US2468017A - Ellipsograph - Google Patents

Description

April '26, 1949.

Filed Dec. 27, 1946 W. AICHROTH ELLIPSOGRAPH 2 E N :0 1- J o Um O N N 2 Sheets-Sheet 1 o as FIG!

' INVEN TOR.

RICHARD w. AICHROTH ATTORNEY April R. w. AICHROTH 2,468,017

ELLIPSOGRAPH Filed Dec. 27, 1946 2 SheetS-Sheet 2 FIG. 2

INVENTOR. RICHARD W. AICHROTH ATTORNEY Patented Apr. 26, 1949 ELLIPSOGRAPH Richard w. Aichroth, United States Navy Application December 27, 1946, Serial No. 718,728'

2 Claims. (Cl.- 3330) (Granted under the act of March amended April 30, 1928; 3'70 0. G. 757) to use, and adapted to cooperate with a drafting machine.

Another object is to provide an ellipsograph capable of making an ellipse of any desired size or eccentricity up to Further objects and advantages of this inven- -tion, as well as its construction, arrangement and operation, will be apparent from the following description and claims in connection with theaccompanying drawings, in which Fig. 1 is a plan view of one embodiment of the invention;

Fig. 2 is a front elevation; and

3 is a side elevation of the device of Fig. 1.

One of the most frequently-occurring geometrical figures is the ellipse, this bein attributable largely to the fact that the projection of a circle upon a plane not parallel to its own plane is an ellipse, as is also the intersection of a right circular cylinder with a plane that is inclined at an angle other than normal to the axis of the cylinder. Again, the intersection of a plane with a right circular cone in a manner to cut completely through the cone from side to side at an inclination to the base describes an ellipse.

Graphical representation of circles in isometric views constitutes perhaps the most common occasion for construction of ellipses, but cases frequently arise where it is necessary to depict circles viewed at an angle other than that incidental to isometric projection, or to show intersections of cylindrical or conical surfaces with inclined planes. Such cases can occur when delineating a mechanism with wheels, shafting, bored holes, or the like, at inclinations other than parallel or perpendicular to the orthogonal projection planes. Another situation that necessitates the construction of ellipses is the design of sheet-metal transition pieces for coupling ducts of different shapes where the intersection in some cases is elliptical.

j For some of the foregoing conditions there are available convenient mechanical aids to facilitate the delineation of ellipses. For example, in

the maximum capacity for which it is intended to be used.

31883, as Q the construction oi isometric drawings, where} he eccentricity is always the same (at' least-for circles lyin in the orthogonal planes on'the act'ual object) it is convenientto utilize templates havin cut-out areas that correspond respectively'to various sizes of circles as they appear when viewed atthe angle of projection that is to be used in constructing the isometric draw-'- ing. Obviously it would be expensive for a drafts man to provide himself with an'as s6r't'ment of templates that covered not only a wide rang'eof sizes, but each size of circle in 'allth e degrees of eccentricity that correspond to projectio'nat a multiplicity of viewing angles. Tocoversuch other angles of projection, recourse is usually had to graphical construction simulating the actual projection of a circle at the desired angle. r 7 It is possible to avoid the necessity tor graph ically laying out ellipses incident to an unusual angle of view by employing one-of-variousmechanical contrivances that depend fortheir operativeness on geometric properties of ellipses. For example, one machine" employs a radius arm rotatable about 'an aX is,' a cursor o *"the arm that can be set at any- 'dsired radiu and that carries a bearing for connection oi a a rectilinear slide bar extending a radial? rection with respect to the axis about'vvhich'the radius arm rotates, a sliding"meinbergonthe slide bar with a bearing to support the'oth'r end of the link, and an adjustable memb'e'rlon the link for carryinga pencil or pen: Rotation of the radius arm'c arries withit one end of the link (the other end being constrained-to mor rectilinearly along the slide bar), and intermediate points on the link describe ovals of- Varying degrees of eccentricity depending on their position on the link. These ovals arenea'rly true ellipses if the link is long compared to theradius arm, but such long' links are inconvenient to use, and a mechanism based on this principle is ill-adapted for use in conjunction with a 'arafh ing machine. v l Another mechanism, thisone producing rue ellipses, utilizestwo perpendicularly intersecting tracks of equal length, a slider on each, and a link connecting both sliders and carrying a 'collinear extension thatsupports the piano} cil. The distance from the pen or pencil the nearer slider is' the semi-minor-axis of the ellipse, and that to the more remote slider is the semi-major axis of the ellipse. This apparatus in its usual form is limited by its structure to the delineation of ellipses having a minor axis greater than the length of one of the two tracks and having a major axis not greater than the sum of the minor axis plus the length of one of the two tracks. Thus the ratio of major axis to minor axis cannot exceed two to one, and can approach two to one only for ellipses having minor axes in excess of but not greatly in excess of the length of a track. These limitations can to some, extent be circumvented by modificationsainsdesign, but such modifications add considerably to the complexity of the instrument or to the inconvenience attendant upon its use, and in any event this apparatus is not well adapted to be used in cooperation with a drafting machine because the path traced by the moving point extends completely around theinstrument.

