 is a perspective view of an alternative target assembly for the apparatus shown in Figure 3, Figure 9 is a perspective view of another alternative target assembly for the apparatus shown in Figure 3, Figure 10 is a perspective view of a further alternative target assembly for the apparatus shown in Figure 3, Figure 11 is a diagrammatic perspective view of part of yet another alternative target assembly for the apparatus shown in Figure 3, Figure 12 is a perspective view of a training device, Figures 13 to 15 are side views showing a simplified training device in use, Figures 16 to 18 are plan views showing the training device of Figure 12 in use corresponding respectively to :,. the side views of Figures 13 to 15, Figure 19 is a perspective view of an alternative training device, Figure 20 is a perspective view of a further training device shown in a dismantled condition, Figure 21 is a plan view of the training device shown in Figure 20 in use, Figure 22 is a diagrammatic perspective view of a (8) measuring and/or training apparatus which is a modification of the measuring and/or training apparatus of Figures 3 to 11.

Referring now to the drawings and particularly to Figures 1 and 2, a measuring and/or training apparatus according to one embodiment of the invention, indicated generally at 10, for measuring a golfers physical characteristics at the address position comprises a base plate in the form of a mat 12, a simulated golf club 14 releasably connected to the mat 12 by a universal joint (not shown) and a control unit 16 having a visual display 18. The simulated golf club 14 is extendable and sensing means such as a variable potentiometer device (not shown) is provided in the club 14 to give a read out of its length on the display 18. The club 14 is provided with a S...

removeable grip 20 and a removeable head 22. A first television camera 24 is provided which is directed to view the club 14 along the centre line of the mat 12 on which : * the face of the head 22 of the club 14 is aligned and a S...

second television camera 26 is provided which is directed to view the club 14 at right angles to the centre line of the mat 12. The cameras 24 and 26 are connected to the control unit 16 and provide images on the display 18. The mat 12 is provided with markings 28 not only of the centre line of the mat 12 but also at right angles thereto at varying distances from the position of the head 22 of the (9) club 14. The simulated golf club 14 shown is a simulated putter and a training device 30 according to a further aspect of the invention is shown placed at the normal ball position adjacent to the face of the simulated putter.

Training devices according to said further aspect of the invention are shown in Figures 12 to 21 of the drawings and can be used not only with the above described measuring and/or training apparatus and the hereinbelow described measuring and/or training apparatus according to said other embodiment of the invention but also as an independent training apparatus.

Referring particularly to Figures 13 to 15 of the drawings, the device 30 comprises in its simplest form two vertically spaced-apart interconnected parts 32 and 34 * S. which are circular in plan view, the lower part 34 being *..

of larger diameter than the upper part 32. In use as shown in Figures 13 to 15 of the drawings, the golfer aligns the the outer peripheries of the parts 32 and 34 to * form a uniform annulus therebetween ie. to produce an S..

eclipse" effect when the golfers eyes are directly above the centre of the device 30 as shown in Figure 12. If the golfer's eyes are not correctly aligned either to the left or to the right of the centre of the device 30 it will be seen from Figures 14 and 15 of the drawings that a view of a uniform annulus can not be obtained.

An alternative form of training device is shown in (10) Figure 12 and Figures 16 to 18 and indicated generally at 36. The upper part still consists of a disc 38 but the lower part is formed of a sphere 40, such as a golf ball, having a diameter equal to the diameter of the disc 38 and provided with a circular stand 42 which is spaced-apart from, is parallel to and is co-axial with the disc 38. In use as shown in Figures 16 to 18 of the drawings which correspond to Figures 13 to 15 in respect of the device 30, the periphery of the disc 38 has to be aligned with the periphery of the sphere 40 in order that the golfer's eyes are directly above the centre of the sphere 40 ie.

the golf ball.

In a modification shown in Figure 19 of the drawings, * the disc 38 is replaced by a solid cylinder 44 having either different coloured or different visible finish or S... * . S...

marking on sections of the curved surface of the cylinder so that they are also visible if the golfer's eyes are *S.

* not directly aligned above the centre of the sphere 40.

* In a further modification, shown in Figures 20 and 21 * ..* of the drawings, a training device indicated generally at 46 comprises a spherical ball 47, ie. a golf ball, and upper and lower discs 48 and 50 of the same diameter as the ball 46. Each disc 48 and 50 is provided with a centrally located spigot 52 which are press fits into diametrically opposite bores (not shown) in the ball 47.

