US 3834028 A
An apparatus to draw an oval is disclosed. The device is characterized by mounting on a stand a rotary plate which turns horizontally and which is provided with a pointer to show its center. A rotary rod is coupled to the rotary plate for movement in the same direction as the latter at a rate of twice the rotation of the plate and positioned beneath the plate such that the rotary rod can move freely in the vertical direction to the center of the rotary plate. A drawing tool holder is positioned at the bottom of the rotary rod such that the degree of eccentricity of said holder from the center of the rotary rod can be adjusted freely.
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Description (OCR text may contain errors)
PAIENIEU SEP] 0 I974 SHEET 1 OF 2 APPARATUS TO DRAW AN OVAL The present invention is related to an apparatus to draw an oval in precisely the desired shape and size.
Hitherto, when drawing a desired oval in accordance with the numerical values of the major and minor axes of an oval prescribed beforehand, there have been two methods. One is to obtain an oval by drawing the locus of a point at which the total of the distances from both ends of the minor axis to one end of the majoraxis is constant, which is the definition of an oval. The other is to obtain an oval by cutting a cylinder or a circular cone obliquely with a plane while letting those crossing lines agree with the prescribed major and minor axises.
An example of a device implementing the former method is a drawing apparatus in which a piece of string is stretched on a drawing paper in such way that it passes one end of the major axis and extends between the ends of the minor axis and a drawing tool is moved by this string. An example of a device implementing the latter method is a drawing apparatus, in which a circular plate is inclined to a prescribed angle and a drawing tool is moved along a projected profile against the horizontal level of said circular'plate.
However, in the case of these apparatus, the drawing tool moves under one-sided restriction by such as a string or the edge of an inclined circular plate and it cannot havea stable'fixing point such as the center of rotation. Thus, it has been very difficult to move a drawing tool while maintaining a profile exactly.
An object of thepresent invention is to carry out the movement of a drawing tool not by sliding but by rotation utilizing the characteristics of an oval in the axis of co-ordinates of an oval which can be considered another definition of an oval.
Other objects and advantages of the invention will become apparent from the following detailed description takenin connection with the accompanying drawings, in which:
FIG. 1 is a general diagram to show the theory of an oval;
FIG. 2 is a diagram to show theprinciple of the present invention;
FIG. 3 is an oblique view to show an embodiment of the present invention;
FIG. 4 is an oblique view to show each part of the apparatus in a disassembled state;
FIG. Sis an explanatory plane view of the gear; and
FIG. 6 is a sideviewof the drawing tool holder. As already known, an oval is expressed by a formula:
x /a y /b I Where a line connecting its two foci is the x axis and its vertical bisector is the y axis and its center is the origm.
Further, intwo concentric circles x y a and x y b a b with the origin 0 as their center as shown in FIG. 1, R expresses a point at which theradius 00 of the larger circle crosses the circumference of the smaller circle and Q-moves on the circumference of the larger circle. In this case, a locus of the crossing point P of a perpendicular from Q to the x axis and a line extendingthrough R in parallel to the x axis is expressed as follows.
Thus, it is observed that the locus is always expressed as an oval. From this it becomes possible to draw a desired oval by obtaining the locus of P in such way that the major axis of a prescribed oval is made the diameter of the larger circle and the minor axis is made the diameter of the smaller circle.
By further study of the matter, it has been discovered that the crossing point R always stands on the vertex of a right triangle with line QR as its base and that P is a fixed point on the circumference of a circle with QR as its diameter and moves about the circumference in accordance with the movement of QR.
Further, as shown in FIG. 2, a method has been devised such that, when a circle E with a diameter corresponding to half of the difference between the major axis and the minor axis of an oval is made between and along a circle C with the minor axis as its diameter and a circle D with the major axis as its diameter while turning on its own axis, a point on the circumference of the circle E draws a prescribed oval.
In this case, as observed from FIG. 2, each successive circle E rotates a half diameter while moving along the circles C and D and accordingly it has to turn on its axis twice while moving round the circles C and D and the rotation of the circle E on its axis is in the same direction as its rotation round the circles C and D. The size of the circles C and D i.e. the central distances from the origin 0 should change on occasions in accordance with the sizes of the prescribed major and minor axises of an oval. Accordingly, the central distance of the circle E from the origin 0 and the diameter of the circle E should naturally change.
Now, an embodiment of the present invention is described below with reference to the drawings attached.
Referring now to FIG. 3, which depicts a general oblique view of an apparatus embodying the present invention and FIG. 4 where each part of the apparatus is shown in a disassembled state, 1 is a stand which is to be placed on the surface of a drawing paper, a metal plate, etc. Each leg 2 of the stand 1 has a length adjusting screw 3 on its end to keep the stand 1 level. An immovable rod 5 having a pointer 4 on one end isfixed to the stand 1 with nuts 5' at the other end so thatthe pointer 4 indicates the position of the origin on the drawing paper. However, the pointer 4 may altematively be provided on a foldable arm to be attached to the stand 1.
