US773299A - Arcofactor. - Google Patents

Description

PATENTED OCT. 25, 1904.

A. P. STOKES.

AROOPAGTOR. I APPLIQATIONIILED 0017. 1903.

2 SHEETSSHEBT 1.

N0 MODEL.

Anson Phegps Szolcesjn Veniar,

by/r-r, 6217, M Aizs Witnesses:

No. 773,299. PATENTED OUT. 25, 1904. A. P. STOKES. ARGOPAUTOR.

APPLIOATION FILED OUT. 7. 1903. N0 MODEL. ZSHEETS-SHEET 2.

Fig.2

Wiinesses: v Anson Phelps Szokes, 11211622502 lay/ W4 1, W AZ Z QS Patented October 25, 1904.

PATENT OFFICE.

ANSON PHELPS STOKES, OF NEW YORK, N. Y.

ARCOFACTOR- SPECIFICATION forming part of Letters Patent N0. 773,299, dated October 25, 1904..

Application filed October 7, 1903.

T0 (LZZ whom, it may concern.-

Be it known that I, Anson PHELPS S'roKEs, a citizen of the United States, residing at New York, in the county and State of New York, have invented certain new and useful Improvements in Arcofactors, of which the following is a specification, reference being had to the drawings accompanying and forming part of the same.

My invention relates to instruments for describing arcs of circles and other curves without reference to the actual center or foci, and therefore provides a means for readily drawing arcs of long radii. Where the radius is not more than about two or three feet, an ordinary beam-compass can generally be used; but where the radius is much longer, up to several hundred feet, it becomes practically impossible to draw the are by continuous motion with a device which is pivoted at the actual center of curvature.

In my device I make use of the geometrical principle that all angles at the circumference of a circle subtended by the same chord are equal. Assuming arbitrarily a line of any convenient length as the chord of the arc to be described, if at the center of this line a perpendicular be erected equal in length to the versed sine of one-half the arc the extremity of the perpendicular will be at the middle of the arc. Then by connecting this extremity with the ends of the chord an isosceles triangle will be formed whose vertical angle is the constant subtended angle of the chord. If now an infinite number of triangles with equal vertical angles be drawn on the chord as a base, the locus of the apexes of the triangles will be the are desired. This latter might be drawn tentatively by erecting a greater or less number of triangles, according to the degree of approximation to geometrical exactness desired; but the preferred method is to describe the locus by the continuous 'motion of a point. Various devices for effecting. this have been proposed, consisting in one form or another of a pair of pivoted arms corresponding to the sides of the constant angle. By clamping the arms rigidly in adjusted position and moving them so that they are .always in contact each with Serial No. 176,038- (No model.)

itsrespective end of the chord the apex will describe the desired arc, as will be readily understood. My present invention, which forms the subject of this application, likewise embodies this idea, but provides for a number of novel features and combinations and has advantages in effectiveness and range and in simplicity, consisting, as it does, of three pieces of wood or of other suitable materials pivoted together, a pivoted tongue, and a device for clamping the parts in adjusted position having also an attachment to hold a pencil or other marker. These features will be easily understood when described in connection with the accompanying drawings, in which Figure 1 is a diagram illustrating the geometrical and trigonometrical principles of the device; Fig. 2, a plan view of the instrument arranged for use; Fig. 3, a detail view of partof the same; Fig. 4.. a diagram-showing amethod of repeating the arc, and Fig. 5 is a side view of a convenient device for securing the arms of the instrument in adjusted position.

In Fig. l the line A B is the arbitrarilyassumed chord. C D is the versed sine of onehalf the arc to be drawn. Then A C B is the inscribed triangle. sides A C and B C be moved bodily, always maintaining the same angle between them and keeping them or their lineal extensions always touching the extremities of the chord,as shown in the fulland dotted lines of the figure, the point C will traverse the desired arc. The preferred embodiment of my invention, which utilizes these principles, is shown in Fig. 2. The instrument consists of a base or bar D of any convenient size, according to the radii of the arcs to be described. For radii from thirty inches to seventy-five feet or more a length of five feet three and one-half inches will be suitable. Pivoted at each end of this, as shown, are arms E F, the three being so constructed that the centers of the pivots are exactly at the verticesof the angles formed by the inner edges of the base D and arms E F. It is now evident that the arms may be swung upward or downward to form Within obvious limits any angle between them. Piv- It is obvious that if the 1 oted at a convenient point in a transverse line bisecting the base D is a tongue (1?, preferably about fifteen inches in length for a base of the size mentioned above. This tongue, which for COHVOIllOI'lCO may be made of transparent material. has a number of perforations therein. In using the instrument one of these perforations will be placed at the point at which the inner edges of the arms cross, and conse quently at the vertex of the constant angle. For securing the movable parts in adjusted position any convenient device may be employedas, for example, a clamp, as H, which may have an extension 1, with an aperture in the latter in which a pencil may be inserted.

