GB2255750A

GB2255750A - Device for drawing arcs of circles.

Info

Publication number: GB2255750A
Application number: GB9110454A
Authority: GB
Inventors: Jonathan Gwyn Adams
Original assignee: Individual
Current assignee: Individual
Priority date: 1991-05-14
Filing date: 1991-05-14
Publication date: 1992-11-18
Anticipated expiration: 2011-05-14
Also published as: GB9110454D0; GB2255750B

Abstract

The device comprises a chassis divided into two sections (16, 17) with wheels (19, 20) fixed to each section thereof. Each wheel revolves independently of the other wheels. The two chassis sections are joined by a pivot (18) with a clamp screw allowing the angle between the two sections to be continuously adjustable and fixable. A callibrated scale (21), together with a clock vernier (23), shows the angle between the two sections of the chassis. The angle is proportional to the radius of the arc defined by the device as it is propelled across the working surface. A pen/pencil holder (26) is provided on a linear scale (27). <IMAGE>

Description

ARC DEFINING DEVICE The present invention relates to a device for defining an arc of a circle on a surface. The invention has particular, though not exclusive, application as a drawing aid for use in drawing arcs of circles of large radii.

A number of devices are available to assist in the drawing of circles or arcs of circles. For drawing a circle, or an arc of a circle, having a radius of up to approximately 300mm, a divider-type compass is most commonly used. Where the arc to be drawn has a radius between approximately 300mm and 1500mm, a beam compass can be used. However, technical draughtsmen frequently need to draw arcs of circles of much larger radii. The circle may be so large that the origin of the circle is located beyond the edge of the drafting surface, or beyond the edge of the drawing board, or even beyond the confines of the room in which the draughtsman is working. In such cases, the use of a conventional compass is clearly impossible since the compass point cannot be supported.The only way that such arcs can be drawn manually is either by approximation, using flexible rules or stencils, or by using "railway curves". These are simple flat stencils, each cut to define a curve of a particular radius. Thus, to cover any useful range of radii, a large number of individual stencils is required. These sets of stencils are very expensive, and are never entirely comprehensive. There is, therefore, a need for a simple, adjustable device which enables draughtsmen to draw arcs of circles over a full range of radii beyond the scope of a conventional compass.

According to the present invention there is provided a device for defining an arc of a circle on a surface, which device comprises a body adapted to carry a tool for defining an arc of a circle on a surface; a wheel or wheels rotatable about a first rotational axis; a wheel or wheels rotatable about a second rotational axis spaced from the first rotational axis, the wheels being mounted on the body for movement over the surface, and the relationship of the rotational axes being adjustable in order to vary the radius of the arc to be defined, and indicator means for providing an indication to a user related to the radius of the arc to be defined.

It is preferred that the angle between the rotational axes is adjustable to vary the radius of the arc to be defined. If the device is adjusted so that the rotational axes are parallel, the device will follow a straight line when propelled across a surface. However, if the angle between the normals to the rotational axes is reduced to, for example, 1700, and the device is propelled across a surface, the device will follow an arc of a circle.

It will be appreciated that operation of the device does not require contact with the surface at the centre of the circle. Thus, the location of the centre is irrelevant, and arcs of extremely large radii can be drawn.

Since the angle between the rotational axis may be continuously adjustable, arcs of circles with a continuous range of radii may be drawn.

A single wheel may be mounted for rotation about each rotational axis. In this case, stabiliser means may be provided to inhibit lateral tipping of the device.

However, the device may comprise a first pair of wheels rotatable about the first rotational axis, the two wheels of the pair being rotatable independently of each other. A single wheel may then be provided for rotation about the second rotational axis. For increased stability, however, it is preferred that the device further includes a second pair of wheels, rotatable about the second rotational axis, the two wheels in the second pair being rotatable independently of each other. The two wheels of each pair must rotate independently of one another since, as the device describes an arc, the outer wheels of each pair must rotate more rapidly than the inner wheels.

Of course, more than two wheels may be provided for rotation about one, or each, rotational axis. As the number of wheels rotatable about a common rotational axis is increased, the total contact area of the device with the surface is increased, providing greater resistance to slippage in use.

