US2300401A - Vector calculating board - Google Patents

Vector calculating board Download PDF

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Publication number
US2300401A
US2300401A US40892941A US2300401A US 2300401 A US2300401 A US 2300401A US 40892941 A US40892941 A US 40892941A US 2300401 A US2300401 A US 2300401A
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Prior art keywords
straight edge
scales
member
members
base
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Donnan E Basler
Harold W Kelley
Bruce O Watkins
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Donnan E Basler
Harold W Kelley
Bruce O Watkins
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    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06GANALOGUE COMPUTERS
    • G06G1/00Hand manipulated computing devices
    • G06G1/14Hand manipulated computing devices in which a straight or curved line has to be drawn from given points on one or more input scales to one or more points on a result scale
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10STECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S33/00Geometrical instruments
    • Y10S33/09Rectangular proportioner

Description

Nov. 3, 1942- D. E. BASLER arm. 2,300,401

VECTOR CALCULATING BOARD Filed Aug. 30, 1941 Bi ycle F290 20 L9 /23 Z0' 4.

WVIIIIIIVVAIFIIIIA HAROLD VIZ/KELL Y BEL/650mm [NVENTORS fibf? W ATTORNEY Patented, Nov. 3, 1942' UNITED STATES PATENT OFFICE" z,s 6o,4o1

VECTOR CALCULATING BOARD pom a Ba'sler, 1m... Mlcla, Harold w. Kelley, Port St Joe, Fla, and Bruce 0. Watkins,

Tucson, Aria.

(Granted under the act of March s, 188:, amended April so, 1928; m o. G. 751;

Claims.

The invention described herein may be manufactured and used by or for the Government of the United States for governmental purposes without the payment to us of any royalty thereon in accordance with the provisions of the act of April 30, 1928 (Ch. 460, 45 Stat. L. 467) This invention relates to a mechanical calties or vectors such as impedances, displacements,

velocities, forces, etc. (all of which are quantities involving the idea of direction as well as amount) must be dealt with in the treatment of many problems. Problems involving addition and subtraction .of vectors may be solved either mathematically or graphically. The instant invention relates to devices for readily solving such problems by graphic methods without thenecessity of laborlus computation.

An object of this invention is to provide a mechanism having intersecting elongated members movable with respect to suitable coordinate scales, together with a graduated elongated member pivoted at the point of origin of or the effective intersection of said scales together with means for maintaining the swinging portion of said graduated pivoted member above the point of'intersection of said elongated members and a protractor scale associated with said graduated member whereby the distance between the point of origin of said scales and the point of intersection of said movable members may be read on the pivoted graduated member while the direction of having a flat top surface and parallel opposite edges resembling a rectangular drawing board. An elongated straight edge member I rests on the base I. A second elongated straight edge member 3 rests on the base I atop the straight edge member {and perpendicular to it. The straight edge members 2 and 3 are provided with 1' square ends engaging the respective edges of the base i so that each straightedge member is capable of sliding movement to and fro over the base along one axis. (It is to be understood however that straight edge members 2 and 3 may be movably mounted with respect to the base I in a manner similar to the mounting of the straight coordinate members shown in United Statespatent to Trueblood et al. No. 1,440,510 or United States patent to Webster No. 1,442,710.)

