GB2059607A - Subdividing the circumference of a circle - Google Patents

Abstract

A device for subdividing the circumference of a circle comprises four blocks 3, 4, 5, 6 mounted for adjustment along arms 1, 2, with the blocks 4, 5 being pivotally connected and aligned by shaft 22. In use, the block 6 is positioned with locating pin 23 at the centre of the circle, blocks 4 and 5 are located on the circumference and block 3 is moved on to the circumference where it indicates the portion of a subdivision. <IMAGE>

Description

SPECIFICATION Title-beam divider The invention relates to tools used in the workshop and is concerned in particular with the methods used to sub-divide the circumference of circles by hand. Although the invention will perform equally well anywhere accurate centre co-ordination or circumference sub-division is required.

The existing method of circumference subdivision is to use dividers and is shown in Fig. 1 to Fig. 3. The method of setting the scribing radius to a given measurement i.e. two inches is shown in Fig. 1. With this distance as the radius the dividers are used to scribe a circle as shown in Fig. 2. The method of spacing out a number of equal divisions of the scribed circumference is shown in Fig. 3.A centre pop mark is placed on the previously scribed circumference line at the desired starting point and with the dividers set at the desired chord distance (i.e. for six divisions the radius of the circle is used) the point of one divider leg is placed on this 'pop' and small arc. struck so as to cut the circumference line, the divider point is then transferred to this intersection, which should first be centre popped and the process repeated until the circumference is sub-divided as desired.

The method described is not a very accurate procedure since the setting of the dividers and the accuracy of placing the 'pop' mark at each subdivision can lead to a build up of error that can make the final sub-division unacceptably inaccurate, i.e. the greater the number of subdivisions required the more difficult it becomes to produce an accurate piece. Although it is possible to achieve almost absolute accuracy by using the various methods of mechanical sub-divisions i.e.

dividing head, rotary table etc., these methods are expensive and need the facilities of a well equiped workshop.

It is improving the existing bench methods of circle circumference sub-division that the invention is aimed although variations of the device may be used on a machine that the smallest workshop will possess, namely the drill press, and give accurate results at low cost.

According to the present invention there is provided a means of carrying, positioning and locating around a circle. Two reference points in relation to a third reference point in a configuration that enables one reference point to represent the centre of the circle and of the other reference points one is used to represent the length of the circle radius and the other is used to represent the length of the circle chord with respect to the radius reference point. Because the shape that is established when using the invention could represent a multi-sided figure the above configuration applies also to the polygon.

By way of example only an embodiment of the invention will be described in greater detail with reference to the accompanying drawings, Fig. 5 shows a plan view and Fig. 4 an elevation of that which is here is known as the device or basic device shown set for making three divisions equally spaced.

Referring to the drawing Fig. 4 to Fig. 8 the device consists of two arms 1 (chord arm) and 2 (radius arm) upon which are mounted four blocks, 3, 4, 5, and 6, two per arm. The blocks are of similar design having a semi-circle 7 around one end face with a diameter equal to the width of the block and a tapped hole 8 in the centre of the other end face. Two holes 9 and 10 are positioned in the blocks with their centre lines exactly at 900 in both pianes to each other. The centre line of hole 9 co-insides with that of the semi-circle 7 and is also square in both planes to the faces 11 oi the block. The tapped hole 8 is also parallel to the ,face 11 and its centre line co-insides exactly with that of hole 10, midway between faces 11, but is at 900 to same.The arms pass through close fitting holes 10 and can slide in same but are prevented from rotating by means of the lock screw 12 which abutts the flat surface 13 cut along the entire length of the arms. A spring loaded ball 14 is mounted in each lock screw, which allows controlled movement of the blocks with respect to the arms when the lock screw is lightly clamped but also enables the block to be firmly and squarely clamped to the arm. The surface 13 also ensures that the blocks on the same arm remain exactly in the same plane whatever their position on the arm.

The blocks 4 and 5 form the radius location point and are hinged together (Fig. 6) by means of a close fitting concentric hollow shaft 1 5 which passes through holes 9 in the blocks. The assembly is held together by means of the thrust washers 1 6 and the circlips 1 7 and the hinge is given some in built resistance to turning by means of the wavey spring washer 1 8 which is compressed by the assembly to give the desired stiffness. The above arrangement in conjunction with the flat surface 13 on the arms ensures the device remains substantially in one plane when in use.The hinge arrangement also allows the arms to be moved from a position in which they are parallel to one another to one in which they are 900 to each other.

