US2532353A

US2532353A - Ellipse generator

Info

Publication number: US2532353A
Application number: US623002A
Authority: US
Inventors: Paul F Boehm
Original assignee: Individual
Current assignee: Individual
Priority date: 1945-10-18
Filing date: 1945-10-18
Publication date: 1950-12-05
Anticipated expiration: 1967-12-05

Description

Dec 5, 1950 P. F. BOEHM ELLIPSE GENERATOR 4 Shees-Sheet 1 Filed Oct. 18, 1945 INVENTOR PAUL F. BOEHM,

ATTORN Dec. 5, 1950 P. F. BOEHM ELLIPSE GENERATOR 4 Sheds-Sheet 2 Filed Oct. 18, 1945 B INVENTIOR PAUL F. BOEHM,

' ATTORNIEY Dec. 5, 1950 P. F. BOEHM 2,532,353

PSE GENERATOR Filed oct. 18, 1945 4 Sheets-Sheet s NNNNNN OR PAUL F. BOEHM,

ATTORNE P. F. BOEHM ELLIPSE GENERATOR Dec. 5, 1950 4 Sheets-Sheet 4 Filed 001;. 18, 1945 FIG. l4

INVENTOR PAUL F. BOEHM, M 9% ATTORNW Patented Dec. 5 1950 tJNITED STATES rarest orricl'li ELLIPSE GENERATOR; Paul F. Boehm, Greenwich,-,Conn.

Application October 18, 194-5; Serial *No. 623,002

In the following specification and in the claimstheterm:elliptic master means any type of a solidzbody having an elliptic contour and also any. typeof an elliptic" groove or opening ina solidrbody'.

Moreover, the term elliptic proportions meansi thenshape of a particular ellipse, regardless-ofrsize, as determined by the projection of aicircle on a given plane under oneselected angle of projection.

ItQis one object: of this invention to provide a device that is suited toderive from one chosen elliptic-master any number of elliptic curves different in size but of the same elliptic proportions as :the master, the variationin size being efiected by exchangin only one element of 'thedevice.

A further object' ofthe invention is the provisionof 'a device or" the abovetype by Whichan elliptic-:curve may begenerated either by means of a pencil, pen or similar implements as for instance in the art of drawing, or by means of a toolofany kind adapted to engrave, cut or otherwise produce an elliptic shape in a given' solid bod-y. In a similar way the device according to the inventionis intended to be used for control ling indirectly the movement of a tool in relation-to the worlc so asto ultimately generate an elliptic curve or shape.

Fnrtherobjects of theinvention willjbecome apparent from the following specification describi g, by Way of-"example, some embodiments of ments; Fig: 5 isthe endwievw of one element'of the said structure;

Fig: G is a verticalcross section of an alterna: tivetype of the attachment;

Flees? andS are avertical crosssectionand a bottom view; respectively, of another alternative type of attachment; Figs; Q and" were top view; andelevatiom partly intsection, of! another) embodiment: of theinvention; Figs. I'Land 12: illustrate the same attachment asshown by Figs; 3' and i, as: applied to the deviceflillustrated; by;

Figs; 9, and lO.

Fig 13:: is a perspective View of: still another.

embodiment of the invention.

l4: lSx a diagram intended: to.- explain the geometricallprinciples governingthe performance.-

of L a device according: to l the invention.

Referring. flrstiitolFi'g: 14, itvmay. ibe. supposed that. alcirclevlfl is given, having aldiameterA. A, number of small circles Ill :may; be drawn in such a Way; that they. contact thetperipheryi'ofscircle llkfromu the inside; Thenathe centers. of: all the small circles M: will be: located on a circle I2 which isconcentricwith circle ill. If the diameterroi the circles N is -B then r the diameter of circle I 2 Wi11be:-A-B

Letus imagine that the. whole system of circles: is now projectedon a given plane under a cer-- tainangle. Thenevery one of the circles Ill, H1

and t2r. is converted l into a corresponding ellipse.

