GB2350324A

GB2350324A - An instrument for drawing circles comprising a perforated disc

Info

Publication number: GB2350324A
Application number: GB0008188A
Authority: GB
Inventors: William Harper
Original assignee: Individual
Current assignee: Individual
Priority date: 1999-05-26
Filing date: 2000-04-05
Publication date: 2000-11-29
Anticipated expiration: 2020-04-05
Also published as: GB2350324B; GB0008188D0; GB9912144D0

Abstract

The instrument for drawing circles having a range of radii comprises a rotatably mounted translucent plastics disc 2 (or semi-circular disc) carrying holes 8 positioned on the arc of an Archimedian spiral. The instrument may comprise a pivot 4 in the form of a spike mounted in a hole. Alternatively the member may be rotatably mounted in a frame.

Description

0. - ---1 - ' ' 2 2350324

DESCRIPTION CIRCLE DRAWING INSTRUMENT

The present invention relates to an instrument for drawing circles of a range of radii.

Several types of instrument for this purpose are known and widely used. The most common such instrument, a pair of compasses, comprises two arms of similar length hinged together in a "V" shape. One arm has at its end remote from the hinge a drawing implement or means for holding a drawing implement. The other arm has at its end remote from the hinge means for anchoring that end on the surface upon which the circle is to be drawn. The radius of the circle to be drawn is set using a ruler or other graduated instrument and is maintained during operation by friction in the hinge between the arms.

Figures drawn using this known instrument are often not circles of the required radius, or are not circles at all, due to, inter alia, inaccuracies in the setting of the instrument, progressive widening of the angle between the arms during operation, movement of the drawing implement within the clamp or, where the anchoring means is a spike, enlargement of a hole in which the spike is anchored.

Where students sitting mathematics examinations are required to draw to an -2accuracy of Imm, as is the case in the British GCSE mathematics exam, these inaccuracies may result in students being penalised for the poor quality of their equipment or a lack of manual dexterity, the testing of which is not the object of the examination.

Another known instrument consists of a translucent plastic strip having small holes through the strip arranged in a straight line, usually at 10min intervals. One hole is anchored using a spike, and the point of a pencil is inserted into another of the holes. The strip is then rotated about the anchored hole and a circle is drawn having a radius equal to the distance between the anchored hole and the hole in which the pencil point was inserted. Instruments of this type suffer from the disadvantage that, since the holes are generally placed at 1 Omm intervals, only circles with a radius of an integer multiple of this distance may be drawn.

Other instruments for drawing circles are also known, e.g. beam compasses and the device disclosed in EP0855961. Neither of these instruments is easy to use, nor are they suitable for use by students in a classroom enviromnent. The former also suffers from some of the disadvantages of the first-mentioned instrument.

It is an aim of the present invention to provide a instrument for drawing accurately circles of a chosen radius which overcomes some of the problems -3associated with the above-described instruments and which may be suitable for use in applications in the fields of mathematics, science, engineering, design, architecture and the like.

It is a further aim of the invention to provide such a instrument which is cheap and simple to manufacture.

In accordance with the present invention there is provided an instrument for drawing circles of a range of radii, comprising a rotatable component carrying a plurality of apertures positioned on at least one are of at least one spiral, each aperture being positioned an integer multiple of a predetermined increment from a centre of rotation of the component.

The apertures may be ofjust sufficient internal diameter to accommodate the point of a sharp pencil.

Preferably, the instrument may further comprise a pivot means, which may comprise at least one hole and/or at least one protrusion from the underside of the instrument, which at least one protrusion may be or may comprise at least one spike. The advantage associated with the provision of a protrusion is that the protrusion not only serves as a pivot but also prevents or inhibits lateral movement of the component.

Preferably, the at least one spiral is of the form r=(0-a)lk (i.e. an Archimedean spiral), where r is the distance of a point on the spiral from the centre of the spiral, 0 is an angle, a is a constant angular offset and k is a constant, r being measured in the same units as the predetermined increment.

In this way, the correct aperture for drawing a circle of the desired radius may be found by following the spiral outwards from the centre of rotation of the component and counting the increments until the required distance is found.

Preferably, the apertures are additionally arranged on a plurality of straight lines radiating from the centre of rotation of the component. This has the advantage that the straight lines form a second aid to the identification of the correct aperture.

Preferably the apertures are arranged on an arc of a single spiral.

In the most preferred embodiment the apertures are positioned on an arc of a single spiral, k---"16', the increment is Imm, and the apertures are additionally arranged on ten straight lines radiating from the centre of rotation of the component and disposed 36' apart. This has the technical advantage that each of the apertures lying an integer number of centimetres from the centre of rotation of the component lie on one line, each of the apertures Imin further than an integer number of centimetres lie on a second line, and so on, up to the apertures which are 9mrn further than an integer number of centimetres from the centre of rotation of the component, which lie on a tenth line.

