US3311981A - Parabola tracing apparatus - Google Patents

Description

April 4, 1967 w. P. POSLUSNY PARABOLA TRACING APPARATUS 2 Sheets-Sheet 1 Filed Aug. 19, 1.966

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$054404 W ulml/fyzgdh JX/orneqs United States Patent 3,311,931 PARABOLA TRACING APPARATUS Warren P. Poslnsny, 460 W. 16th St., Apt. H, Chicago Heights, 111. 60411 Filed Aug. 19, 1966, Ser. No. 573,596 Claims. (Cl. 33 27) The present invention relates to a device for inscribing a parabola.

A geometric consideration of a parabola defines it as a curve consisting of the points in a plane which are equidistant from a line in the plane called the directrix and a point on the plane called the focus. The point of sharpest curvature of the parabola is at the vertex which is on a straight line drawn through the focus perpendicular to the directr ix. The equation of a parabola with its vertex at the intersection of the x and y axis and its focus on the y axis is x =4Py where P=the distance from the focus to the vertex. Obviously a parabola cannot be drawn with a compass or a straight edge or the like because the slope of a parabola constantly changes. Thus, a parabola can only be drawn with conventional drawing tools by the tedious time consuming plotting of points. Consequently, it is primary object of this invention to provide a device for drawing a parabola.

A further object of this invention is to provide a device for drawing a parabola quickly, easily and conveniently.

Related objects and advantages will become apparent as the description proceeds.

One embodiment of this invention might include a device for tracing a parabola comprising a frame, a first carriage guided on said frame for linear movement in a first direction and opposite to said first direction, a second carriage guided on said first carriage for linear movement in a second direction and opposite to said second direction, said second direction being perpendicular to said first direction, a flexible cord connected at one end to said frame and connected at its other end to said first carriage, said cord extending from said other end in said second direction and around said second carriage thence to its one end connection with said frame, and a marking device mounted on said second carriage for inscribing a parabola when said second carriage is moved and said cord is maintained taut.

The full nature of the invention will be understood from the accompanying drawings and the following description and claims.

FIG. 1 is a top plan view of a parabola tracing device embodying the present invention.

FIG. 2 is a vertical section taken along the line 22 of FIG. 1 in the direction of the arrows.

FIG. 3 is a schematic diagram forming a part of a proof of geometric construction.

FIG. 4 is a schematic diagram forming a part of an explanation of geometric construction.

For the purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiment illustrated in the drawing and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, such alterations and further modifications in the illustrated device, and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates.

Referring now more partciularly to the drawings, there is illustrated a parabola tracing device including a frame consisting of four side walls 11, 12, 13 and 14. The side walls 11 and 12 are parallel to one another as are the side walls 13 and 14. The frame 10 is supported by four legs 15 located adjacent the four corners of the rectangular frame. It can be seen that the frame also has an open top and an open bottom.

A pair of rods 20 and 21 are fixed at their opposite ends to the side walls 11 and 12 and are spaced from one another so as to be closely adjacent to the side walls 13 and 14. The rods 20 and 21 are parallel and slidably mount a carriage 22 which comprises a pair of bearings 25 and 26 and a pair of rods 27 and 30 fixed to and extending between the bearings 25 and 26. The respective bearings 25 and 26 are slidably received on the respective rods 20 and 21 and the rods 27 and 30 are spaced from one another and are fixed at their opposite ends to the bearings 25 and 26 by screws 31 so as to provide rigidity to the carriage 22. As suggested by the solid line and dotted line illustrations of FIG. 1, the carriage 22 is slidable from the left side of the frame 10 to the right side thereof.

A second carriage 35 is slidably mounted upon the rods 27 and 30 by means of suitable elongated bores 36 through which the rods 27 and 30 extend. The rods 27 and 30 are arranged perpendicularly to the rods 20 and 21, whereby the slidable movement of the carriage 35 on the carriage 22 is in a direction perpendicular to the slidable movement of the carriage 22 on the rods 20 and 21.