The major axes of these ellipses Illa, l laand lZc; respectively, are equal toi the circlediameterseA B; Cfirespectively'. It is to be understood changing the prevailing conditions it may as Well be assumed that one circle His moved in contacting position along circle |0 which will cause the center of that cirole I I" to generate'the circle- 1 2 All of these conditions are necessarily maintained also in the projection with the only (lif ference that the-circles arereplaccd=by-- ellipses; This means that if a small ellipse Ila having a major axis B is moved'along a-larger ellipse Ilia of" identical elliptic proportions and in permanent contact therewith and their major axes being: maintained parallel with each ether; then the center of ellipse -l l a will generate another el lipse IZa-Which is concentric with ellipse Illa and has the same elliptical proportions, its major axisbeing Gand parallel with that of-e1lipsel0a. While in the above example the sma'llioircljes llor ellipses Ila-are located and moved insidethe main circle ID or ellipse main-order to genmate a circle 12 or ellipse Ila, respectively,

smaller than the-maincircle or ellipse, itwill ice-readily understood that in the same waya 3 circle or ellipse larger than the main circle or ellipse may be generated by moving the small circles or ellipses along the outside of the main circle or ellipse.

The devices according to the present invention are based on the geometrical principles just explained above.

The common feature of all the embodiments of the present invention is the fact that they comprise means adapted to guide a tracing or guided element of given elliptical shape along a given elliptic master or guiding element in such a way that the major axes of the tracing element and of the master are maintained parallel with each other. By using alternatively tracing elements of different size a practically unlimited number of ellipses concentric with each other and the master, of same elliptic proportions but differing in size may be produced from one particular master. The difference in size, i. e. the difference between the major axis of the master and that of the generated ellipse will always be equal to the major axis of the elliptic tracing element provided the point of the scribing or cutting device is located within the center line of, and perpendicular to the plane of, the elliptic contour of the tracing element.

Referring to Figs. 1 .to 5, the device comprises a base 20 of rectangular shape which in this case is provided with an undercut 2i and two engaging pins 22 intended to serve as means for attaching the base 28 to a plate or stencil of flat stock which contains one or more elliptic openings serving as masters. A stencil or master of this type is not shown in connection with the first twoexamples as it does not necessarily form part of the device proper. However, reference may be had in this connection to Fig. 13 which illustrates a stencil or master plate. It will be understood that suitable holes may be provided in the stencil plate adapted to be engaged by the pins 22 so as to hold the base 28 in a predeter mined position in relation to the ellipse openings in the plate.

The base 20 is provided, along a center line parallel with the undercut edge, with two solid pivots 23. One swivelling slide block 24 is mounted on each of the pivots 23 and held in position by a nut 25 screwed on the end of the pivot. The blocks 24 are each provided with a bore 25 at right angles to the holes engaging the pivots. Preferably the blocks 24 are split at 2'1 and provided with adjustment screws 26 permitting to slightly adjust the size of the bore 28.

A parallelogram frame or linkage is composed of two slide bars 29 of equal length and of a diameter permitting them to slide smoothly through'the bores 23 of the blocks 24; the rest of the linkage is constituted by flat end link 39 and a similar flat front link 3!, both links pivotally connected at either end with the corresponding ends of the slide bars 29.

Bearing in mind that the center distance between the two stationary pivots 23 is equal to the distance between the pivotal joints of each of the links 36 and 3!, respectively, it will be understood that the parallelogram frame may be moved both lengthwise and, in a swinging movement, sidewise without the front link 3! getting out of alignment parallel with the center line of the pivots 23 or a given line on the master plate attached to base 20.

The front link 3! is provided with means for securing to it a tracing element adapted to be guided along the elliptic contour of an elliptic master and having itself an elliptic contour adapted to be kept in contact with the master during the tracing operation.

In the present instance the tracing element shown in Figs. 3 and 4 consists of a substantially conical piece 32 that may be clamped to the link by means of a forked bracket 33 and a clamping screw 34 to be threaded into a screw hole 35 of the link 3!. A straight shoulder 35 suited to bear against the front edge of link 34 serves to assure a definite position of element 32 with respect to the base 28 and thereby also with respect toa given line contained in the master plate to which base 22 may be attached.

