US831314A - Apparatus for drafting and measuring angles. - Google Patents

Description

No. 831,314. PATENTED SEPT.18, 1906.

W. J. VARLEY.

APPARATUS FOR DRAFTING AND MEASURING ANGLES.

APPLIGATION FILED APR. 6. 1906.

2 SHEETSSHBBT 1.

rm: mmms PETERS Cw. nmsuuvmoy. u. c.

No. 831,314; I PATENTED SEPT. 18, 1906.

W. J. VARLEY.

.APPARATUS FOR DRAFTING AND MEASURING ANGLES.

APPLIOAIION TIL E1) APR. 6. 1906.

2 SHEETS-SHEET 2.;-

HWHIIWHUII for Drafting and Measuring UNITED STATES PATENT OFFICE.

APPARATUS FOR DRAFTING AND MEASURING ANGLES.

Y No. 831,314.

Application filed April 6, 1906. Serial No To all whont it may concern: I

Be it known that I, WILLIAM J. VARLEY, a citizen of the United States, residing at Englewood, in the county of Bergen and State of New Jersey, have invented certain new and useful Improvements in Apparatus Angles, of which the following is a full, clear, and exact description.

My invention relates to the art of drafting and measuring, and pertains particularly to the provision of an instrument used in these arts and the method in the performance of which the instrument is conveniently used.

The principal object of the invention is to enable draftsmen and engineers. to perform operations on the drawing-board which have hitherto been altogether impossible, or only possible by the aid of trigonometrical tables, protractors, and other machinery with which the average draftsman is ordinarily unsupplied and with the use of which he is not particularly familiar.

A further object of the invention is to enable results to be determined with absolute accuracy, or as nearly absolute accuracy as graphical methods can attain, in place of approximate results, which depend on mathematical tables and constants.

' With these and other objects in view my invention consists in the methods and in the construction and arrangements, as hereinafter set forth and shown and finally par ticularly pointed out in the appended claims.

In the drawings, Figure 1 is a diagrammatic view illustrating the formation of what I shall term an arcuate rectification curve, and which embodies the essential principles of my invention. Fig. 2 is a diagram illustrating the curve and some of its properties. Fig. 3 is a similar view designed to show still further properties. Fig. 4 shows a drafting implement embodying the curve above mentioned. Fig. 5 shows another form of drafting implement also making use of the curve.

In modern engineering a wide variety of mathematical operations are performed by raphical methods directly upon the drawingoard. T-squares and steel straight-edges are now brought to such perfection that horizontal and vertical lines are obtainable with great accuracy, as well as forty-five-degree an sixty-degree lines, circles, and arcs of circles. With these a wide variety of problems can be solved; but so far as I am aware a certain class of problems have fallen out of the range Specification of Letters Patent.

' very troublesome,

each other in a vertical line passing Patented Sept. 18, 1906.

of utility of drafting methods hitherto used and have had to be solved by the aid of mathematical tables and constants. Foremost of such problems are those relating to laying off or measurement of special angles. Protractors with verniers are sold for doing this; but the instrument is an expensive and delicate one and out of place when exposed to the rough usage of the ordinary drafting-board. On this account it is more usual for draftsmen to lay off special angles by natural sign or tangent tables, which of course is a round about operation and somewhat liable to error. In carrying out my invention I pro vide an instrument which is as cheap and simple as the ordinary draftsmans triangles and which is capable of measuring off arcs and angles of any value and with absolute accuracy.

In addition to the laying off or measurement of angles problems frequently arise involving the measurement of sectors and the areas of segments. These are ordinarily and my invention pro vides a graphical method of obtaining the desired results with absolute accuracy or with as much accuracy as drafting implements can attain.

A further object of the invention is to divide a circle into any number of parts with the same facility as is possible in the subdivision of a straight line.

In order that my invention may be fully understood, I will state the essential principles which I have discovered, and of which I make use and embody in the structure or instrument later described.

Referring to the drawings, in which like parts are designated by the same reference sign wherever they occur, Fig. 1 shows a diagrammatic generation of the arcuate rectification curve. In this figure, A designates a roller or wheel revoluble on a fixed axis 0, and C represents a rod having a straight-edge D, which bears against the periphery of the wheel A and is constrained to have a rectilinear or right-line movement on the line (1 d. E indicates a pointer fixedly attached to the wheel A, so as to turn therewith, and F indicates a straight-edge fixedly attached to the as to rectilinearly move therewith. Now sup osing the straight-edges E andF are initia ly arranged, so as to coincide with through the axis 0, and then the members C and A or idealized apparatus for the are moved or rolled in the direction of the arrows, the intersection of the straight-edges E and F will describe a curve G, which somewhat resembles a parabola in general form, passing through an originat the point 0 and approaching a pair of parallel asymptotes h and i. The essential characteristic of the curve G is that any point therein is the same linear distance from the line 0 0 as the arc subtended by such point on the periphery of the wheel A. Expressed in other words, the curve G is the locus of a right line having a uniform rectilinear motion and of another right line having a uniform angular motion about a fixed point. It is evident that the angle E 0 0 is always proportional to the distance of the intersecting point in the curve from the line 0 0. If this distance is w, it may be stated that w=K d, where 6 is the angle E 0 0. Another expression for the curve is y =00 cot (9, where y is the distance of the point on the curve from a horizontal line passing through -0. This equation, therefore, is based on rectangular coordinates whose origin is 0. The angle 6 may be expressed in terms of 00, since 0: where 1' is the radius of the wheel A. The