A suitable spiral spring 37 is connected between the carriage 35 and the bearing 26 and acts to yieldably urge the carriage 35 toward the bearing 26. The spring 37 normally coils within a suitable casing 40 within the carriage 35 and has its outer end 41 fixed to the bearing 26. The spring 37 operates similarly to the spring action in a measuring tape and, in view of its commercial availability, will not be further described in detail.

A flexible cord 45 is connected at one end 46 to the frame 10 and is connected at its other end 47 to the bearing 25 of the carriage 22. The connection of the end 46 of the cord 45 to the frame 10 is accomplished by means of a block 50 through which bolts 51 extend, said bolts 51 having wing nuts 52 thereon. The block 50 is inscribed with a scale 55 which operates in combination with a pointer 56 fixed to the side wall 11 of the frame 10. The purpose of the scale 55 and the pointer 56 will become more evident below. Generally speaking, the purpose of the scale and pointer is to adjust the sharpness of curvature of the parabola. Alternatively, the calibrations may be placed on the frame side wall 11 and the pointer 56 secured to the block to better provide for the considerable travel of the block 50. The slot 54 in the side wall 11 through which the bolts 51 extend permits such travel for adjustment.

The cord 45 extends from its connection with the bearing 25 in a direction parallel to the rods 27 and 30, thence around a roller 60 rotatably mounted upon the carriage 35, thence around a roller 61 fixed to the block 50, thence to its connection with the block 50. At the axis of the roller 60 and on the carriage 35 is mounted a scriber 59 which may be a pencil or an engraving tool of some type or any suitable inscribing device. Two of the legs 15 (through the axis of which the dotted line 64 is drawn) are in alignment with the axes of the two rollers 60 and 61.

The carriage 35 has a handle 62 fixed thereto. Assuming it is desired to draw a parabola on the paper resting on the support 66, the user draws a line to represent the axis he desires for the parabola. The dotted line 64 represents such an axis. He then positions the two leftward legs 15 on this axis. The user then grasps the handle 62 and moves it rightwardly so that the apparatus moves from the solid line position of FIG. 1 to the dotted line position of FIG. 1. The rightward movement of the handle 62 will cause the carriage 35 to move upwardly and cause the pencil or scriber 59 to mark the parabola 70 on the paper 65 because of the fact that the cord 45 will remain taut throughout the movement by reason of the action of the spring 37. Alternatively, the parabola can be drawn from the dotted line position to the solid line position of FIG. 1, or any portion of the parabola may be drawn to the left or to the right of the dotted line position of FIG. 1. No matter what the direction or location of the carriage 35 in drawing the parabola, the spring 37 will maintain the cord 45 taut and the scriber 59 at the path of the parabola.

It should be noted that the roller 61 extends beyond or outboard in a rightward direction as viewed in FIG. 1 of the block 50. Also, the roller 61 has the same diameter as the roller 60. In order to simplify the proof of geometric construction set forth below, the rollers are assumed to be points. It has been found, however, that as long as the rollers 60 and 61 are the same diameter, parabolas are generated. Further, this fact can be mathematically proven. Also, the purpose in having the roller 61 extend outboard of the block 50 in a rightward direction as viewed in FIG. 1 is to permit the present device to be able to reach the zero position at the vertex of the parabola.

Set forth below is a proof of geometric construction which should be read in connection with FIG. 3.

Prove: A+C=B+D Given:

(1) A and B are vertical and have the same maximum point. (2) y :iflx is a parabola by definition 2y3 B=Y2ZV4 Proof:

(1) C=F and D=G By definition of a parabola. (2) A+C=A+F and B+D=B+G Addition property of equality.

therefore A+F=B+G by substitution A+C=B+D=constant=length of cord Set forth below is an explanation of geometric construction which should be read in connection with FIG. 4.

(1) 1:1 and K=K By definition of a parabola.

By observation.

(3) HI=JK By substitution.

It will be evident from the above description that the present invention provides a device for drawing a parabola. It will also be evident that by use of the present device it is unnecessary to use the tedious time consuming plotting of points which would normally be necessary in drawing a parabola, and instead the parabola can be quickly, easily and conveniently drawn.