The lower end of element 32 has an elliptical contour as shown at 31. In the present example the major axis of this elliptical contour 3i is parallel with the shoulder 36 and therefore remains parallel with the front edge of base 20 no matter what movements are carried out by the parallelogram frame. Assuming the device is used for drawing ellipses on a sheet of paper on a drawing board and in connection with a flat stencil or template as shown in Fig. 13 having elliptical openings the major axes of which are parallel with base 2%) as attached thereto, then the elliptical tip 3'! of the tracing element 32 may be guided freely within any one of the elliptic openings of the stencil and in continuous contact with the edge of such opening. During such movement of element 32 the center point of the elliptical tip 3'? will generate an ellipse which is of identical elliptical proportions with that of the stencil ellipse provided the elliptical contour 31 meets this condition. The difference in size of the generated ellipse will correspond to the difference established by the major axis of the elliptical contour 3?. Assuming the master ellipse in the stencil has a major axis of 2" and the tip 31 has a major axis of e then the generated ellipse will have a major axis of 1%.

In order to permit drawing t -e generated ellipse by means of an ordinary pencil the element 32 is provided with a conical bore 33 suited to accommodate the tip of the pencil and ending with a small opening 39 in the center point of tip 31.

In order to permit drawing or generating ellipses differing from given master ellipses by a variety of difierentials, a number of elements 32 having elliptical tips 31 of different sizes may be provided and clamped to the parallelogram frame alternatively.

Fig. 6 illustrates a modified form of a tracing device. The conical piece 32a is again provided with a bracket 33, a shoulder 36 and an elliptical tip However, the inside bore is not conical throughout but provided with a screw 4 having a narrow central bore l! corresponding in size to the bottom opening 39 so that a thin lead of the type used for mechanical pencils may be inserted and adjusted to project through opening 39.

It will be understood without an illustration that the tracing device may be'modified in various ways so as to be adapted to hold other means for producing the generated ellipse on some object or surface, for instance a steel needle for scribing, a lettering pen for drawing an ellipse in ink, or a cutting tool of any suitable kind. Also the tracing element according to this invention may serve as a means for controlling other mechanisms intended to be used for cutting or otherwise producing ellipses or elliptical shapes, for instance a copying or duplicating machine of the pantograph or equivalent type.

Thereris: no. necessity Jo having :the :major exist on the; elliptical tip 31 of: the: tracing elements: parallelawith thesbaseifl orirather with Lthevcens terlinesconnectmgztlieepivots 23. Itl'lS only-requireditoxarrangethe; major axis of tip; 31 at the rsamelanglezwith respect towsome partof the" perallelogramwframe which that particular part. maintainer during: its movements with respect tor tlielmaioriaxis .of the master ellipse:

Since, as a rule, it will be. necessaryvandde sirablev to use various tracing elements differing from eachzotheri by, the size, shape. opposition: of the; elliptical contour i at the lower tip: 3.! i an: advantageous modification of the: tracingzelement 1.

maybe provided alternatively; This salternative issillustratedby way? of;examplez by .Figs. 7 and :81

In this instance, eight elliptical tips. 42 areare ranged-1' evenly spaced, along. circle 'on :a turret head 1.43. The headrdtrissrotatably mounted ibya:

means of apinor screw on a bracket Whl0h;

has a forked endeefi and awstraight shoulderssimilar to. the corresponding parts of theaelementsa 3210p Mir-and therefore niay be attached tolink 1.

3! as described above; The pivot pin Mris angularly disposed with respecttogthe working-sur face; and the individual tips are. so positioned on head AS that by'turningthe -turret head 43 any one of the elliptical tips: 42 may be brought in correct position with regard to the working; sur= fa/Ce. lock spring iawhich in appropriate positionsof the head 43 will snapinto the upper endsof the individual. conical bores .561. arranged centrally An extension lfiaofibracket 45 container-a with the individual tips 4am accommodating the.

tipzof-apencil used for: drawing the generated" ellipse.