The body may comprise first and second body portions, each rotational axis being fixed with respect to a corresponding body portion, and the first and second body portions being pivotable relative to one another to adjust the angle between the rotational axes.

Where the angle between the rotational axes is adjustable, the reading given by the indicator means changes with this angle since this is related to the radius of the circle that will be defined by the device in use.

In order to enable fine calibration of the indicator means, and hence high precision readings to be taken, it is desirable to maximise the movement of one body portion relative to the other as registered by the indicator means.

Accordingly, it is preferred that the body portions overlap one another over the majority of the length thereof, and the pivotal axis of the body portions is located nearer to one end of the body than to the other. For a given pivotal angle, the degree of relative movement of the body portions is then a maximum at the ends of the body portions furthest from the pivot, and the movement here can be sensed by the indicator means.

In this case, the indicator means may comprise a scale provided on one of the body portions and a reference indicator provided on the other of the body portions so that, as the body portions are pivoted relative to one another, the reference indicator moves relative to the scale. The scale may be calibrated in length of radii of circles to be defined. Alternatively, for example, the scale may be calibrated in degrees of arc corresponding to the angle between the normals to the rotational axes. Of course, more than one scale, each measuring a different quantity, may be provided.

For greater precision in readings as previously described it is preferred that the scale is provided at or near one end of the corresponding body portion, and the pivotal axis of the body portions is located at or near the opposite end of the said corresponding body portion.

The indicator means may further comprise a vernier scale to provide an extra order of accuracy in adjustment of the angle between the normals to the rotational axes.

In some applications, it may be desirable to be able to define a series of parallel arcs of circles on a surface. To achieve this without having to move and reset the device, it is desirable for the body to include moveable tool carrying means to enable the position of the tool relative to the body to be adjusted in use. For example, in use, the tool may be moveable relative to a linear scale on the device, enabling measurement of the distance moved by the tool, so that a series of parallel arcs can be defined without the need to move the apparatus.

At least a portion of the body may be transparent and inscribed with one or more reference lines to assist in location of the device at the desired position on the surface prior to use.

It will be appreciated that the invention extends to a method of defining an arc of a circle on a surface, which method comprises placing on the surface a device as hereinbefore described carrying a tool for defining the arc on the surface, and propelling the device over the surface.

Embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings in which: Figure 1 is a diagrammatic representation of a device for drawing an arc of a circle embodying the invention; Figure 2 is a diagram illustrating the principal of operation of the device of Figure 1; Figure 3 is a diagrammatic representation of a further embodiment of a device for drawing an arc of a circle; Figure 4 is a simplified representation of the device of Figure 3 after adjustment thereof; Figures 5a and 5b are a cross-section and side view respectively of a wheel of the device of Figure 3;; Figure 6 is a diagram illustrating the principal of operation of the device of Figures 3 and 4, and Figure 7 is a diagrammatic cross-section of an alternative wheel arrangement for the devices of Figures 1 and 3.

The device of Figure 1 comprises a body 1 consisting of first and second body portions 2, 3 connected together for relative pivotal movement about a pivot 4. A clamp screw 5, coaxial with the pivot 4, is provided for clamping the body portions 2, 3 together to fix the relative positions thereof.

A first pair of wheels 6 is mounted on the body portion 2 for rotation about a first rotational axis. The two wheels 6 are rotatable independently of one another.

Similarly, a second pair of wheels 7 is mounted on the body portion 3 for rotation about a second rotational axis, the two wheels 7 being independently rotatable. The rotational axes of the wheels 6, 7 are each perpendicular to the longitudinal axis of the corresponding body portion, and the rotational axes are equidistant from the pivot 4.

The body portions 2, 3 overlap one another in the region of the pivot 4. Indicator means are provided to indicate to a user the angle between the body portions 2, 3, ie the angle between the normals to the rotational axis of the wheels 6, 7. The indicator means comprise a scale 8 provided on the body portion 2 and a reference indicator line 9 inscribed on the body portion 3. As the body portion 3 is pivoted relative to the body portion 2, the line 9 moves relative to the scale 8 which is calibrated to give a direct reading of the angle between the body portions 2, 3. This angle is related to the radius of the arc that will be drawn by the device as will be described hereinafter.