The training device 46 can be used in the same manner as (11) the above described training devices 30 and 36 but in addition can be disposed with the axis connecting the discs 48 and 50 and the centre of the ball 47 horizontally to enable the device to be struck with a putter head 54 long a line perpendicular to said axis. When the putter head 54 is aligned correctly it simultaneously strikes the periphery of the ball 47 and the peripheries of both discs 48 and 50 and the device rolls along a line perpendicular to said axis. However, if the putter head 54 is incorrectly aligned and strikes the periphery of one of the discs first, the device rolls or even tumbles unevenly on a line directed to the opposite side of the device 46 having the disc which was contacted first by the putter head 54. * S.

Reverting now to the measuring and/or training device * 10, in operation, a golfer who is to choose a new set of clubs stands on the mat 12 of the apparatus 10 and selects a suitable size and shape of grip 20 which is then fitted : * * onto the simulated golf club 14. It has been found to be * S..

* 20 desirable to provide simulated golf clubs which start with a putter and then working outwardly from the golf hole select short, medium and long irons followed by woods. In order to assist the golfer to adopt the correct address position for the simulated putter, the positioning device 30 is placed in position so that the golfer can ensure that his eyes are vertically above the position of a golf (12) ball.

Once the required position is achieved and the golfer adopts his normal address position gripping the simulated golf club 14, the length of the simulated golf club 14 can be read off from the display providing one parameter for the putter. The cameras 24 and 26 also provide readings respectively of the lean angle and the lie angle of the putter which suits the particular golfer.

This static measurement can then be repeated for each one of the other clubs such as the set of irons and woods in turn and each particular club head 22 can be mounted in turn on the simulated golf club 14 thus enabling the parameters for each club to be measured.

Although this static measurement from the golfers body * S. position at address enables the parameters of the required S..

clubs to be more accurately determined than the rule of thumb method previously adopted, it is also possible to further enhance the accuracy of matching the clubs to the : *. * golfers physical characteristics by using the apparatus to * **.

provide measurements derived from the golfers swing, ie. a dynamic set of measurements. The simulated golf club 14 can be removed and the cameras 24 and 26 can be aligned to follow the path of a golf club which is swung by the golfer particularly the position and line through the ball and also the club shaft angle during the downswing or part of the down swing, such as the 9 o'clock position. The (13) downswing attack angle of the club shaft can be determined at this 9 o'clock position where the golfer's arms extend substantially parallel to the ground which is found to be an important factor in governing an accurate strike on the ball. All of these dynamic measurements provide fine tuning of the parameters of the golf club required to match the golfers particular shape of swing which it is found materially enhances the performance of a golfer.

Referring now to Figures 3 to 10 of the drawings, a measuring and/or training apparatus according to another embodiment of the invention is indicated generally at 60 comprises a substantially rectangular ground engaging base 62 having an extension mat 64 extending from one side edge of the base 62. The mat 64 has a longitudinal slot 66 formed therein of sufficient width to allow a golf ball when correctly struck to travel freely along the longitudinal axis of the slot 66 towards a measurement card 68 disposed remote from and extending at right angles : * * to said longitudinal axis. The base 62 is provided at each corner with an adjustable height foot 70 and is also provided with four bubble spirit levels 72 to enable the base 62 to be accurately levelled. The base 62 is also provided with holes (not shown) to enable the base 62 to be secured by pegs (not shown) to the floor on which it is to be positioned. Each end of the base 62 has an arm 74 extending upwardly therefrom over the extension mat 64. A (14) ruler 76 is carried by the arms 74 in an upright orientation and extends parallel to and is spaced- apart above the centre line of the slot 66. A vertically upwardly extending cylindrical support 78 is mounted on the base 62 and carries a ball positioning arm 80 having a semi-circular end 82 for receiving a golf ball, which can be swung into position over the end of the slot 66 where a golf ball is to be positioned and then swung out of the way when a stroke such as a putting stroke is to be executed by a golfer. A target arm 84 having a solid cylindrical target 86 at its free end is also mounted on the support 78 above the arm 80 and is capable of being swung into position above the ball position. The arm 84 * is of adjustable length and adjustable pitch angle of the target 86 so that it can be accurately positioned in the *.q S sight line of the golfer to enable it to be aligned, as previously described with reference to the training device shown in Figure 19, by the golfer at his address position :,::.. for not only a putter but also irons and woods. In addition to the solid cylindrical type of target 86, alternative target arms indicated generally at 88, 92, 96 and alternative targets 90, 94, 98 and 100 are shown in Figures 8 to 11 of the drawings. The support 78 also carries an adjustable length posture maintaining spindle 102 whose upper end is maintained in contact by the golfer with a suitable part of the golfer's torso such as the (15) breast bone or the golfers chin or mouth during execution of a stroke. In addition, a laser device 104 is mounted on an extension on the arm 74 remote from the measurement card 68 and is focussed on the card 68 along the line of the longitudinal axis of the slot 66 and along which the ball is to travel during the execution of a stroke.