While the invention has been illustrated and described in detail in the drawings and foregoing description, the same is to be considered as illustrative and not restrictive in character, it being understood that only the preferred embodiment has been shown and described and that all changes and modifications that come within the spirit of the invention and the scope of the claims are also desired to be protected.

The invention claimed is:

1. A device for tracing a parabola comprising a frame, a first carriage guided on said frame for linear movement in a first direction and opposite to said first direction, a second carriage guided on said first carriage for linear movement in a second direction and opposite to said second direction, said second direction being perpendicular to said 'first direction, a flexible cord connected at one end to said frame and connected at its other end to said first carriage, said cord extending from said other end in said second direction and around said second carriage thence to its one end connection with said frame, and a marking device mounted on said second carriage for inscribing a parabola when said second carriage is moved and said cord is maintained taut.

2. The device of claim 1 additionally comprising a first roller mounted on said frame about an axis perpendicular to the plane in which the parabola is to be inscribed, a second roller of the same diameter as the first roller rotatably mounted on said second carriage about an axis perpendicular to the plane in which the parabola is to be inscribed, said flexible cord extending from said one end around said first roller to and around said second roller to the connection with said first carriage, and spring means connecting said first carriage and said second carriage and acting to maintain said cord taut.

3. The device of claim 1 wherein said frame has a rectangular shape with an open bottom and an open top and four side walls, a pair of rods fixed at their opposite ends to a first and second of said side walls and extending parallel to a third and fourth of said side walls, said rods being spaced from one another with one of said rods located closely adjacent to said third side wall and the other of said rods located closely adjacent to said fourth side wall, said first carriage including a pair of bearings one slidably received on one of said rods and the other slidably received on the other of said rods, said first carriage further including a further pair of rods extending between said bearings, said second carriage being slidably received on said further pair of rods, and spring means connected between said second carriage and said other bearing and urging said second carriage toward said other bearing.

4. The device of claim 2 additionally comprising a block adjustably fixed to said frame and adjustable in said second direction and opposite to said second direction, said first roller being mounted on said block, said cord having its one end secured to said block.

5. The device of claim 3 additionally comprising a block adjustably fixed to said first side wall and adjustable in said second direction and opposite to said second direction, a first roller mounted on said block about an axis perpendicular to the plane in which the parabola is to be inscribed, a second roller of the same diameter as said first roller rotatably mounted on said second carriage about an axis perpendicular to the plane in which the parabola is to be inscribed, said flexible cord extending from said one end around said first roller to and around said second roller to a connection with said first carriage at said one bearing.

References Cited by the Examiner FOREIGN PATENTS 7/1919 France. 12/1936 Germany.

Claims (1)

1. A DEVICE FOR TRACING A PARABOLA COMPRISING A FRAME, A FIRST CARRIAGE GUIDED ON SAID FRAME FOR LINEAR MOVEMENT IN A FIRST DIRECTION AND OPPOSITE TO SAID FIRST DIRECTION, A SECOND CARRIAGE GUIDED ON SAID FIRST CARRIAGE FOR LINEAR MOVEMENT IN A SECOND DIRECTION AND OPPOSITE TO SAID SECOND DIRECTION, SAID SECOND DIRECTION BEING PERPENDICULAR TO SAID FIRST DIRECTION, A FLEXIBLE CORD CONNECTED AT ONE END TO SAID FRAME AND CONNECTED AT ITS OTHER END TO SAID FIRST CARRIAGE, SAID CORD EXTENDING FROM SAID OTHER END IN SAID SECOND DIRECTION AND AROUND SAID SECOND CARRIAGE THENCE TO ITS ONE END CONNECTION WITH SAID FRAME, AND A MARKING DEVICE MOUNTED ON SAID SECOND CARRIAGE FOR INSCRIBING A PARABOLA WHEN SAID SECOND CARRIAGE IS MOVED AND SAID CORD IS MAINTAINED TAUT.

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