US2845500A - Trigonometric switch - Google Patents

Description

July 29, 1958 J,B HATHER 2,845,500

TRIGONOMETRIC SWITCH Filed April '7, 1955 nited States This invention relates to an electrical contacting device which provides digital or multi-digital representation of trigonometric functions.

The object of the invention is to provide a simple switch by which the trigonometric functions, such as the sine, cosine, etc., of an angular rotation are directly available in digital form. Various other objects and particular advantages will be apparent as the nature of the invention is fully disclosed.

In the accompanying drawings I have illustrated a very simple and useful application of the invention. In these drawings similar reference numbers refer to corresponding parts, and:

Fig. l is an isometric view of a switch by means of which the digital values of the cosine of the angle a are obtained.

Fig. 2 is a plan view of the layout of the contacts in the first quadrant of the switch shown in Fig. 1.

Referring to the drawings, the switch illustrated consists of the forty contacts -49, suitably held and insulated from each other by any convenient means, the rotatable shaft 8, held in convenient bearings, and the wiper 9 fixed to this shaft. The wiper 9 passes over the contacts 10-49 as the shaft rotates, making contact with each, and thus completes an electrical circuit from any convenient fixed contact such as the brush or Wiper 7, through the shaft 8 and wiper 9, to whichever of the forty contacts 10 to 49 is beneath the contact tip of the Wiper. The essential feature of the invention thus disclosed is the position of the contacts; they are arranged so that each one corresponds to some specific value of the cosine of the angle a, where or is, as shown, the angle of rotation of the shaft and attached wiper. Thus contact corresponds to cos 1.0; contacts 19 and 49 correspond to cos u=0.9, contacts 18 and 48 to cos a=0.8, and so on to contacts 10 and 40, for cos 06 0.

In a similar manner contacts 21 and 31 represent cos u=-O.l, contacts 22 and 32, cos ot=0.2, and so on to, finally, contact represents cos oc=1.0.

Thus each contact represents a specific digital or unit value of the trigonometric function, and extremely simple output circuits can be utilized to record, transfer, or otherwise manipulate, as desired, these digital values of the trigonometric function of the shaft rotation angle 0:.

Since each contact represents a single specific value of the trigonometric function desired, the limiting resolution depends 011 the number of contacts provided. There is no theoretical limit to this resolution or number of contacts; however, when it is desired to utilize a large number of contacts so arranged the permissible width of a contact for some values (e. g., cos a O) will be very small unless the radius of the contact circle is very large. This practical difitculty can be avoided by the simple expedient of utilizing more than one deck for such a switch, with appropriate gearing between the wipers, so that an expanded scale is provided on a small radius. The placement of the contacts, to correspond to equal in atent 0 'ice crements of values of the trigonometric function is still in accord with the invention described.

Ambiguity, which results when the wiper is in contact with two contacts simultaneously, can be completely avoided by a variety of methods, such as using mechanical detents or electromechanical methods to avoid any dead center positioning of the wiper or contacting means on two adjacent contacts, or by the use of output circuits which respond to only one of the two bridged contacts, such as, for example, the lower valued contact. However, if the separation between the contacts themselves is very small, the width of the wiper can also be small, to the extent that the range of possible ambiguity is thereby made so small that in many practical applications it can be ignored. Since each contact represents a range of values of the trigonometric function (and hence of the angle) to which the particular digital value applies, the desirable low ambiguity can be achieved by utilizing contacts of varying width, with each contact extending over nearly the full range to which it applies.

This is illustrated in Fig. 2, which is a plan view of the layout for the contacts of the I quadrant of the particular cosine switch shown in Fig. l. (The remaining quadrants, II, III, and IV of the whole circle of Fig. 1 are either identical or mirror images of this arrangement). Contact 20, corresponding to the value of cos oc=1.00, should extend, in this quadrant, from cos tx=1.00 to cos 0c=0.95; contact 19, corresponding to the value of cos a= 0.9, should extend from cos 04:0.95 to cos a=0.85, and so on to contact 10, which should extend from cos a=0.05 to cos 04:0. The line of separation between contacts 20 and 19 is thus at the angle 18 41 40"; the line between contact 19 and 18 is at 31 47' 18", and so on, since these are the angles whose cosines are 0.95 and 0.85 respectively. In actual construction it is convenient to utilize the geometrical fact also illustrated in Fig. 2, that the appropriate angle to the point of separation of any two contacts will be given by the intersection of the circle and lines perpendicular to the initial fixed position from which the angle a is to be measured for these cosine contacts. If the radius of the circle is taken as unity, as shown, the intersecting lines will be spaced at distances corresponding to the appropriate cosine a values, as shown. (For equal width or point type contacts the positions of the individual contacts can of course be described in a similar geometrical manner.)