Other ellipsographs employ gearing, or a multiplicity of linkages, or other complicated mechanisms, usually not suited for use with the drafting machine, and often, in spite of their com- :plexity, of limited application. Nearlyall of them suffer from the deficiency that computation must be resorted to before they can be set to generate an ellipse to represent a circle of given radius .as it appears when viewed at a given angle of inclination. Many of them also require several interrelated adjustments to be made when either the radius of the basic circle or its inclination. is altered.

-The present invention, on the other hand, is yvelladapted for cooperation with a drafting machine, .can describe ellipses of any size or eccentricity from a point or straight line to the maximum size for which the device is built, and requires merely two types of adjustment, which are direct reading and which correspond respectively to the radius and to the inclination of the basic circle that .is to be depicted in projection. The manner in which these advantages are gained willbeevident from the following description and the annexed drawings, in which i is a base, and I2,,|,4 are twostandards that carry brackets l6, l8 rotatably connected to the standards about a horizontal axis. 20, 22 are radius arms rotatably mounted on brackets [6, I8 about axes perpendicular to the axis of rotation of the brackets, and-24 .is a connecting rod adjustably attached to the two radius arms and adapted to carry penoil 26., It is desirable to design the device so that connecting rod 24 is parallel to the forward edge of base I0. Radius arms 20, 22, and connecting rod 24,. are preferably supplemented by eccentries 28, 3B, and link 32, to insure accurate parallelism of the radius arms during their passage through horizontal dead center, although with precise construction and careful use the instrument will operate satisfactorily without such eccentrics and link.

Base I0 is preferably made in the general form of a semicircle with a radial extension at one side, the open semicircular area comprising part of the,,w orking space in which the pencil describes the ellipse to be made, and the radial extension affording. means for attachment to a draftin machines. The details of the attachment are not shown since these should be developed to suit the type ofdrafting machine with which the device is to cooperate. Facilities for attachment to a drafting, machine. are highly desirable since they afford meansto place the ,device in any desired di ection and at any selected position on the drawing, the entire device thereby being movable parallel to its original direction without requiring reorientation at a new location so long as ellipses with parallel axes are to be drawn.