In another advantageous embodiment the apertures are positioned on an arc of a single spiral, k--30', the increment is 1 twelfth of an inch, and the apertures are additionally arranged on twelve straight lines radiating from the centre of rotation of the component and disposed 30' apart. The advantage of this embodiment is similar to that of the previous one, except that there are twelve lines and each of the apertures is an integer multiples of 1 twelfth of an inch from the centre of rotation of the component.

In another embodiment the apertures are arranged on arcs of nine spirals, k--20', a first spiral has an offset a=O', the second spiral has an offset a= 160% the third spiral has an offset a=320' and the nth spiral has an offset a=((n-1) x 160') mod 3 60, apertures at a distance of less than 1 Ornin from the centre of rotation of the component lying on the first spiral, apertures at a distance of 10-19min from the centre of rotation of the component lying on the second spiral, apertures at a distance of 20-29mm from the centre of rotation of the component lying on the third spiral, etc, apertures at a distance of 90-99min from the centre of rotation of the component lying on the first spiral and an aperture at 1 0Omm from the centre of rotation of the -6component lies on the second spiral.

Preferably in any embodiment. the apertures may be adapted to accommodate a blade. This has the advantage that a circle of a desired radius may be cut from paper, card or textiles accurately and without separate drawing and cutting stages.

Advantageously, the instrument may comprise a plurality of circular template holes of various sizes. Since the first-mentioned apertures are positioned closer together in the vicinity of the centre of rotation of the component, it is difficult or impossible to position an aperture at, for example 1 m_m distance and at 2mm distance from the centre of rotation of the component. It is therefore advantageous to have, elsewhere on the sheet, e.g. towards its circumference, circular template holes having radii of, for example lmm, 2nim, 3min and 4min. It will also be obvious to the skilled man that this modification could be equally well applied to embodiments having imperial measurements.

Advantageously, the instrument may have at least one edge formed as an arc of a circle and upon which degree or other angular graduations are marked.

Preferably, the component is formed of a plastics material and may be translucent. This allows the user to place the instrument more accurately when if is desired to draw a circle around a particular centre.

Specific embodiments of the invention will now be described, with reference to the accompanying drawings, in which:

Fig. I shows a first embodiment of the invention; and Fig. 2 shows a second embodiment of the invention.

The embodiment shown in figure I comprises a substantially circular disc 2 of translucent plastics sheet material. At the centre of disc 2 in a hole 4 is mounted a spike (not shown) which acts as an anchor for the disc and about which the disc pivots.

Arranged in an Archimedean spiral (i.e. a spiral of the form r--O/k) around central hole 4 are a plurality of further holes 8 (which may be countersunk), each big enough to accommodate the point of a pencil or other writing or drawing implement. The equation of the spiral in the embodiment shown is r--0/36 (r and 0 are measured in millimetres and degrees respectively). It will be obvious to the skilled man that this equation is equivalent to the equation r--(O-a)/36, when a=O.

A first hole 8a is at a distance of 5mm from central hole 4 and a last hole 8b is at a distance of 100min from central hole 4. The remaining holes 8 are situated on the spiral with an angular separation of 36' between holes of a consecutive number of millimetres distance ftom central hole 4. There is a single hole 8 at each integer -8 number of millimetres distance (between 5mm and 1 0Omm) from central hole 4. As a result, holes 8 are additionally arranged on ten radii 1 Oa,. .., 1 Oj of disc 2, separated by an angle of 3 6'. Radii 10 are marked on the surface of disc 2.

Also marked on the surface of disc 2 are eight loops 12a,..., 12h formed of line segments between holes 8. Loop 12ajoins holes 8 at 10, 11,..., 19mm distance from central hole 4; loop 12b joins holes 8 at 20, 21,..., 29min distance from central hole 4; and so on. No loop connects holes 8 at 5, 6, 7, 8, 9 and 1 0Onim distance from central hole 4 to any other hole.

Each of the holes 8 on radius 1 Oa is an integer multiple of 1 Omm from central hole 4. Moving anti-clockwise, each of the holes 8 on radius 10b is an integer multiple of 1 Omm. plus 1 mm from central hole 4 (e.g. holes 8 on radius 1 Ob are at a distance of 11, 21,..., 9 1 min from central hole 4). Similarly, each of the holes 8 on radius 1 Oc are an integer number of 1 Omm plus 2mm from central hole 4 (e.g. 12, 22, 32,..., 92min). The holes on the other radii are positioned in a similar manner, no hole 8 being closer than 5rnrn to central hole 4.