A third straight edge member 4 is pivotally mounted on pin 5 carried by the bracket 6 mounted on the base i. The, straight edge member 3 overlies the straight edge members 2 and 3. The pivot pin 5 is so positioned that the straight edge member I pivots about the zero-zero point on the coordinate scales 1 and 8 engraved or otherwise marked upon the base I. Adjacent to the ordinate scales 1 the base I is provided with grooved slots Ill carrying additional scales 9. Adjacent to the abscissa scales 3 the base is provided with grooved slots l2 carrying additional scales ii. The base i is also provided with two pairs 0! narrow parallel slots. The slots I are parallel to the ordinate scales and the slots ii are parallel to the abscissa scales. The slots l3 and I! are provided for the purpose of receiving the spring ends of U-shaped index tabs designated I3 and i5, respectively. The straight edge members 2, 3 and 4; while they may be made of wood, metal or the like, are shown as being made of transparent plastic. The members land 3 are provided with hair line index markings I1 and I8, respectively, engraved thereon for association with the respective coordinate scales 1 and 8 on base I. Encompassing the point of crossing of straight edges 2, 3 and 4 there is located a slide member l9 (Figure 2). This member includes a straight edge holding portion 20 provided with an aperture therethrough of such size as to snugly receive the straight edge member 4. The slide member I! also includes second and third straight edge holding portions 2| and 22 having apertures therethrough of such a size as to snugly receive the straight edge members 3 and 2, respectively.- The last mentioned portions are made integral and the apertures therein are at right angles to each other with the straight edge members 3 and 2 passing through their respective apertures. The straight edge holding portion 20 of the slide member I! is pivotally fastened to the lower portion of this member by the pivot bolt or pin 23. -The straight edge holding portion 20 of the slide member may be made of metal or transparent plastic. In the illustrated embodiment it is shown as being made of metal with a rectangular portion cut out as viewed in Figure 1, with a cross hair 34 stretched thereover perpendicular to the straight edge member 4 carried thereby. When this member is made of transparent plastic or is provided with a transparent top of plastic or glass, a line taking the place of the cross hair 24 can be engraved or etched directly upon its top without the necessity of cutting out material to make the graduations on the straight edge member 4 visible. The pivoted straight edge member 4 is provided with one or more sets of graduations thereon corresponding to the coordinate scales to be used. The member 4 is also provided with a hair line marking longitudinally thereof. The line established by this marking passes through the pivot axes of the pivot pins 6 and 24. The pivot axes of the pins and 29 are both normal to the plane of the upper face of the base I and the pivotal axis 22 passes through the point of intersection of the lines established by the hair line marks I1, 24, and IS. The top of the base I may be ruled to resemble polar coordinate graph paper with the pivotal axis of the pin 5 as the origin, or these rulings may be omitted, but in any event the top of the base I is preferably provided with the an gular graduations thereon, as shown schematically by the scale 25.

In operation the straight edge members 2 and I are moved with respect to their coordinate scales, thus moving the slide member IS in accordance with the resultant compound motion imparted thereto. As the slide member I9 is moved, the straight edge member 4 is moved thereby, pivoting about the fixed axis of the pivot pin 25. The device can also be operated by moving the slide member l9 to cause its cross hair 24 to overlie a selected graduation thereon and a desired angular setting of the straight edge member 4 may be made with respect to the angular graduations 25, in which case the straight edge members 2 and 3 will be moved to resolve the vector quantity represented by the distance read ofl on the scale carried by the straight edge member 4 and its direction into two components at right angles to each other.

It will be apparent from the above description that when either the scales 1 and 8 or other suitable scales are employed, this equipment may be used to perform vectorial addition, subtraction and many other allied problems. One example will be given illustrating the use of the equipment for the adding of vectors. In this example it will be assumed that it is desired to determine the impedance of an electrical circuit having three ohms of inductive resistance at a particular frequency and having four ohms of ohmic resistance. Here the magnitudes of the components are different and their directions differ by ninety degrees. Vectorial addition of these two components is established by moving the straight edge member 2 to bring its hair line mark il above the, scale I to the numerical value 9 and then moving the straight edge member I to bring its hair line mark i9 over the scale 8 to the numerical value 4. With the movement of the straight edge members 2 and 3 the slide member I 9 is moved so that its cross hair 24 lies directly over the numerical indication 5 on the scale carried by straight edge member 4 and the angular displacement of this quantity with respect to either the resistance or the inductance can be read on the scale 25. Where for instance it is desired to resolve a vector having a magnitude of 183 plus and a direction of forty-five degrees with respect to the horizontal and vertical axes, the straight edge member 4 may be resistance or reactance values.