Standards or uprights i2, is are attached to base ill by the use of screws 34 or other convenient means, and are provided near their upper ends with mutually aligned holes for supporting brackets l5, $53 so that the latter can be rotated about a common axis. The brackets are bored to receive shafts 3t, 33 that are perpendicular to the aforementioned common axis about which the brackets can be rotated. Indicia are provided on standards 42, i l as shown in Fig. 3 to indicate the inclination of shafts 3t, 38 with respect to the horizontal. Thumbscrews 40, 42 are adapted to secure brackets i6, ill in any selected angular position. Brackets it, I8 can alternatively be yoked together so that they rotate as a unit and thus require only one thumbscrew to be fastened in order to establish the angular position of both brackets. Shafts 36, 38 carry radius arms 28, 22 and eccentrics 28, 30. The two eccentrics are of identical eccentricity and are coupled by means of link 32 which is bored at each end to fit the corresponding eccentric. Link 32 is so shaped as to avoid permitting any part thereof to interfere with the motion of pencil 2e irrespective of the size or eccentricity of the ellipse to be drawn. Radius arms '28, 22 are installed on shafts 33, 38 respectively at substantially from the direction in which eccentrics 28, iii? are offset, the angles between the radius arms and their respective eccentrics being identical although not necessarily right angles. The equality of these angles is easily maintained if each arm and its associated eccentric'are fastened securely together, either directly or by virtue of both parts being secured to the respective shaft. The object of so doing is to insure that when the radius arms are approximately on horizontal dead center the eccentrics actingthrough link are effective to cause the radius arms to remain accurately parallel. Each radius arm carries a cursor it, ll? which can be fixed at any selected radius by application of thumbscrews it, at. Each cursor carries a pin 52, it parallel to shafts 3Q, 38 and adapted to fit a hole at one end of connecting rod Connectingrodfi l is provided at about its middle with a cylindrical portion upon which is rotatably mounted pencil carrier 56 that can be set at any desired angle with respect to the connecting rod by application of thumbscrew Pencil carrier 56 comprises, in addition to the bored hole and thumbscrewifl for affixing the pencil carrier to connectingrcd 2d, another bored hole El? or equivalent means for carrying pencil 2% in a plane normal to the .connecting rod and in a. direction in the plane that is determined by the angular setting of the pencil carrier on the connecting rod. .-It is desirable also to provide on connecting rod i i and on pencil carrier 55 cooperating means such as scale pointer Ell, respectively, for indicating such angular setting. The indicia on scale 62 are preferably arranged to be complementary to those on standards i2, ill, so that when brackets l5, it are set to a desired angle, thereby rotating connecting rod 2d about its longitudinal axis through the same angle, and when pencil carrier is rotated on the connecting rod until pointer i l indicates the same angle on scale 62, bored hole as will be oriented vertically and pencil 25 will thereforebe vertical. The pencil slidably carried in, bored hole 50, and because of its ownv weight, orby the action of an attached supplementary weight or spring (not shown), rests with its point against the paper or other medium on which the device is placed. In operation, the device is aligned so that connecting rod 2d extends in the direction in which it is desired to orient the major axis of the ellipse to be drawn. Cursors 44 and 6 are set at zero radius on radius arms 20 and 22 and can be secured in this position by application of thumbscrews 48 and 5t. Brackets I6 and I8 are set at an angle corresponding to the desired angle of projection to be represented by the ellipse that is about to be constructed, and are fixed in position by turning thumbscrews 40, 42. Pencil carrier 56 is adjusted to the corresponding angle on connecting rod 24 as read on scale 62, and is fixed in position by means of thumbscrew 58. This done, pencil 25 is aligned vertically and its point indicates the center of an ellipse that would be formed if the device were put into operation in its present location. Should the desired center be elsewhere, the device is moved as a unit to cause the pencil to point to the desired center. If the ellipsograph is attached to a drafting machine, its orientation will remain correct without further attention; otherwise connecting rod 24 should be re-aligned with the desired direction of the ellipses major axis. The alignment of the connecting rod is most readily accomplished if the device has been designed so that the connectin rod is parallel to an edge of the base, as aforementioned, since in that case the parallel edge of the base may be aligned at the desired angle. and orientation of the device have been satisfactorily established, cursors M, 45 are set on radius arms 20, 22 at the desired radius of the circle that is to be represented in projection (this radius being equal to the semi-major axis of the resulting ellipse) and are fastened by applying thumbscrews d8, 59. The radii are most conveniently set if the radius arms are first arranged horizontally (in alignment), whereupon the adjustment of one cursor will carry the other with it through longitudinal movement of connecting rod 24. When the angles and radii have been set as described, the pencil point will lie on the periphery of the desired ellipse, and it will trace out the complete curve when the radius arms are rotated so as to describe a circle about their shafts 35, 38. Only one radius arm need be ro-. tated manually and the other follows.