While. the eight different elliptical tips 152 areal shown in Fig. ahaving all thesame elliptical.

proportion and the same angular position of their major. axes. with respect to. the pertaining: radius of X the turret 43,- thi may be arranged difierently:

aswelL. For instance; tips 42 with elliptical contours. or different shapes and different angular positions may be assembled on one turret;

It isthoughtthatin certain cases the parallelogram frame. described above will not be the most. efficient .orsuitable means in guiding the .tracing mainly of two pairs of connecting rods of identicallengths 5! and 52, respectively, moreover of a; center link 53 and a irontlink 54. The rods 5! are rotatablymounted by means of fiat extensions on the pivotszt, .and..by pins=56 at zone-side of center link 53.. The rods 52 are similarly jointedby pins 5? and 58 respectively to the ope positeside of centertlink 53 and to front link 54, respectively. Again the front link 54 is provided with a clamping. screw (Mi-suited for attaching whatever tracing element i to be used as for instance element 32 shown in Figs. 3 and 4, or element 32a as per Fig. 6 or the turret head illustrated by Figs. 7 and 8. Figs. 11 and 12 are only added to help in understanding Figs. 9 and 10 and do not require further description as they are otherwise identical with Figs. 3 and 4.

It will be understood by those skilled in the art that the parallelogram linkage illustrated by Figs. 9 and 10 permits moving a tracing element L of. the other.

uppeiurodr52 in; the said position will have therei a attached-to the fr'oiit sl m-thin ia consider able range". oi? movement 1 alway maintaining a! certain angularr position of the r tracing element? with respect to base 23 and thereby with respect? to amaster plate to -which the base" may be attached:

Fig: i 13 illustrates a -sti'll further modification or the present device, thisncasethemeans for maintaining. an certain angular position of the- 1 tracing: element with respect-to: tlr'e*'-base'=of the device 1 and thereby to the elliptic master being i used, consistsot a tripIe Iink parallelograihlink age considerably Widens-the range of move= mentor the tra ng element! In 1 general, this-" embodiment of the: invention is very similar to those described before-p There'sfore, the description may be confinedto th'oseelments wl'lich are different;-

Thekbase Ma isof angular-shape so' that the center line connecting the pivots 23- is at ri'g'ht angles withthe center line connecting the pins Bibi means of which zbase 29a -is"'attached5to an"- ellipseeistenci'lfifli The-linkageponsists of three"- pairs soil connecting rods 5t 54 a" and" 52 more over ofla-link- 53a similar toilinlcl53; afront link 54w: similar: to! link? Ell and additional crosslink 'iifli The cross linlcfifi has two arms t lex tendingxparallel s withlink: 53a anditwor arms 6.21 extendingiat rightiangles theretm. One roi the' arms: 52 oiiisetr and: J the. pertaining-l pivots 64-? proj act in opposite .directions sofias. tofipermititlie twoerod 522 1 to eswing at different levelswvitl'iout interferi withr-th'e resttofathe linkage. COIIG-l spondingl-yithe-zpivotsififizs providedifori joiningrthei rodsr: 52::to theriront lii ikrfi lwproject alsolinsopl pcsiteixdirectionsxz.

Itxwill: aberunderstood'. thatth'e -link-age described permitstoimovingr the tracing element: 66. veryv' close: toxtheabasetZfla and; .onlthe other hand; .to: points comparatively; far awayfrom. that: basel.

The tracing. element 1 6Siis1 not attached by a. bracket-randzscrew. connection but maybe in serted througharcentral .ihole. in; link 54a: and lis heldr in 1 position by: a; Wire. spring: 6'! which is IIlCfllIlllBdiOlI link .5ddiinzsucnacway thatflitimay' berbroughtrto snaprinto aigroove 58:.cutsi1rcthe scanningelem-ent z 66 can :be easily positioned at w various-.7. angles: corresponding; to various positions of the ellipse.openingsrpossibly: occurring-inn the. stencil ormaster plate 59.

It has been found advantageous to provide means; for safeguarding against improper func i tion-cof the parallelogram linkage that otherwise may happen when the rods 52 are to beswung'z through the position in which they areone on top t A friction .device acting uponlthe feet that the other rod 52 continues its rotary movement slightly ahead of the upper rod whereby the angular position of link 54a with respect to the arms 62 is maintained. In the present instance, the friction device may consist of an extension !3 of spring 61 projecting upward so as to rub against the upper rod 52 in the above mentioned critical moment.

In the above description of certain embodiments of the invention the base of the device has been described always as being directly attached to the ellipse stencil or master plate. This, however, is not a condition that has to be maintained strictly. The device proper may be held independently of the elliptic master provided that their relative position is maintained during its use, for instance by holding either one in fixed position relatively to a common support.