moved to bring its hair line over ,the graduation of scale 24 and then the slide l9 can be slid therealong to indicate the magnitude of this vector, whereupon the slide members 2 and 3 are moved to bring their respective hair lines I! and II to overlie the values and 130 on coordinate scales 1 and 8, respectively, thus resolving the vector of a given magnitude and direction into two components at right angles to each other. I

In the above description simple numerical values have been assumed for the purpose oi simplicity. It is to be understood that the scales shown on the instrument are not necessarily as accurately laid out or proportioned as the scale graduations in an actual instrument. For the solution of a great number of problems of this type the additional scales 9 and II could be graduated to represent ohms, amperes, volts or some other quantity. In impedance problems scales 8 or II would represent resistance values in ohms and scales 1 and 9 would represent reactance values. The total impedance therefore is read on the scale carried by the straight edge member 4. For voltage or current, scales 8 and H would represent real values while scales I and 9 would represent imaginary values. The magnitude of the resultant vector would be read on the scale carried by straight edge member 4 and the angular displacement by reading the angle between this member and the horizontal. Certain of the removable or interchangeable scales 9 and II could be graduated in other manners. For example, a certain size of conductor has a certain resistance and reactance per mile. Therefore, one of the scales of the set ll could he graduated in miles for No. 4 conductor size resistance- Another could be graduated in miles of N0. 6 wire, etc. Similarly, the scales 9 could be graduated in miles for conductor reactance. Then the total impedance could be found on straight edge scale 4 by simply applying the proper miles of the conductor on scales 9 and II, without referring to either the By the use of the tabs l3 and I5 this process can be conducted along the line if the conductor size changed, by placing the index of the proper conductor scale to the previous value of the preceding conductor at the distance where the change in conductor size occurs.

In lieu of the slide mechanism IS the coordinate arms or straight edge members 2 and 3 and the pivoted straight edge member 4 could be maintained in proper relation by making these members slotted and by having a pin extend through all three. The device shown in the drawing is limited to a single quadrant, but it is to be distinctly understood that the idea could be carried forward where desired to include two or more quadrants, thus making possible the more ready handling of negative quantities. Other and further modifications could be made without departing from the spirit of this invention.

What we claim is:

1. A device for mechanically producing the addition and subtraction of vectors comprising a base, a pair of mutually perpendicular straight edge members mounted on said base and arranged for independent movement thereon in paths perpendicular to their respective longitudinal axes, a plurality of individually slidable difierently calibrated coordinate scales mounted on said base associated with respective ones of said straight edge members, a graduated straight edge member, means for pivoting one end of said graduated straight edge member at the effective origin of said coordinate scales, and means carried by the first two mentioned straight edge members for maintaining the graduated straight edge member in such a position as to always overlie the intersection of said members, whereby vectors in quadrature may be added or subtracted.

2. A device in accordance with claim 1, including index marker tabs and means for holding said tabs in predetermined selected locations with respect to said individually slidable differently calibrated coordinate scales whereby said scales may be readily set opposite said tabs to attain certain predetermined selected positions.

3. A calculating device comprising a frame having indicia thereon, members slidable on said frame and crossing each other at right angles to form opposed rectangles of lesser size than said frame, a plurality of individually slidable differently calibrated coordinate scales mounted on said frame associated with respective ones of said members, a divider pivotally mounted on said frame, means for moving said divider to intersect the point of crossing of said slidable members, at least one scale carried by said divider, and a protractor scale on said base,

whereby the length and direction of a line extending between the pivot of said pivotally mounted divider and the point of intersection of said slidable members may be readily ascertained.