A section through block 6 which forms the circle centre location is shown Fig. 7. It consists of a stepped diameter concentric hollow shaft 1 9 which is a close fit in hole 9 in block 6. The assembly is held together by means of thrust washer 1 6 and circlip 1 7. A wavey spring washer 18 is provided to prevent easy rotation of shaft 19, in hole 9.

Fig. 8 shows a section through blocks 3 which forms the chord location. This assembly is very similar to that shown in Fig. 6 and consists of a concentric hollow shaft 20 which passes through hole 9 in blocks 3. The spacing piece 21 is used to accommodate the shaft length, the assembly also consists of the wavey washer 18, and is held together by means of the thrust washer 1 6 and circlip 17.

A suitable marking piece 22 Fig. 6 is shown in its working position. It consists of a hardened and tempered shaft that is a close fit and may float in hollow shaft 15, its work end is ground concentrically to a 600 inclusive cone.

What is considered to be a suitable location piece is shown at 23 Fig. 7 and Fig. 8, it consists of a hardened and tempered shaft with one end threaded to accept head 24 and the other end concentrically ground to a 600 inclusive cone.

It will be noted from Fig. 7 that the overall length of this assembly is slightly shorter than those of Fig. 6 and Fig. 8. This is to allow the location pin 23 of this assembly to protrude through the bottom of the stepped hollow shaft 1 9. It is held in this position, which is determined by the assembled device lying in a level plane (Fig.

4) with the ends of hollow shafts 1 5 and 20 in square contact with the work piece surface and the conic end of the circle centre location piece 23, Fig. 7 lying in a conic depression or 'pop' mark in the workpiece surface, by means of lockscrew 25.

The chord location piece 23, Fig. 8 is a close fit in the hole in the hollow shaft 20 and is allowed to float in same. This is to prevent possible damage to the conic end of the location piece when the device, in use, is rotated around the circle centre location piece. The assembly Fig. 8 may be replaced by that shown in Fig. 13, which is an arrangement similar te that shown in Fig. 7 but inverted. In this assembly the chord location piece is set to a pre-determined height (as explained for the circle centre location) and is held in position by means of the lockscrew 25. Although this arrangement makes it slightly easier to locate the chord location piece care must be taken not to damage the protruding conic end of same when using the device.

Both the marking and location pieces have been arranged to be easily removable and allowance has been made so that regrinding of the cones is possible before renewal becomes necessary.

The device shown has been arranged so that it is possible to use it either way up i.e. the marking and location pieces may be placed in the other direction. This has an advantage in respect of "error splitting" (described later) which may only be achieved without resetting if complete squareness and alignment of the device is maintained in its manufacture.

Setting of the device is achieved by means of caliper vernier, slip guages or micrometer and is carried out by measuring over the reference diameters Fig. 1 6. These diameters are principally those of the thrust washers 1 6, stepped shaft 1 9 and spacing piece 21 which are all exactly the same diameter, lie in the same plane and are concentric to the holes through which the marking and location pieces pass.

The setting measurements which must be made with respect to the centre line of the holes in which the marking and location pieces pass is achieved, depending on the type of setting instrument used by either adding to or subtracting from the measurement desired, the diameter of one roller (Fig. 1 6 add roller diameter).

Alternatively setting paces may be provided on the centre line Fig. 19 either by using setting rods Fig. 1 7 that replace temporarily the marking and location pieces, two only being required since the chord and centre location setting rod would interchange from one to the other or by using headed hollow shafts in place of the hollow shafts 1 5 and 20 and cutting reference faces to bisect the centre line of the holes through which the location and marking pieces pass Fig. 1 8.

To set the device one arm is set to the radius of the circle desired (radius arm) whilst the other arm is set to the chord length (chordarm). The latter dimension is determined from the number of circumference sub-divisions required and it is possible to calculate a constant for any number of sub-divisions on the basis of unity circle diameter.

It is then only necessary to multiply the constant chosen by the diameter of the circle required. Both settings are taken as shown Fig. 1 6 or Fig. 1 9 from the radius location reference face to the chosen arm.