During the use of the apparatus 60 by a golfer who is addressing the ball to execute a putting stroke, the golfer is able to align his eyes vertically above the centre line of the ball by using the ruler 76 which gives a two dimensional view showing one or the other side of the ruler 76 unless his sightline is directly above the centre of the ball and the ruler also enables the golfer to correctly align the head of his putter and to strike 4* * S S the ball along the longitudinal axis of the slot and along * PS S the laser line to the correct point on the measurement card. It will be appreciated that the apparatus can be used to provide measurements to be applied to a putter : , * which is manufactured to match the club to the particular se golfer's physical characteristics. The alignment of the golfer at the address position for other types of shots with an iron or a wood can also be checked and measured utilising the target arm facility and a full stroke can be executed as the club head swings under the projecting parts of the arms 74 and if necessary the target arm can be swung out of its position away from the path of the (16) club head if necessary.

Referring now to Figure 22 of the drawings, in a modification of the measuring and training apparatus shown in Figures 3 to 10 of the drawings, the same parts are denoted by the same reference numerals. The base 62 is provided with a measuring scale 106 having slidable pointers 108, said scale extending across the front of the base 62 and being slidably connected at one end to one side of the base 62 which is also provided with a measuring scale 110. These measuring scales 106 and 110 enable the foot positions 112 of a golfer from the centre line of the golf ball and from an aim line 114 to be measured.

The measurement card 68 is provided with a targeting * s. ** .

plate 116 which is slidable on the measurement card 68 to S...

show the golfer the effect on the path of the ball when there is a breaking put. This can be achieved by placing the base 62 of the apparatus on a sloping surface.

: *. * Simulated golf holes 118 can be provided on said surface 5iS c". : 20 and markings representing a golf hole are also provided on * (I the the measurement card 68 and the targetting plate 116.

The measuring and training apparatus also includes visual display apparatus facilitating not only the recordal of measurements to be used in the manufacture of golf clubs but also training a golfer whose address, back swing, downswing, strike through the ball and follow (17) through can be displayed to the golfer to facilitate correction of any errors. The target arm 84 has a downward looking camera 120 and an upward looking camera 122 both located in the target 86 giving a "balls eye" view of the golfer's eyes and upper torso during the execution of an entire golf stroke. The cameras 120 and 122 are shown separated from the target 86 in figure 22 for the sake of clarity, A camera 124 looking towards the golfer is mounted on the support 78 and a camera 126 looking along the aim line 114 is mounted on the base 62.

The display from each of the cameras 120, 122, 124 and 126 is overlaid on cross hair sights to improve accuracy of alignment of the golfer, particularly alignment of the golfers eyes and upper torso. Although the visual display apparatus, normally including a programmable computer and 1s'* visual display unit, can be used with any suitable :. software program, the cross hair sights on the display * S..

unit are created by permanently embedded hardware in : * * either the camera or in the computer in view of the S..

importance of the accuracy of this cross hair feature to the overall accuracy of the alignment of the golfer by the apparatus.

A putting board 128 extends upwardly from the rear edge of the measuring scale 106 to provide a guide for the putter during execution of a putting stroke. The upper surface of the board 128 can be straight, curved, Vshape (18) or of adjustable height to accommodate different shapes of putter.

In a further modification, the ruler 76 can be replaced by two vertically spaced-apart strings positioned to correspond to the upper edge and the lower edge of the ruler 76.

Although each one of the above described measuring and/or training apparatus is particularly suitable for determining the parameters of a golf club to match the requirements of a golfer, it will be appreciated the apparatus can be used as a training aid for golfers and also for training for other sports and measuring their required types of sports equipment such as cricket bats, hockey sticks or the like without departing from the scope * S. * S * c'f this invention.

ISIS e I I... I. * . * S.. I.. * S * S S 555. SI *

S SS

S IS (19)

Claims

Claims: 1. Measuring and/or training apparatus for determining one or more

parameters of a golf club by measuring a golfers physical characteristics at address position comprising a base member on which a golfer can stand in his normal address position whilst gripping a golf club or a simulated golf club and measuring means for determining at least one parameter of a golf club.
2. Apparatus according to claim 1, wherein the simulated golf club is connected to the base plate by a universal joint.
3. Apparatus according to claim 1 or claim 2, wherein the base plate is in the form of a mat having markings thereon to enable the golfer to align himself correctly with ::::. 15 reference to the simulated golf club at address position. S...
4. Apparatus according to any one of the preceding claims, wherein the simulated golf club has a removable grip portion to allow various shapes and sizes of grip to : * be mounted thereon to meet the golfers preference. *..
5. Apparatus according to any one of the preceding claims, where the simulated golf club is of a variable length so that a shaft length which is suitable for the golfer can be determined.
6. Apparatus according to claim 5, wherein the length of the golf club is measured by measuring means which gives a read out on a control unit of the length of the simulated (20) golf club.
7, Apparatus according to any one of the preceding claims, wherein additional measuring means is provided for measuring the lie angle of the simulated golf club and providing a read out on the control unit of said lie angle.
8. Apparatus according to any one of the preceding claims, wherein further measuring means is provided for measuring the lean angle of the simulated golf club and providing a read out on the control unit of said lean angle.
9. Apparatus according to claims 7 and 8, wherein the additional and/or further measuring means comprise television cameras to provide views of the simulated golf club when the golfer has positioned it at address S...