Each radius 10 except radius 1 Oa is marked towards its outer end with a numeral 14 related to the distance of the holes on that radius from central hole 4, e.g. radius 1 Ob is marked '. F, radius 1 Oc is marked '. 2', and so on.

Each hole 8 on radius 1 Oa is marked with a numeral 16 indicating the number of centimetres between it and central hole 4.

Additionally arranged on disc 2 are circular stencil holes 18 of radii I min4min. These holes may be inscribed when it is desired to draw a circle having one of these radii.

To use the embodiment shown in figure 1 to draw a circle of radius 76min, for example, the instrument is placed such that the spike mounted in central hole 4 is over the point intended to be the centre of the circle. Downward pressure may be applied to disc 2 in the vicinity of central hole 4 such that the point of the spike forms a depression in, or penetrates, the material upon which the circle is to be drawn. The point of a pencil or other implement (e.g. a crayon, felt tip pen, etc) is then inserted into the hole 8 found where loop 7g, marked 7and radius 1 Og, marked '.6', intersect. To aid in this operation, loops 7 may be marked in more than one colour, for example loop 7a may be red, loop 7b blue, loop 7c red, etc. The pencil is then drawn around the central hole 4 causing disc 2 to rotate about that hole. Downward pressure may continue to be applied to the tool in the vicinity of central hole 4 during the drawing of the circle if necessary to prevent the point of the spike from sliding along the surface upon which the circle is being drawn.

This embodiment has the advantage that it rotates about its centre of mass.

Figure 2 shows a second embodiment of the invention which comprises a substantially semicircular component 102 of translucent plastics material 102. Substantially midway along the straight edge 103 of component 102 is a pivot hole 104.

A plurality of holes 108 (which may be countersunk) are arranged about component 102 on arcs of Archimedean spirals of the form r=(0-a)/20. Each hole is an integer number of millimetres distance from pivot hole 104 and there is one hole 108 at each distance in the range 5min to 1 0Omm.

Holes 108 at distances 5mm-9mm and 90nun-99mm from pivot hole 104 are arranged on arcs 112a and 112j of a first spiral having equation f-e/20 (r and e in millimetres and degrees respectively); holes 108 at distances 1Omm-19mm from pivot hole 104 are arranged on an arc 112b of a second spiral having equation r--(0160)/20 and the hole 108 at distance 1 0Omm. is also arranged on this spiral; holes 108 at distances 20=-29mm from pivot hole 104 are arranged on an arc 11 2c of a third spiral having equation r--(0-320)/20; holes 108 at distances 30mm-39mm. are arranged on an arc 112d of a fourth spiral having equation r--(0-120)/20; holes 108 at distances 40mm-49mm from pivot hole 104 are arranged on an arc 1 12e of a fifth spiral having equation r=(0-280)/20; holes 108 at distances 50mm-59min are arranged on an arc 112f of a sixth spiral having equation r--(0- 80)/20; holes 108 at distances 60mm-69mm are arranged on an arc 112g of a seventh spiral having equation r--(0-240)/20; holes 108 at distances 70nim-79mm are arranged on an are 112h of an eighth spiral having equation r--(0-40)/20; and holes 108 at distances 80mm-89mm are arranged on an arc 112i of a ninth spiral having equation r--(0200)/20. As a result, the holes are also arranged on ten radii 110a,..., I Oj of component 102, separated by an angle of 20'. Radii 110 are marked on the surface of component 102.

Also marked on the surface of component 102 are the nine arcs 11 2a,..., 11 2j, formed of line segments between holes 108.

Each of the holes 108 on radius 11 Oa is an integer multiple of 1 Omm from pivot hole 102. Moving anti-clockwise, each of the holes 108 on radius 11 Ob is an integer multiple of 1Omm plus Imin from pivot hole 104 (e.g. holes 108 on radius 10b are at a distance of 11, 21,..., 91min from central hole 104). Similarly, each of the holes 108 on radius 11 Oc are an integer multiple of 1 Omm plus 2min from pivot hole 104 (e.g. 12, 22, 32,..., 92mm). The holes on the other radii are positioned in a similar manner, no hole 108 being closer than 5mm to pivot hole 104.

Each radius 110 except radius 11 Oa is marked towards its outer end with a numeral 114 related to the distance of the holes on that radius from pivot hole 104, e.g. radius 11 Ob is marked '. F, radius 11 Oc is marked '.2.', and so on.

Each hole on radius 11 Oa is marked with the number of centimetres between it and pivot hole 104.

Marked around a substantially semi-circular edge 113 of component 102 are degree graduations 116 (separated in the drawing by 5').

Arcs 112 may be marked in more than one colour, as in the first embodiment.