An additional aid to setting may be provided on blocks 3 and 6 in the form of a fine adjustment Fig. 5 This arrangernent allows the block to which it is attached to be adjusted via the adjusting nut 26 after first clamping the adjusting block 27 to the arm.

To allow a "quick set" of the device spacing pieces of predetermined length may be used. Fig.

11 shows piece 10 on chord arm only although the idea may be applied to both arms. Because, to cover the range of the device, a large number of setting pieces would be required they could be adopted for popular or regularly used sizes only.

To use the device, it is placed on the work piece with the centre location piece mounted in the centre location and placed in a previously marked 'pop' locating the circle centre, being held in this position by one hand. The marking piece is placed in the hole in the radius location position of the device and a 'pop' mark made, by striking the head of the same, at the desired starting point thus producing a 'pop' at the circle radius. The device is then rotated about the centre location piece until the chord location piece on the chord arm is in the said 'pop' mark and holding it firmly in this position a further 'pop' is made in thQ new position occupied by the marking piece. This process is repeated until the circumference of the circle is sub-divided as required. In each case the circle centre and chord location points are held in their respective 'pop' marks by one hand whilst the marking piece is operated by the other hand.

In cases where the radius is so large that it is impossible to hold both location pieces with one hand an arrangement as shown in Fig. 9 to Fig. 11 may be used. It consists of two housings 1 which are a close fit on rod 3 and may be clamped to same by means of screws 4. Two hardened and tempered shafts 5 which have their ends concentrically ground to 600 inclusive cones are a close fit in the chord and centre location holes 2 and also in the housing 1. They are held in the latter by means of clamp screws 6. The housings are held in a common plane when clamped by means of the flat surface 7 on rod 3. This assembly which effectively locks the locating pieces together may be also used independently to perform as a beam compass or a precision divider.When used as the latter the housings 1 should be made equal in diameter and the holes that locate the shafts 5 be concentric with the housing diameter.

Additional security for the circle centre location pieces is possible by using button magnet 8 Fig.

1 0. The location piece is a close fit in the bore of the said magnet which fits against the face of the stepped shaft 9 which in turn has been shortened to accommodate themagnet.

This arrangement would adhere to magnetic surfaces and help prevent the centre location peice from being easily dislodged from its 'pop' mark. Also this arrangement of the centre location assembly with the magnet removed would readily adapt to the centre finder location pin mounted in the adaptor block 1 Fig. 21. The minimum number of circumference sub-divisions that the device could be expected to be used te obtain is three but this is not a design requisite because the circumference may be sub-divided into multiples of the desired number and only the points required used ii.e. for three division mark six, for four mark eight etc.) This means that the limit of the device is governed by the length of the radius arm and not the chord arm (i.e. for equal divisions less than six the chord length is greater than the radius).An ideal arrangement seems to be to make both arms the same length thus for the largest radius available a minimum of six sub-divisions would be possible, although interchangeable arms of different length is another possibility.

The arrangement of the device shown in Fig. 4 can cope with a range of subdivisions from the smallest 1" diam. circle having either 3, 4, 5, or 6 sub-divisions up to a 12" circle having any from 8 to 75 sub-divisions. The smallest chord is dictated by the minimum distance between the locating hole and the marking hole centre lines on the chord arm whilst the largest chord is dictated by the maximum distance between same.

This reasoning also applies to the radius and the radius arm.

It will be obvious from the way in which the device works that if only one starting point is used, it will be possible over large numbers of divisions to have an accumulation of error i.e. .001" error in setting of chord dimension can lead to .050" error on the last of fifty divisions. It is possible to practically eliminate this error by adopting a method in which the divisions are built up in multiples of the desired number i.e. for fifty divisions first mark five equal divisions around the desired circumference, thus five starting points are created each of which may be used in turn to divide each division into ten equal divisions giving fifty in all. The process may be repeated as many times as the final figure required will allow.

Alternatively if the device can be used either way up it is possible to begin marking the division in a clockwise direction for 1 80 degrees then to reverse the device and mark in an anti-clockwise direction from the original starting point, for 1 80 degrees. This procedure halfs any possible error in the chord arm setting and it may be combined with the multiples method described earlier.