position.
10. Apparatus according to any one of the preceding claims, wherein the simulated golf club is provided with a : * * removable head so that different shapes and sizes of head *S S *:*. 20 can be mounted thereon to meet the golfers preference.
11. Measuring and/or training apparatus for a golfer comprising a ground engaging base having ball positioning means on or adjacent to which a golfer can stand at an address position and alignment means interposed between the ball position and the golfers eyes to facilitate correct positioning of the golfer at the address position. (21)
12. Apparatus according to claim 11, wherein the ball positioning means comprises an arm mounted on the base for pivotal movement about an axis extending perpendicularly to the plane of the base whose free end has a location means for locating a golf ball therein and which is capable of movement from a ball locating position to an out of use position so that the ball can be struck by a golf club.
13. Apparatus according to claim 11 or claim 12, wherein the alignment means comprises a ruler mounted in an elevated position on the base and extending through the centre of the positioned ball along the line which the ball is to be struck by a putter towards a remote measuring means.
14, Apparatus according to claim 13, wherein the ruler is S...

disposed in an upright orientation relative to the plane of the base to give a two dimensional view showing one side face or the other side face of the ruler to the : . e golfer unless his sightline is directly above the centre of the ball when addressing the ball with a putter.
15. Apparatus according to any one of claims 11 to 14, wherein the alignment means comprise a laser device providing a line on which the ball is to be struck by a putter to a point indicated by the laser on the remote measuring means.
16. Apparatus according to any one of claims 11 to 15, (22) wherein the alignment means comprise an arm pivotally mounted on the base for movement about an axis perpendicular to the plane of the base and having a target at its free end to be interposed between the golfers eyes and the ball to facilitate correct positioning of the golfer at the address position when using irons or woods.
17. Apparatus acording to claim 16, wherein the arm is of adjustable length and the free end including the target thereon is of adjustable pitch angle.
18. Apparatus according to any one of claims 11 to 17, wherein a posture maintaining adjustable length spindle is mounted on the base and extends upwardly to contact a suitable part of the golfer at address position and through the swing of the golfer.
19. Measuring and/or training apparatus for facilitating I...

I.'. the correct positioning of a golfer at the address position when using a putter comprising a positioning or training device for ensuring the golfers eyes are : * vertically above the golf ball, said device being disposed S.,.

at the normal ball position adjacent to a putters face and comprising two vertically spaced-apart inter-connected parts which are circular in plan view.
20. Apparatus according to claim 19, wherein the lower part of the positioning or training device has a larger diameter than the upper part.
21. Apparatus according to claim 19, wherein the upper and (23) the lower parts of the positioning or training device have the same diameter.
22. Apparatus according to any one of claims 19 to 21, wherein the upper and lower parts have a sphere of the same diameter interposed therebetween.
23. Apparatus according to claim 22, wherein the sphere comprises a golf ball.
24. Apparatus according to any one of claims 19 to 23, wherein the upper part of the positioning or training device is a solid cylinder having a depth which allows the sides of the cylinder to be discerned by a golfer when the golfers eyes are not vertically aligned above the centre of the cylinder.
25. Apparatus according to claim 24, wherein sections of ::. 15 the curved sides of the solid cylinder are provided in * ** * different colours or visual finishes or markings to facilitate the golfers eye alignment vertically above the centre of the cylinder.

: * *
26. Apparatus according to any one of claims 22 to 25, the a.

upper and lower parts are formed of discs and the discs and the central sphere have the same diameter to allow the apparatus to be disposed with the axis connecting the centres of the upper and lower parts and the sphere horizontally to enable the apparatus to be struck with a putter to roll the apparatus along the ground.
27. Apparatus constructed, arranged and adapted to operate (24) substantially as hereinbefore described with reference to, and as illustrated by, Figures 1 to 11 and 22 of the drawings.
28. Apparatus constructed, arranged and adapted to operate substantially as hereinbefore described with reference to, and as illustrated by, Figures 12 to 21 of the accompanying drawings. * a. *1 S 5.. S... *

* p. P * S p .5 * I * * S a. a

S SI S.