equation therefore becomes y=0c cot I consider the form in which the equation is expressed as, however, relatively unimportant, since it. would be expressed in different ways for the varying systems of coordinates used. In all cases, however, its essential characteristic is illustrated by the diagram of Fig. 1, the essential characteristic being that every point on the curve intersects every radius of a certain are at the same distance from a base-line as the length of the arc. The base-line in Fig. 1 is the line 0 0, and the arc is of course the circumference of the wheel A. The arcuate rectification curve being obtained by the above or any other method, it may be embodied in various ways and used for various now describe. In Fig. 2 the curve is shown at G, the base-line at 0 0, and the arc at a. 0 1" is a radial line. Such a radius cuts the are a at the point r and the curve G at the point 1'. If a perpendicular r s is erected at the point r, the distance 0 s will be e ual to the arc 0 r. This gives a ready met 0d of laying off and measuring angles. For ex ample, supposing it were desired to lay off an angle of 36.47 from the line 0 0, the curve G being drawn from a base-circle a of any radius, it is merely necessary to lay off the distance 0 s proportional to the angle wanted. In the present case the line 0 8 would be 36. 47 units long. The perpendicular s 1" being dropped to cut the curve G, the angle 0 0 1* is formed, which is the angle 36.47

purposes, which I will required. If the base-circle a, is taken of the right radius, it is obvious that the units used in measuring off the line 0 8 may be inches or centimeters or any other unit which is obtainable on the scales sold upon the market. In practice I make the radius of the circle at equal to or 5.729578 inches, as by this figure the distance 0 8 may be measured off as 3.647 inches in order to get the angle mentioned. The measurement of any unknown angle is effected by the simple reversal of the above process. In ordinary practice the curve G would of course be drawn with an instrument having a fixed contour or edge to guide the pencil, and the various horizontals and perpendiculars would be made by the T-square and triangles. It is this fact that renders the method useful and practical for draftsmen and others who desire to secureaccurate results quickly and easily.

In Fig. 3 I have reproduced the essential parts of the diagram of Fig. 2 in order to illustrate another field of utility of my inventionnamely, to measure the areas of sectors and segments. Supposing it is desired to obtain the area of the sector 0 0 r. The point 8 is obtained, as before, by erectin a perpendicular from the point 1" and a racIial line 0 s is drawn. Then the area of the triangle 0 0 s is equal to the area of the sector This follows since the line 0 s is equal to the arc 0 1". Thus the draftsman obtains at once a triangle of area equal to the sector. If it is desired to measure the area of the segment 0 r, a second perpendicular is erected from the point r to the point 8. Then the area of the segment is equal to that of the triangle o s s. This follows from the fact that the segment equals the area of the Sector minus the area of the triangle 0 o 1" equals the triangle 0 o 8 minus the triangle 0' 0 7" equals the triangle 0 r 8. When itis desired to divide a circle into any number of parts, it is merely necessary to lay off the angle corresponding to any chosen number of parts by linear measure on the line 0 s and subdivide this measure into the chosen number of parts. Radial lines from the point 0 through the intersection of perpendiculars from the divisions on the line 0 s with the curve G then cut the circle into the number of divisions required. The number of applications of my invention is practically unlimited; but the above will serve as illustrative examples and will sufficiently indicate the field of utility thereof.

Referring now to Figs. 4 and 5, I illustrate one form of practical construction which embodies my invention. This comprises a plate 1, of sheet metal, having straight edges 2 and 3 at right angles to one another and having a curved'edge 4, which corresponds exproperly divide the circle.

actly to the curve G above described, and l which I term the arcuate rectification curve. The edges 2 and 3 are respectively parallel to the diagrammatic lines 0 and 0 s above described. 5 indicates a hole which is accurately situated in the plate 1 at the point 0 of the above diagrammatic representation. The plate 1 is conveniently cut away at 6 and 7 so as to lighten the construction; but a web 8 may be left for greater strength and for the attachment of a handle 9. The device illustrated in Fig. 4 may be termed a right-hand instrument. A left-hand instrument would be similar, except that all of the parts would be transposed from right to left. If the knob 9 were omitted, the instrument shown would serve equally well as a right or as a left hand instrument by merely turning it upside down.

In Fig. 5 another form of tool is shown which embodies a different portion of the curve. The portion of the curve is denoted by G and comprises a section extending equal distances from either side of the point 0 in the diagrams previously described 10 designates a hole which can be registered with a line corresponding to the line 0 0. The edge 11 is straight and corresponds with a horizontal line intersecting the circle a at a fortyfive degree radius thereof. This instrument is particularly convenient for the sub division of circles, since it is merely necessary to register the edge 11 with the four sides of a suitable square and then after having divided the square into a suitable number of divisions to draw perpendiculars therefrom intersecting the various curves G. Radial lines through the intersecting points will then What I claim is 1. A drafting implement comprising a plate or sheet of material having one edge curved in accordance with the equation y =w cot and having means whereby the coordinates of the curve may be located.

2. A drafting implement comprising a plate or sheet of material having two straightedges at right angles to one another, and a' third edge curved in accordance with the gr; equation y=0c cot and having means whereby the coordinates of the curve may be located.

3. A drafting implement comprising a plate or sheet of material having a pair of straight-edges at right angles to one another and having a third edge curved in accordance with the equation y=zr cot i, said plate having a hole centered at the origin ofthe coordinates of said curve, and having means whereby the coordinates of the curve may be located.

. 4. A drafting implement having one curved edge any point of which is the same distance from the diameter of a base-circle as the length of the arc subtended by a radius through such point, and having means whereby the coordinates of the curve may be located.

In witness whereof I subscribe my signature in the presence of two witnesses.

WILLIAM J. VARLEY. Witnesses:

FRANK S. OBER, ALFRED W. PRocToR.

Images