The body portion 2 has a hole 10 therein, aligned with the longitudinal axis of the body portion 2, and hence the line 9 when the device is arranged as shown in Figure 1.

The hole 10 receives a pen 11 in use in such a manner that the tip of the pen contacts the surface on which the device is placed.

The body 1 is formed of a transparent plastic material to enable a user to see through the body to the surface on which the arc is to be drawn to facilitate correct location of the device on the surface.

Figure 2 is a diagram illustrating the relationship between the angle between the normals to the rotational axes of the wheels 6, 7 and the radius R of the circle to be drawn. In this diagram, the distance between the rotational axes of the wheels 6, 7 and the pivot 4 is X.

The angle between the body portions 2, 3 as shown by the scale 8 is 20. It will be seen that: tan6 = X R Therefore: R = X tane and e = arc tan X R Since X is known, the correct setting for the angle between the normals to the rotational axes of the wheels 6, 7 as shown on the scale 8 can be determined to enable an arc of the desired radius R to be drawn. However, since the angle shown on the scale 8 will be 28, the more useful expression of the above formulae will be: R = 2X 2tan9 28 - 2 arc tan X R Figure 3 shows a more sophisticated device for drawing an arc of a circle. This device comprises a body 15 comprising first and second body portions 16, 17 which overlap one another over the majority of the length thereof.The body portions 16, 17 are connected together for relative pivotal movement at a pivot 18 which is located nearer to one end of the body than the other. A clamp screw (not shown) is provided coaxially with the pivot 18 to enable the body portions 16, 17 to be clamped in a desired relative pivotal position.

A first pair of wheels 19 is mounted on the body portion 17 for rotation about a first rotational axis which is fixed with respect to the body portion 17. A second pair of wheels 20 is mounted on the body portion 16 for rotation about a rotational axis which is fixed with respect to the body portion 16. The two wheels 19, 20 in each pair are rotatable independently of one another.

The device includes indicator means for providing an indication to a user related to the radius of the arc to be drawn. The indicator means comprises a first scale 21 on the body portion 16 and a reference indicator 22 which is fixed with respect to the body portion 17. As the body portions are pivoted relative to one another, the reference indicator 22 moves along the scale 21, which is calibrated in 0.25 units, giving a first order reading of the angle between the normals to the rotational axes of the wheels 19, 20.

The indicator means further comprises a clock vernier 23 which is fixed relative to the body portion 17. When the body portions 16, 17 are pivoted relative to one another, an arm 24 of the body portion 16 moves through the mechanism of the clock vernier 23 enabling the clock vernier to register relative movement of the body portions.

The clock vernier is calibrated in 0.025 units and may be read in conjunction with the scale 21 to give a further order of accuracy in the reading of the angle between the normals to the rotational axes of the wheels.

A further scale 25 is provided in the body portion 16.

This scale is calibrated to show approximate values of the radius of the arc that will be defined by the device for various relative pivotal positions of the body portions 16, 17.

It will be appreciated that provision of the scales 21, 25 towards one end of the body portion 16 and the displacement of the pivot 18 towards the opposite end of the body increases the accuracy with which the scales can be read, since the degree of relative movement of the body portions is greatest furthest from the pivot. Similarly, for a given angular change, the arm 24 moves a greater distance through the mechanism of the clock vernier 23 than if the mechanism were located nearer to the pivot, so increasing the accuracy with which this scale can be read.

The body 15 is provided with a pen/pencil holder 26 which is mounted for sliding movement parallel to the rotational axis of the wheels 19 along a linear scale 27.

The pen holder 26 comprises a threaded circular ring 28 suitable to receive all forms of draughting pens and pencils in common use.

The body portions 16, 17 are formed of transparent plastics material to assist in correct placement of the device on the draughting surface.

Figure 3 shows the device set with an angle of 0 between the normals to the rotational axes of the wheels 19, 20. Figure 4 is a simplified representation of the device of Figure 3 after relative pivotal movement of the body portions 16, 17.