The operation of the instrument will be readily understood from the following. In Fig. 2, J represents the surface on which an arc is to be drawn as, for example, a drawil'igboardon which is tacked a sheet of paper K. On the sheet draw two straight lines, crossing at right angles at L. Below the horizontal line and touching it place two stout pins A B on opposite sides of L and each fifteen inches therefrom.- This part of the horizontal line represents the chord of the are to be drawn. Then one-half this chord, lifteen inches, is the sine of one-half the are to the given radius R, and the extremity of the versed sine of one-half of the same, laid off on the perpendicular, will mark the highest point of the whole are. To determine the value of the versed sine, the formula versin I R E1i may be used. the formula becomes versin R F i5 and the value of R. the radius, having been inserted the value of the versed sine is readily found. Having determined the extremity of the versed sine, as at C, place the base of the arcofactor below the horizontal line, as follows: Central pivot on perpendicular line. Inner edges of arms touching the pins, so that the junction of the inner sides of arms and one of the holes in the transparent tongue shall be over the upper extremity of the versed sine. Clamp arms and tongue in this position by means of the clamp. Insert the sharp point of a marker in this hole and swing the arcofactor as far as the pins will permit, keeping the inner edges of the arms constantly touching the pins, and the required are will be drawn to within a short distance of each end. On a sheet of sufiicient size the first are may be completed and extended in the following manner, as illustrated in Fig. 4:. \Vith one end of horizontal line as a center and with a radius equal to the versed sine describe The sine being fifteen inches,

This will give a new chord base-line of thirty inches by which a second arc of the required radius may be described with the arcofactor and forming a continuation of the first are. The curve may be extended farther in the same direction by describing a second small are, U, with the point C as a center and drawing the line A B" tangent thereto and thirty inches in length, as before, for a new base-line. This procedure may be carried out on either side of the first are as often as permitted by the size of the drawing-surface. If it is desired to draw a number of trial arcs, as in preliminary work of ship or yacht designing, laying out railways, &c., it will be found convenient to have the horizontal and perpendicular lines in ink and with ink-markings for inches and fractions thereof on the latter up and down from the point of intersection.

The perforations in the transparenttongue G (shown in detail in Fig. 3) are of course all located in line with its pivot, and since naval architects and civil engineers in this country usually employ a scale in which one-eighth of an inch or a multiple thereof, as three-eighths, is the unit length the perforations are placed one-eighth of an inch apart, beginning, say, one inch from the pivot. If new a second series of perforations one-eighth of an inch apart be located alongside the first, but beginning one and one thirty-second of an inch from the center of the pivot, the difference in distance from the center of the pivot M between corresponding openings in the two rows will be one thirty-second of an inch on the principle of the well-known diagonal scale. lVhen the arms of the areofactor are crossed at the next higher perforation in the adjoining row of perforations, however, the arms will no longer touch the pins, and the instrument must therefore be moved downward until they are in contact. The increment actually added to the versed sine will therefore not be one thirty-second, but one sixty-fourth instead. In Fig. 3 l have shown a tongue with four radial rows of perforations, beginning, respectively, one, one and one thirty'second, one and one-sixteenth,and one and three thirtyseconds inches from the pivot. In using an instrument with the holes so located the following simple rules may be followed: 1f the versed sine be a multiple of one-sixteenth of an inch, use a hole in the left-hand row; if one sixtyfourth more than a multiple of one-sixteenth of an inch, use the next row; if one thirty-second more than a multiple of one sixteenth of an inch, use the third row; if three sixty-fourths more than a multiple of onesixteenth of an inch, use the fourth row. 1f the arc is given and it is desired to find the radius, the problem may be readily solved by means of the arcofactor. Draw a chord thirty inches in length, and placing the instrument over the same as if to draw an arc arrange the arms so that they intersect at the extremity of the versed sine. Then adjust the trans parent tongue so that one of its perforations coincides with the point of intersection, and the length of the versed sine can be read directly from the tongue. By the formula Yglll the value of R will be 2 versin 2 found in inches, or by referring to a table giving radii for versed sines of from one sixty-fourth of an inch to four inches, Witha constant sine of fifteen inches, the radius may be found directly. Such a table may be printed or pasted on the instrument itself.

Having now described my invention and in what manner the same may be used, What 1 claim as new, and desire to secure by Letters Patent, is

1. In an instrument for describing arcs, the

combination of a rigid, rectilinear base, an

arm pivoted at each end of the base and adapted to cross at the side of the base, a tongue pivoted to the base midway between the arms, having a row of equidistant perforations radiating from the pivot, and one or more similar rows, each beginning on an are passing between adjacent perforations in the next preceding roW, as set forth.

ANSON PHELPS STOKES. Witnesses:

S. S. DUNHAM, J. R. JoHNsoN.

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