In order to make the device eassier to use on small radius settings Fig. 20 adjustment and locking is provided on all blocks so that the arms may be positioned to balance the device.

Alternatively shorter arms may be used.

An example of the basic device being used on a commercially available centre finder is shown Fig.

21. It is adapted by means of the adaptor block 1.

This allows the device to be supported for use in marking annular rings. Although by using a suitably designed adaptor block that would allow the centre finder blade 2, to lie close to the surface to be marked the arrangement could be used for marking sub-divisions on circular discs.

Modification to the basic device to make it suitable for marking the edge of discs is shown Fig. 1,2 to Fig. 1 5. The modification is to the radius arm 1.

and consists of an extension 2 to the basic arm which lies at 900 to the said arm as shown and upon which is mounted a marking piece arrangement 3, which may be positioned as required along the arm. The extension may be as shown in Fig. 12, formed as part of the radius arm or it may be a clamp on arrangement. Fig. 12 and Fig. 1 5 shown an elevation and plan of the device, the flat surface 4 which continues into the extension arm 5 performs the function described previously of ensuring all the blocks on the same arm lies in the same plane also in this case ensures that the centreline of the marking piece arrangement 6 lies on the same projected centre line 7 of the blocks on the radius arm 1. The marking piece arrangement is similar in design to that of the location piece assembly Fig. 13 and is clamped to the arm by means of the lockscrew 8.

The marking piece 9 consists of a hardened and tempered shaft that is a close fit in the hollow shaft 10 of the marking piece arrangement and has its work end concentrically ground to a 600 inclusive cone. The device is set as described previously. The radius chosen should be as large as possible for reasons of stability and the marking arrangement 3 should be set as close as possible to the edge 11 of disc to be marked. The technique is first to mark out the surface 12 with the number of sub-division required then to transfer these spacings to the edge of the disc by means of the marking piece 9.

Although the design of the basic device shown is not the cheapest possible it does appear to offer the best compromise in the use of common parts.

The geometric cross-section shape of the chord and radius arms may be as shown 'D' shaped (Fig.

9 show rectangular shaped arms) or of any other shape providing the blocks can be accurately located and slide on same. The arms may be made in the form of slotted links in which the blocks slide in the slots therein.

In a crude version of the device the location pieces may be mounted directly into the blocks and the marking piece may also form the hinge pin. Setting of the device being possible by measuring over the marking and location pin diameters which may also differ in design from those shown providing they perform the necessary functions of marking and location. A further development of the device, this time in instrument form, is shown in Fig. 22 and 23. Here, one of the arms preferably the chord arm, and its associated locating and hinge blocks are incorporated as part of the beam and slide of a vernier gauge. The advantage of this arrangement is that no separate setting instrument is required.The radius dimension is set as shown by rotating the radius arm into the position 1. and locating its reference bore 12 on the chord arm, by means of the location pin 2 which is a close fit in hoth bores.

The radius length is then set on the vernier scale 3 and the centre location block locked to the arm by means of lockscrew 4. The location piece 2 is then removed to free the radius arm and the chord arm is then set direct from the vernier scale and locked by means of the lockscrew 11. Fine adjustment fo setting is provided at 8. An automatic centre punch is shown in the marking position 10. The device is used as described for Fig. 4 and may if constructed as described be used with the arrangement shown in Fig. 12-Fig. 1 5 (Marking edges of discs).

By addition of the jaws 6, the scale 9 and its vernier 7 the device could double as an inside and outside vernier caliper.

By building the basic device in a more substantial form, it may be made into a variable pitch circle diameter drill jig. The centre location mounted on a suitable pivet which is attached to a base plate. A drill bush placed in the marking location and a suitable coned or ball ended pin mounted in the chord location position is one possibility. Alternatively, the marking location containing the drill bush may be mounted on the base piate and the centre location fitted with a cone ended pin which would locate the work piece centre and allow the workpiece to rotate about the same. The chord location being as described for the first arrangement. The technique involved in the use of the jig is to drill the first hole on the chosen radius then to position the chord location in this hole and to drill another hole in the position occupied by the marking location.This process is repeated until the workpiece is drilled as required.

A simple rotary indexing arrangement is also possible. Consider the device as shown in Fig. 9 to Fig. 11 (the basic arrangement could be used instead) and simplify it Fig. 24. The two radius arms 1 and 2 are mounted on a common centre 3.