Figures 5a and 5b are a diagrammatic representation of a wheel 19, 20 in Figure 3. Each wheel 19, 20 has an outer narrow rim 30 to provide a small contact area with the draughting surface. This reduces the risk of the wheels slipping over the surface in use due to the fact that, when the wheel moves along an arc, the outer edge of the rim must travel a slightly greater distance than the inner edge of the rim. The rim 30 is preferably formed of rubber or another material which provides high friction between the wheel and the draughting surface and hence high resistance to slipping.

Each wheel 19, 20 includes a roller bearing 31 to enable the wheel to rotate about a wheel axle 32 which is connected to an axial flange 33 of the corresponding body portion 16, 17. The wheels are tapered outwardly towards the wheel axles to keep the wheels stiff, to add weight, and to allow enough width at the wheel axles for a good, wide bearing and a secure fastening.

Figure 6 illustrates the relationship between the angle e between the normals to the rotational axes of the wheels 19, 20, as shown by the scales 21, 23, and the radius R of the arc to be drawn. In this diagram, X represents the perpendicular distance between the rotational axis of the wheels 19 and the pivot 18, and Y the perpendicular distance between the rotational axis of the wheels 20 and the pivot 18.It will be seen that: tane = X + (Y/cose) R Thus: sin6 = X + (Y/cose) cose R Rearranging gives: R sine = X cose + Y Hence: R = X cose + Y sine Similarly: e = a + = arc sin X + arc sin Y r r Since: r = f(R2 + x2) e = arc sin X + arc sin Y f(R2 + x2 ) f(R2 + x2 ) Thus, from the known values of X, Y and R, the correct angle 6 between the normals to the rotational axes of the wheels 19, 20 can be determined to enable an arc of the desired radius R to be drawn.

The overall size of the devices shown in Figures 1 and 3 may vary, but the size is preferably such that the device sits comfortably upon an Al sized drawing surface (this being the most popular draughting format) with ample room to travel. Thus, for example, an overall length of 300mm when the device is set to a pivotal angle of 0" would be suitable.

Figure 7 shows an alternative wheel arrangement for the devices of Figures 1 and 3. A pair of wheels 6, 7, 20 may be replaced by a row of smaller wheeels 40, each supported by a pair of ball bearings 41 which are threaded on a common axle 42. The length of the axle may be approximately the same as the width of the body of the device. In the device of Figure 1, both pairs of wheels 6,.

7 may be replaced by the wheel of Figure 3, the wheels 20 may be replaced by the arrangement of Figure 7.

Providing a plurality of wheels 40 along at least one rotational axis increases resistance to slippage in use due to the greater contact area of the device with the surface.

The device of Figure 1 is used as follows. The correct value for the angle between the normals to the pivotal axes of the wheel 6, 7 is calculated from the desired radius R of the arc to be drawn and the distance X between the rotational axes and the pivot 4 as described above. The body portions 2, 3 are then pivoted relative to one another until the line 9 on the body portion 3 indicates the calculated angle value on the scale 8 on the body portion 2. The clamp screw 5 is then tightened to clamp the body portions 2, 3 in this relative pivotal position. A pen 11 is inserted in the hole 10 in the body portion 2 and the device is placed on the draughting surface. Since the body 1 is transparent, the user can easily locate the device such that the end of the pen coincides with the desired position of the start of the arc to be drawn. A line or series of lines (not shown) may be inscribed on the surface of the body portion 2 to enable the user to align the device with a line previously drawn on the draughting surface.

The device is then propelled by the user across the surface over the desired distance. As the device moves, the pen draws an arc of a circle on the surface, the rotational axes of the wheels 6, 7 being aligned at all times with radii of the circle.

The device of Figure 3 is used in a similar manner.

Since the scale 25 on the body portion 16 is calibrated in terms of the length of the radius of the arc to be drawn, this scale can be used to set the relative pivotal positions of the body portions 16 to approximately the correct position. Final adjustment of the pivotal position is made with reference to the scale 21 and clock vernier 23. The correct value for the angle e can be calculated as described above from the known values of X, Y and R and the pivotal position of the body portions adjusted until this angle is indicated by the scales 21, 23.