In the use of this switch the input variable is a, the angle of rotation of the-shaft 8 and wiper 9 relative to the contacts. Since each contact represents a specific value of cos a, the output variable is a digital representa tion of cos a. Sin a is readily obtained from this switch, since sin a=cos (-a); the zero or x=0 position being taken at 90 to the position shown in Fig. 1. Other trigonometric functions can be obtained simply by placing the contacts in positions corresponding to the proper values of the function desired. And, of course, other trigonometric functions can be obtained by simple arithmetical manipulation of the sines and cosines in the output circuitry used, since, for example,

cot a=(cos a)/(sin 0:), etc.

As an example of a specific, particular, and important use of this invention, one application in connection with weather observations will be given. One of the most useful meteorological observations or quantities is the vector average wind velocity; this can be defined as the vector average of the individual instantaneous vectors representing the wind velocity and direction during the period over which the average is taken. However, no simple means for recording directly this particular quantity has been developed; the general meteorological practice has been to compute an approximate value based in the average velocity values obtained from typical cup anemometers and separate values of the wind direction by tedious essentially hand calculations. The importance of the vector average has recently been demonstrated by the development of expensive and elaborate electronic analog type computer equipment to permit direct recording of the components of this vector average.

This invention permits the direct recording of the vector average wind velocity components utilizing only a standard cup type anemometer and a wind vane; the components can be directly recorded in the same manner as the average velocity would be recorded from the anemometer itself. A typical cup anernometer provides a circuit closure or pulse for each unit of wind travel, independent of the wind direction. Usually the pulses are accumulated on a simple totalizing register for some period, say an hour, and the total number of pulses is directly the average wind velocity in say miles per hour. To provide instead a proper vector average component on the same register, the shaft of a trigonometric switch such as that shown in Fig. 1 is coupled (as for example by a Selsyn system) to the wind vane, and the anemorneter pulse circuit is led through the switch contacts. There is also provided a simple relay and stepping switch output circuit which has the property that each input pulse through any particular contact will be multiplied by the number corresponding to the cosine value represented by that particular contact. (The circuit merely needs to count the number of contacts between the active or energized one and the value Contact.) The total number of pulses (i. e., the number of anemometer pulses multiplied by the appropriate cosine values) are now accumulated on the register, and this total actually represents one component of the desired vector average wind velocity. In practical use for meteorological purposes two components are necessary; the second compo nent could be obtained from a second switch, or more simply, a second wiper oriented 90 with respect to the first, together with the appropriate output circuitry.

The utility of this invention is not limited to this particular field or application. It may be used in connection with the usual types of read-out processes for many types of computers, or even within the computer to provide trigonometric function values. In any servo-mechanism for computing or control where the desired digital value is representable as a trigonometric function of some variable, the variable may be introduced as a linear rotation of the shaft, and the values of the function are directly obtainable at the digital contacts.

I claim:

1. A multiposition switch device comprising, a series Cit of separate output contacts arrayed in a circular arc with substantially equal spaces between adjacent contacts in said series, a wiper pivotally mounted at the center of said circular arc to successively engage said contacts in moving from a first position through a predetermined angle to a second position, said spaces between adjacent contacts in said series being disposed at the intersections of uniformly spaced parallel lines with said circular arc, said parallel lines being perpendicular to said wiper when said wiper is in one of said positions, and each contact being disposed between adjacent ones of said parallel lines and having a width for engagement by said wiper substantially equal to the portion of said circular arc between such adjacent parallel lines;

2. A multiposition switch device as recited in claim 1 wherein said circular arc is 360 and said one of the wiper positions bisects one of said contacts.

3. A multiposition switch device as recited in claim 1 wherein said circular arc is at least and said positions of said wiper are angularly spaced 90 on said circular arc with said parallel lines perpendicular to said first position of said wiper.

4. A multiposition switch device comprising, a series of separate output contacts arrayed in a circular arc with substantially equal spaces between adjacent contacts in said series, a wiper pivotally mounted at the center of said circular arc to successively engage said contacts by relative movement between said wiper and said contacts from a first position through a predetermined angle to a econd position, said spaces between adjacent contacts in said series being disposed at the intersections of uniformly spaced parallel lines with said circular arc, said parallel lines being perpendicular to said Wiper when said Wiper is in one of said positions, and each contact being disposed between adjacent ones of said parallel lines and having a width for engagement by said wiper substantially equal to the portion of said circular are between such adjacent parallel lines.

References Cited in the file of this patent UNITED STATES PATENTS 2,481,649 Doucette Sept. 13, 1949 2,528,345 Champs Oct. 31, 1950 2,608,094 Best Aug. 26, 1952 2,629,056 Goodwin Feb. 17, 1953 2,649,513 Luhn Aug, 18, 1953 2,658,963 Krahulec Nov. 10, 1953 2,678,985 Smith May 18, 1954 2,719,194 Stack Sept. 27, 1955

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