Further, a rotary table 6 is pivotally mounted beneath the upper part of the stand 1. The immovable rod 5 extends centrally through the table 6. The periphery 7 of the rotary table 6 has notches for turning the plate 6 by grasping the circumference 7. A gear 8 is fixed on the center of the upper surface of the table.
Near the gear 8 is provided an arc-shaped slit9 along a radius of the rotary plate 6. On the rotary plate 6 is set a short shaft 10, about which gear 11 extends. A nut 11' is used to secure the gear 11 in position. The gear 11 engages with the gear 8 and itsnumber of teeth is half of that of gear 8, due to which, when the rotary plate 6 turns, the gear 11 turns at a rate which is twice to the rate of rotation of the plate 6.
Then, a cylinder 12 is inserted through said slit 9 and a rotary rod 13 is inserted into the cylinder 12. The cylinder 12, by turning a fastening nut 14 which is screwed on the lower end of the cylinder 12, can press the surface of the rotary plate 6 from both sides and hold the cylinder 12 itself firmly at an optional position in the slit 9. The slit 9 has an arc-shape with the short shaft as its center, due to which the rotary rod 13 can move round the gear 11 while being kept level by the cylinder 12.
On the upper end of the rotary rod 13 is fixed a gear 15, which is of the same size as the gear 11 and which always engages the gear 1 1 and turns at the same speed. (cf. FIG. 5) Thus, the rotary rod 13 turns in the same direction as the rotation of the rotary plate 6 at a rate double to the rotation of the latter.
The lower end of the rotary rod 13 extends to the surface of a drawing paper and has a drawing tool holder 16 by which a scribing needle or the like is held. As seen in FIG. 6, the drawing tool holder 16 can be freely slid aside from the center of the rotary rod 13. This operation can be done by extending the tool holder to position 16' and by holding it there firmly with a fastening screw 17, as shown in FIG. 6.
The present invention may be carried out by the following steps.
The stand 1 is placed on a drawing paper or a metal plate and the position of the origin on the paper or the plate is suitably chosen by means of the pointer 4 which is provided at the bottom of the immovable rod 5.
Next, the drawing tool holder 16 is extended to the position 16' which is chozen so that, when the rotary rod 13 is turned, its pointed end can draw a circle with a diameter corresponding to half the difference between the major axis and the minor axis of the desired ellipse. This circle corresponds to the circle E shown in FIG. 2.
Then the rotary rod 13 is pulled out by sliding the cylinder 12 along the slit 9 and the cylinder 12 is adjusted so that the circumference of the circle drawn by the drawing tool holder 16 passes through one end of the major axis of the prescribed oval. By this, the positions of the circles C and D as shown in FIG. 2 are theoretically established.
Finally, the rotary plate 6 is turned in the direction A as shown in FIG. 2 slowly by hand. In response, the end of the drawing tool turns with the rotary plate 6 and reaches the B point while drawing an oval locus as shown in FIG. 2. By repeating such process as above, a required oval is drawn.
As has been described in the foregoing paragraphs, the present invention aims to draw a precise oval by making use of the characteristics of an oval and has a great advantage that the apparatus is very simple in structure and that no special skill is required to operate it.
What we claim is:
1. An improved apparatus for drawing an oval, comprising:
a support member having a plurality of legs downwardly extending therefrom;
a circular table pivotally coupled to and beneath said support member, said circular table having an arcshaped slit along the radius thereof, having a first aperture therein at a position corresponding to the origin of the arc-shaped slit and having a second aperture centrally of said circular table;
a fixed rod positioned beneath said circular table and having a top portion extending through said second aperture, the lower end thereof being pointed for indicating the origin of the oval being drawn;
a first gear rigidly mounted on the upper portion of said circular table and centrally thereof;
a second gear pivotally mounted on the upper portion of said circular table and centered over said first aperture, said first and second gears being of suitable diameter for engagement therebetween, said second gear being rotated by said first gear at twice the rate of rotation of said first gear;
a rotary rod positioned beneath said circular table and having a top portion extending through the slit in said circular table;
means coupled to the top portion of said rod for firmly positioning said rod at any desired location along said slot;
a drawing tool holder coupled to the rotary rod at the bottom portion thereof; and
a third gear pivotally mounted on the upper portion of said circular table on said rotary rod for engagement with said second gear, said second and third gears having equal diameters and having a gear ratio of one to one,
whereby an oval design may be precisely drawn by rotation of said circular table.