While I have shown and described certain embodiments of my invention I wish it to be understood that I do not want to be limited to the details thereof as many variations and modifications may be found by those skilled in the art without departing from the substance and gist of the invention.

What I claim is:

1. In a device for generating elliptic curves, in combination, an elliptically-shaped guiding element, and elliptically-shaped guided element, the

ellipses of said elements being of the same elliptic proportions but differing in size from one another, means mounting said guided element for movement around said guiding element with the elliptically-shaped edges of said elements in contact with each other, and means for maintaining the major axes of said ellipses at all times parallel with respect to each other, whereby the axis of said guided element generates an ellipse concentric to the ellipse of said guiding element.

2. In a device for generating elliptic curves, in combination, an elliptically-shaped guiding element, an elliptically-shaped guided element, the ellipses of said elements being of the same elliptic proportions but differing in size from one another, a parallelogram framework pivotally mounted at one end at a point of fixed relationship with respect to said guiding element, and means mounting said guided element on the free end of said framework with its major axis parallel to the major axis of said guiding element ellipse, said framework maintaining the major axes of said elements parallel at all times.

3. In a device for generating elliptic curves, in combination, a working surface, an ellipticallyshaped guiding element, means for holding said guiding element in a fixed position with respect to said working surface, an elliptically-shaped guided element, the ellipses of said elements being of the same elliptic proportions but differing in size from one another, means mounting said guided element for movement around said guiding element with the edges of said ellipses in contact with each other, means for maintaining the major axes of said ellipses at all times parallel with respect to each other, and means positioned at the axis of said guided element for scribing an ellipse on said working surface.

4. In a device for generating elliptic curves, in combination, an elliptically-shaped guiding element, an ellipticaliy-shaped guided element, the ellipses of said elements being of the same elliptic proportions but differing in sze from one another, a parallelogram framework pivotally mounted at one end at a point of fixed relationship with respect to said guiding element, said framework 8 l maintaining the major axes of said elements par allel at all times and mounting said guided element so that it may be moved around said guiding element with its elliptically-shaped edge in contact with the edge of said guiding element, and means detachably mounting said guided element on said framework, whereby ellipticallyshaped guiding elements of different sizes may be mounted on said framework to generate ellipses of different sizes.

5. In a device for generating elliptic curves, in combination, an elliptically-shaped guiding element, a turret member having a plurality of elliptically-shaped guided elements mounted thereon, the ellipses of said elements being of the same elliptic proportions but differing in size from one another, a support, means rotatably mounting said turret on said support, whereby said guided elements on said turret may be selectively moved into operative position, means mounting said support to permit movement of the guided element in operative position on said turret in a path around said guiding element with its edge in engagement with the edge of said guidin element, and means for maintaining the major axis of the guided element in operative position parallel to the major axis of said guiding element, whereby the axis of the guided element in operative position generates an ellipse concentric to the ellipse of said guiding element.

6. In a device for generating elliptic curves, in combination, a fiat plate having an ellipse cut therethrough, an element having an ellipticallyshaped edge, the ellipses of the ellipse in said plate and said element being of the same elliptic proportions but differing in size from one another, means mounting said element for movement with its elliptfcally-shaped edge in contact with the edge of the ell pse cut in said plate, means for maintaining the major axes of said ellipses at all times parallel with respect to each other, and means positioned at the axis of said element for scribing an ellipse concentric to the ellipse in said plate.

7 In a device for generating elliptic curves, in combination, an elliptically shaped guiding element, an elliptically-shaped guided element, the ellipses of said elements being of the same elliptic proportions but differing in size from one another, a parallelogram framework pivotally mounted at one end at a point of fixed relationship with respect to said guiding element, said framework maintaining the major axes of said elements parallel at all times and mounting said guided element so that it may be moved around said guiding element with its elliptically-shaped edge in contact with the edge of said guiding element, and means positioned at the axis of said guided element for scribing an ellipse on a working surface positioned beneath said guided element, the ellipse scribed being concentric to the ellipse of said guiding element.

PAUL F. BOEHM.

No references cited.