The moveable pen holder 26 is positioned with reference to the scale 27 so that it is aligned with the normal to the rotational axis of the wheels 19 which passes through the pivot 18. A pen is inserted in the pen holder 26 and the device placed upon the draughting surface such that the tip of the pen coincides with the desired position for the start of the arc to be drawn. As before, the body 15 may be inscribed with one or more reference lines (not shown) for alignment with a line previously drawn on the drafting surface to assist in correct placement of the device. The device is then propelled across the draughting surface by the user until an arc of the desired length has been drawn.

If another arc is to be drawn parallel to the first, this can be achieved simply by moving the pen holder 26 along the linear scale 27 the desired distance, and then propelling the device in the opposite direction back to the original position. Thus, this operation does not require movement and re-setting of the device.

It will be appreciated that many variations and modifications may be made to the specific embodiment described above. For example, The device may be adapted to carry a tool other than a writing instrument. The device may be adapted to carry a circular saw, or jig-saw, for example, for cutting a surface along an arc.

The indicator means may comprise a digital or other form of display as opposed to the scales described above.

The apparatus may include means for continuously adjusting the pivotal angle between the normals to the rotational axes of the wheels as the device moves. Such means may be activated at the option of the user to enable the device additionally to define curves other than arcs of circles.

Claims

1 An arc defining device which is a chassis comprising linear elements joined by a pivot, the axis of the pivot being perpendicular to the chassis, allowing the linear elements to be adjusted across a contiuous range of angles relative to eachother. Means by which the pivot action can be restricted, so holding the chassis elements firmly at any particular angle relative to eachother. Wheels fixed to each element of the chassis, each wheel being capable of revolving independently of the others. Means by which draughting instruments can be fixed to the chassis such that the movement of the device is recorded on a surface across which it is propelled.

2 An Arc Defining Device as claimed in Claim 1 whereon a callibrated scale is provided such that the angle between the elements of the chassis is indicated to the user, this angle being proportional to the radius of the arc defined.

3 An Arc Defining Device as claimed in Claims 1 and 2 whereon a callibrated scale is provided so as to give a direct indication of the radius of the arc that the device is adjusted to define.

4 An Arc Defining Device as claimed in any preceding claims which is provided with a guide means such that an arc to be defined by the device can be located on the working surface relative to other points previously made on the working surface.

5 An Arc Defining Device as claimed in any previous claims whereon the means of attatching draughting instruments allows a draughting instrument to be moved across a range of positions normal to the direction of travel of the device and which allows the draughting instrument to be restrained firmly in any position across that range.

6 An arc defining device as described herein and with reference to the drawings. figures 1 to

7.

6 An Arc Defining Device as described herein and with reference to the drawings, Figures 1 - 6.

Amendments to the claims have been filed as follows 1 An arc defining device which is a chassis comprising two linear elements joined by a pivot, the axis of the pivot being perpendicular to the chassis, and positioned close to one end of the chassis, allowing the linear elements to be adjusted across a continuous range of angles relative to each other such that the divergence of the angle is reflected in the largest possible differential movements to optimise callibration. Means by, which the pivot action can be restricted, so holding the chassis elements firmly at any angle relative to eachother. Multiple wheels fixed along two axles. one axle being fixed at the end of each of the two chassis elements. each wheel capable of independent rotation.Means by which draughting instruments can be fixed to the chassis such that the movement of the device is recorded on a surface across which it is propelled.

2 An arc defining device as claimed in claim 1 whereon a callibrated scale is provided such that the angle between the two elements of the chassis is indicated to the user together with a direct indication of the radius of the arc that the device is adjusted to define, (the angle angle being proportional to the radius of the arc).

3 An arc defining device as claimed in claims 1 and 2 whereon the means of attatching draughting instruments allows the instruments to be moved across a range ofpositions normal to the direction of travel of the device and allows the draughting instrument to be held in any particular position across that range.

4 An arc defining device as claimed in any preceding claim which is provided with a guide means such that an arc to be defined by the device can be located on the working surface relative to other points previously made on the surface.

5 An arc defining device as claimed in claim 1. whereon the independently revolving wheels are of rhomboidal section with wide bearing at the axle and narrow edges to reduce to a minimum any innacuracy caused by differential in angular velocity across the wheel edge while in arcuate motion.