An analysis that shows that a true ellipse with the desired properties will be formed is as follows: Cursors 44, 43 are set at a radius from shafts 35, 38, respectively, equal to the radius of the basic circle to be projected. It therefore follows that they will describe circles equal to the basic circle when radius arms 28, 22 are rotated about those shafts as axes, and so also will pins 52, 54 that connect the cursors to connecting rod 24. The linkage formed by the radius arms and by connecting rod 24 constitutes three sides of a parallelogram, the fourth side being the straight geometric line that joins shaft 35 to shaft 38. That geometric line is not evident as a tangible entity, but its location and length are established by the stationary structure comprising base l0, standards l2, l4 and brackets l5, E8 (the several thumbscrews having been set to retain otherwise adjustable parts in specific positions). Connecting rod 24, being the side of a parallelogram opposite a fixed side, always remains parallel to that fixed side and hence every point on connecting When the location rod 24 as well as every point fixedlyattached'toc it describes the same motion, This motion,.how-.p

ever, is determined by the points of attachment of the connecting rod to the linkage, namely pins 52, 54, which movein a circular path with a radius equal to that of the chosen basic circle,

as aforesaid. Therefore every point on the conwith the same radius. The plane in which this motion takes place is also determined by the motion of pins 52, 54, and since these rotate about the axes of shafts 36, 38, the said plane is normal to those axes and is therefore inclined to the vertical at the same angle that exists between shafts 35, 38 'and the horizontal. Shafts 35, 38, however, have been set at an angle with the horizontal equal to the angle at which the basic circle is to be viewed; hence the plane in which pencil carrier 56 moves is inclined to the vertical at the angle at which the basic circle is to be viewed. Hole 60 in pencil carrier 56 has been set vertical by adjusting the pencil carrier on connecting rod 24 until the reading on scale 52 is the same as that on scales establishing angular position of brackets l6, 18. Therefore the axis of hole intersects the plane of the paper at points which describe the vertical projection of the curve traced out by the motion of the pencil carrier. Pencil 25, being vertically slidable in pencil holder 56, ignores any vertical component of motion of the pencil holder and merely follows the horizontal component of such motion. That horizontal component, however, has been shown to be the vertical projection on the paper of the motion of pencil carrier 55, or in other words, the projection at the desired angle of View of a circle with the desired radius. The correctness of the curve is therefore proved.

Modifications and changes may be made in this invention without departing from the spirit and scope thereof as set forth in the appended claims.

The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.

I claim:

1. A frame having dual upstanding supports and defining a working space between said supports; a pair of arms, each rotatable about an axis on a respective one of said supports, said axes being adjustable to make equal angles respectively with said frame; a connecting rod carried by said arms and journalled thereto at selected points thereof that can be made equally distant respectively from said axes; a carrier attached to the connecting rod; and a marking element oriented by and slidable with respect to the carrier and having a point thereof adapted to move in the working space and on a plane that makes a selected angle with said axes.

2. A frame defining a reference plane and having dual upstanding supports and defining a Working space between said supports, means associated with each of said supports for defining respective circular paths of arbitrary and equal radii and settable to establish arbitrary angles between the planes of said paths and said reference plane, means having two points thereof constrained to move respectively in said paths and to be at corresponding points thereof, means carried on said moving means and adapted to orient a marking element with respect to said reference \plane, and means for arbitrarily setting the 7v orientation ofasa-id carried means wi'iahsrespect to: Number 1 the'mlanesmflsaid paths. '7 15,

RICHARD W2 AICI-IRUll-I. 828,372

2,182,707' REEEBENGES; CITED 5 l The following; references are of record in .the Number file-offlnspatenb. 1 1415400 UNITED STATESPATENTS 59'7: ,1'11- 8 v Name" Date Sherman Dec.' 16 1902- Becker Aug. 14; -1906 Shipman Dec; 5531939 FOREIGN PATENTS Country: Date 7 Great Britain Apr; 12, -1920 France Aug. 21; 1925

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