This embodiment is used in a substantially similar manner as the first embodiment. More care is required since the instrument does not rotate about its centre of gravity.

A third embodiment (not shown in the drawings) comprises a rotatable component, substantially as shown in figure 1 with the exception that central hole 4 is not provided. This component is rotatable mounted within a frame.

To use the third embodiment, the frame is held in place on the surface upon which the circle is to be drawn (manually or with the aid of one or more spikes or other protrusions from the underside of the frame). The circle is then drawn in a substantially similar manner.

Additionally or alternatively, the holes in any embodiment may be adapted to accommodate a blade so that a circle of desired radius may be cut quickly and accurately from paper, card, etc without separate drawing and cutting stages. For example, the holes may be substantially keyhole or slot shaped.

p k_ c f -,:-,- -, &

Claims

-14CLAIMS

1. An instrument for drawing circles of a range of radii comprising a rotatable component carrying a plurality of apertures positioned on at least one are of at least one spiral, each aperture being an integer multiple of a predetermined increment from a centre of rotation of the component.

2. An instrument as claimed in claim 1, wherein the apertures are ofixist sufficient internal diameter to accommodate the point of a sharp pencil.

An instrument as claimed in claim 1 or 2, further comprising a pivot means.

4. An instrument as claimed in claim 3, wherein the pivot means comprises at least one hole.

5. An instrument as claimed in claim 3 or 4, wherein the pivot means comprises at least one protrusion from an underside of the instrument.

6. An instrument as claimed in claim 5, wherein the at least one protrusion comprises at least one spike.

7. An instrument as claimed in any of the preceding claims, wherein the at least one spiral is of the form r--(0-a)/k, where r is a distance of a point on the spiral from the centre of the spiral, 0 is an angle, a is a constant angular offset and - 15 k represents a constant, r being measured in the same units as the increment.

8. An instrument as claimed in claim 7, wherein the apertures are additionally positioned on a plurality of straight lines radiating from the centre of rotation of the component.

9. An instrument as claimed in claim 8, wherein the apertures are arranged on an arc of a single spiral.

10. An instrument as claimed in claim 9, wherein k--3 6' and the increment is 1 min and the apertures are arranged on ten straight lines radiating from the centre of rotation of the component, the lines being disposed at angles of 36' degrees to one another.

11. An instrument as claimed in claim 9, wherein k-3 0' and the increment is 1 twelfth of an inch and the apertures are arranged on twelve straight lines radiating from the centre of rotation of the component, the lines being disposed at angles of 3 0' to one another.

12. An instrument as claimed in claim 7, wherein the apertures are arranged on arcs of nine spirals, k--20', a first spiral has an offset a=O', a second spiral has an offset a-- 160% a third spiral has an offset a=3 20' a fourth spiral has an offset a=120% a fifth spiral has an offset a=280% a sixth spiral has an offset a=80' -16a seventh spiral has an offset a=240' and an eighth spiral has an offset et=40', a ninth spiral has an offset a=200', apertures at a distance of less than 1 Omm. from the centre of rotation of the component lying on the first spiral, apertures at a distance of 1019mm from the centre of rotation of the component lying on the second spiral, apertures at a distance of 20-29nim from the centre of rotation of the component lying on the third spiral, apertures at distance of 30-39mm from the centre of rotation of the component lying on the fourth spiral, apertures at a distance of 40-49nun from the centre of rotation of the component lying on the fifth spiral, apertures at a distance of 50-59mrn from the centre of rotation of the component lying on the sixth spiral, apertures at a distance of 60-69mm from the centre of rotation of the component lying on the seventh spiral, apertures at a distance of 70-79min from the centre of rotation of the component lying on the eighth spiral, apertures at a distance of 80-89min from the centre of rotation of the component lying on the ninth spiral, apertures at a distance of 90-99mm from the centre of rotation of the component lying on the first spiral and an aperture at 1 0Omm from the centre of rotation of the component lies on the second spiral.

13. An instrument as claimed in any of the preceding claims, wherein the apertures are adapted to accommodate a blade.

14. An instrument as claimed in any of the preceding claims, wherein the component has a plurality of circular template holes of various sizes.

15. An instrument as claimed in any of the preceding claims, wherein the component has at least one edge formed as an arc of a circle which arc comprises degree graduations.

16. An instrument as claimed in any of the preceding claims, wherein the component is formed of a plastics material.

17. An instrument as claimed in any of the preceding claims, wherein the component is translucent or transparent.

18. An instrument as claimed in any of the preceding claims, wherein the component is rotatably mounted within a frame.

19. A tool substantially as hereinbefore described with reference to and as illustrated in figure 1.

20. A tool substantially as hereinbefore described with reference to and as illustrated in figure 2.