4. A device of the class described comprising a rectangular frame having a plurality of separately adjustable coordinate scales mounted on two of the adjacent sides thereof, a pair of elongated adjustable members mounted on said frame crossing each other at right angles, said members being movable with respect to the coordinate scales along the respective edges of said member, a graduated pivoted member pivoting at the effective intersection of said coordinate scales, and means for maintaining said graduated pivoted member above the intersection of said movable members.

5. A device in accordance with claim 4, including tabs for locating reference points on said coordinate scales, said tabs having means for holding them in predetermined selected positions on said frame whereby said separately adjustable scales may be readily set with respect to said predetermined selected positions occupied.

by said tabs.

DONNAN E. BASLER, HAROLD W. KELLEY. BRUCE O. WATKINS.

US2300401A 1941-08-30 1941-08-30 Vector calculating board Expired - Lifetime US2300401A (en)

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Cited By (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2469672A (en) * 1946-06-01 1949-05-10 William A Wartinen Calculator
US2627114A (en) * 1949-02-03 1953-02-03 Noah E Sprecher Impedance rule
US2646626A (en) * 1951-01-09 1953-07-28 Palin Abraham Stamp layout device
US2682367A (en) * 1951-10-30 1954-06-29 A V Roe Canada Ltd Weight and balance calculator for load carrying structures
US2682709A (en) * 1948-08-20 1954-07-06 Clement H Watson Plotting device
US2759267A (en) * 1952-12-16 1956-08-21 Rufus C Wood Measuring and computing device
US2866270A (en) * 1954-03-19 1958-12-30 Johnson Donald Clair Angle determinator and bisector
US3053445A (en) * 1957-08-05 1962-09-11 James H Armstrong Computing device
US3409216A (en) * 1967-04-18 1968-11-05 Texaco Inc Grease flow predictor
US3473731A (en) * 1967-07-13 1969-10-21 Jerome J Kurland Speed register
US3766652A (en) * 1972-04-05 1973-10-23 Raymond Lee Organization Inc Trigonometric aid
US3805397A (en) * 1970-02-18 1974-04-23 G Wilamowski Geometrical measurement devices
US4117973A (en) * 1976-07-06 1978-10-03 Bold Eugene W Calculating devices
US5551160A (en) * 1994-08-24 1996-09-03 Ferris; Byron S. Calculating graphic scaler
US5892212A (en) * 1998-02-02 1999-04-06 Rentsch; Frederic Nomographic computing device

Cited By (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2469672A (en) * 1946-06-01 1949-05-10 William A Wartinen Calculator
US2682709A (en) * 1948-08-20 1954-07-06 Clement H Watson Plotting device
US2627114A (en) * 1949-02-03 1953-02-03 Noah E Sprecher Impedance rule
US2646626A (en) * 1951-01-09 1953-07-28 Palin Abraham Stamp layout device
US2682367A (en) * 1951-10-30 1954-06-29 A V Roe Canada Ltd Weight and balance calculator for load carrying structures
US2759267A (en) * 1952-12-16 1956-08-21 Rufus C Wood Measuring and computing device
US2866270A (en) * 1954-03-19 1958-12-30 Johnson Donald Clair Angle determinator and bisector
US3053445A (en) * 1957-08-05 1962-09-11 James H Armstrong Computing device
US3409216A (en) * 1967-04-18 1968-11-05 Texaco Inc Grease flow predictor
US3473731A (en) * 1967-07-13 1969-10-21 Jerome J Kurland Speed register
US3805397A (en) * 1970-02-18 1974-04-23 G Wilamowski Geometrical measurement devices
US3766652A (en) * 1972-04-05 1973-10-23 Raymond Lee Organization Inc Trigonometric aid
US4117973A (en) * 1976-07-06 1978-10-03 Bold Eugene W Calculating devices
US5551160A (en) * 1994-08-24 1996-09-03 Ferris; Byron S. Calculating graphic scaler
US5892212A (en) * 1998-02-02 1999-04-06 Rentsch; Frederic Nomographic computing device

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