The chord arm is constructed from the setting tube 4 and threaded shaft 5 which are locked together by nuts 6 (length of 4 and 5 to suit chord dimension required) location holes 7 and 8 are provided at the end of the radius arms at radius R.

This arrangement is mounted by its centre 3 on the centre 3 of disc 9 which has a hole la positioned on Radius R, and a means of locating hole 10 with either hole 7 or 8 provided.

To allow this assembly to be used to index it is necessary to provide a means of preventing rotation about the common centre 3 by clamping to a fixed base both the disc and its associated arrangement (which we will label 'A' for clarity) in a manner that will allow one to be free to rotate while the other remains clamped. For some applications the disc may be replaced by an arm carrying the location hole 10.

To operate the indexing arrangement the following procedure is adopted.

If we assume a condition Fig. 25 in which the disc 9 and the arrangement 'A' are clamped and thus are unable to rotate about centre 3. Also the hole 10 in the disc 9 is located with hole 7 with a suitable location pin. The disc only is then unclamped, the location pin withdrawn and the disc rotated in this case clockwise, until the location pin may be entered in hole 8 Fig. 26 at which point the disc is reclamped. The location pin is then drawn ad the arrangement 'A' unclamped and rotated clockwise until hole 7 can be located once more with hole 10. The arrangement 'A' is then reclamped Fig. 27. Hole 8 is now in a new position on the circumference ready to begin a new cycle of the procedure.

Since the clamping procedure alternates between disc 9 and arrangement 'A'. A common clamp which could be incorporated with the location pin thus allowing a single motion operation is envisaged.

Claims (6)

CLAIM What I claim is reasonable means of the kind set forth for sub-dividing the circumference of a circle around a projected or prescribed radius by the use of at least three reference points arranged in a configuration that will allow one reference point to be used to represent the circle centre, one to represent the length of the radius and the third to represent the length of the chord line (ie distance between sub-divisions) with respect to the radius reference point. To ensure the configuration may cover a range of circle diameter and sub-divisions or only the latter when using a prescribed radius, means of adjustment is provided that will allow the desired radius and chord lengths to be set and also cater for the change in sector angle that occurs when the chord length is altered. A means of transferring the afore-mentioned reference points into or onto, depending on which point is being considered, physical characteristics on the workpiece or any associated surface is incorporated or capable of being incorporated at each of the said points. New claims filed on 22-10-80. Superseded claims "Claim as filed". New or amended claims: What I claim is reasonable means of the kind set forth for

1. Sub-dividing the circumference of a circle by use of the geometric chord and radius dimensions arranged in a configuration that will allow a common point (radius reference point) on the circle circumference to be used for the projection of the said dimensions. The radius line is projected toward the circle centre (centre location point) and the chord line is projected toward a circumferential point (chord location point) a calculated chordal distance from the common circumferential point.The calculated chordal distance is a function of the number of subdivisions and is preferably derived from the geometric formula for the circular segment.

2. A configuration as described in (1) in which a means of accurately transferring the common or radius reference point into a physical characteristic (e.g. concentric conical-indent) on the workpiece or any associated surface is incorporated or is capable of being incorporated at the said point.

3. A configuration as described in (1) in which there is provided at the chord location point a suitable location piece that will accurately and concentrically locate the said point within the physical characteristic provide at (2) (e.g. cone in conical indent, sphere in conical indent, sphere in hemisphere etc.,).

4. A configuration as described in (1) in which' there is provided at the centre location point a means of accurately and concentrically locating the centre location point in a manner that will allow the configuration to be rotated around the -said point.

5. To ensure the configuration described in (1) may cover a range of circle diameters and sub divisions means of adjustment is provided that will allow the desired radius and chord lengths to be accurately set and also to cater for the change in segment angle (angle projected at the circle centre from the ends of the chord length) that occurs when the chord length is altered. (To allow setting the chord and radius dimensions suitable means (e.g. setting scale(s), may be incorporated in the said configuration, alternatively a separate setting.

device may be used.)

6. A configuration as described above in which the said segment angle is created and maintained by,the accurate and secure location of the circle centre and chord location pieces in their associated pre-formed location indents.