May 30, 1967 H. W. GRANTAND 3,322,340 INSTRUMENT FOR COMPUTING UNKNOWN MEASUREMENTS Filed July 27, 1966 OF TRIANGULATIONS 3 Sheets-Sheet l 2 2 Z INVENTOR Henry V. Grant land ATTORNEY May 30, 1967 H. v. GRANTLAND 3,322,340 INSTRUMENT FOR cóMPUN UNKNOWN MEASUREMENTS OF TRIANGULATIONS Filed July 27, 1966 3 Sheets-Sheet a READS 30 FROM Vert CA READS 250 Fig. IO INVENTOR Henry V. Grontlond C = C, x C ose can C C - 250 x 2. OOO ... a = 5oo' au BY (2-4-6%2-2 Fig. ATTORNEY May 30, 1967 H. V. GRANTLAND 3,322,340 . INSTRUMENT FOR COMPUT ING UNKNOWN MEASUREMENTS OF TRIANGULATIONS Filed July 27, 1966 5. Sheets-Sheet : 3 READS 6O FROM VERTCA b = c x Cot angent C b = 250 x 1.732O b = 433' As 58-24S& 66 Fig. 16 5759-22 2S 2222 INVENTOR Henry V. Grant and Fig.19 BY (2-4%. ATTORNEY 3,322,340 United States Patent Office Patented May 30, 1967 1. 2 3,322,340 line 2-2 of FIGURE 1, illustrating the movable asso INSTRUMENT FOR COMPUTING UNKNOWN ciation between the upper micrometer and the protractor MEASUREMENTS OF TRANGULATIONS plate. Henry V. Grantland, Rte. 3, Box 105, FIGURE 3 is a fragmentary elevational illustration of Arlington, Tex. 76010 the lower micrometer barrel and the vernier dial mount Filed July 27, 1966, Ser. No. 568,250 ing attached thereto. 4 Claims. (C. 235-61) FIGURE 4 is a side elevational view of the invention. This invention relates to calculating devices, and it has FIGURE 5 is a fragmentary sectional view showing the particular reference to an instrument for computing un pivotal and slidable connection between the lower mi known measurements of either side of a triangle where O crometer and the angle scale, and between these elements the measurements and angulation of an acute angle and and the protractor plate. One lateral side thereof are known. FIGURE 6 illustrates a right-angle triangle by which A prime object of the invention resides in the provision the side a thereof has been determined by use of the in of an instrument which embodies a protractor scale and vention as set in the manner shown in FIGURES 8, 9, a vernier alignable therewith and operative in combina 5 and 10. tion with a pair of micrometers, each having a vernier FIGURE 7 is another right-angle triangle by which the dial associated therewith and operated thereby to indicate side a has been determined by setting the angle scale and fractional spacings such, for example, as a division of micrometers as indicated in FIGURES 8, 9 and 10. A000 representing .001', whereby accurate calculations FIGURE 8 illustrates a vernier and protractor setting to can be made with a minimum of effort and by persons 20 30 degrees from vertical, both micrometers reading zero. lacking in mathematical training. FIGURE 9 shows the micrometers in locked positions at 30 degrees from vertical whereby the stock of the An object of the invention is that of providing a rela upper micrometer is adjusted to be adjusted to engage the tively simple instrument, possessing few mechanical parts, angle scale arm. enabling untrained persons to make calculations in tri 25 FIGURE 10 illustrates another setting of the angle angulation or trigonometrical surveys, when used in con scale, and both micrometers to 30 degrees from vertical junction with an engineer's transit, or the like, and is reading, respectively 250 and 500. adapted to be scaled in such manner as to compute FIGURE 11 illustrates a trigonometrical solution of the measurements in inches, feet, yards or miles, depending measurement of the side c of the right-angle triangle upon the purpose for which it is to be employed. 30 shown in FIGURE 7. In computing the distance across one side of a triangle, FIGURE 12 illustrates a right-angle triangle whose where the measurements of two of its sides are known, side b is determined by the settings illustrated in FIG it is necessary to use mathematical formulae by way of URES 13, 14 and 15. trigonometry, or other methods, such as by a slide rule, FIGURES 13, 14 and 15 illustrate the steps in setting or the like. Such methods are sometimes tedious and 35 the invention to determine the measurement of the un generally beyond the knowledge of untrained individuals. known side of the triangle shown in FIGURE 12. The invention is designed for the purpose of construct FIGURE 16 illustrates a trigonometricol solution to de ing such geometrical figures as right-angle triangles, equi termine the side b of the triangle shown in FIGURE 12. angular or equi-lateral triangles, isosceles triangles, and FIGURE 17 illustrates an obtuse triangle whose un often the scalene or obtuse angle triangle, or any polyg 40 knowns can be determined by computing the right-angle onal figure that is capable of being segregated or broken laterals shown in dotted lines. down into right-angle triangles, depending upon the FIGURE 18 fragmentarily illustrates, in elevation, the known factors at hand, such as an acute angle. An impor sliding association between the angle scale with the pro tant object of the invention, therefore, is that of providing tractor plate, and an instrument which possesses features by which the lengths of any side of many triangles can be determined FIGURE 19 is a fragmentary sectional illustration on when the other sides are known factors. line 19-19 of FIGURE 18, showing the locking and im Broadly, the invention contemplates the provision of pelling device for the angle scale on the protractor plate. an instrument by which the measurement of any side of a The mechanical structure of the invention is best illus triangle of any type of angulation can be readily deter 50 trated in FIGURES 1, 2, 3, 4, 5 and 19, and comprises, mined when the measurements of the other sides thereof primarily, a protractor plate 10 which is generally semi are known, and such calculations can be made without circular in form, as shown in FIGURE 1, and has an the aid of mathematical formula. If a definite perpendic angular portion 11 which affords a convenient handle. ular can be assumed or established, in many cases the A protractor scale 12 is imprinted on the face 13 of the length of the unknown sides of some triangular figures plate 10 and spaced inwardly from and conforming to can be determined. An obtuse triangle, for example, show the outer semi-circular periphery 14 thereof. An annular ing an established perpendicular line within so as to con boss 15 is formed about the periphery 14 and on the vert the obtuse angle triangle into two right angle triangles rear face 16 of the plate 10, as shown in the fragmentary can be delineated. The same procedure is applied to isos sectional view of FIGURE 2, and has an annular channel celes triangles and equi-angular or equi-lateral triangles, 60 17 therein with an annular slot 18 open to the face 13 simply by separating into two right angle triangles, for comeof the apparent. plate 10 and whose function will presently be making calculations possible with the invention. The face 13 of the plate 10 is divided by vertical and While the foregoing objects are paramount, other and horizontal lines 19 and 20, respectively, defining a pair lesser objects will become manifest as the description 65 of segments 21 and 22, each bearing division markings proceeds, taken in connection with the appended drawings indicating 90 degrees. In alignment with the vertical line wherein: 19 and spaced below the horizontal line 20 is a vertical FIGURE 1 is an elevational view of the invention slot 23 formed in the angular portion 11 of the plate 10, showing the semi-circular protractor scale, and the angle the purpose of which will also become apparent as the scale co-operating therewith, and illustrating a pair of 70 description proceeds. co-acting micrometers on said protractor. Attached to the lowermost point 24 of the angular FIGURE 2 is a fragmentary sectional illustration, on portion 11 of the plate 10 is a micrometer 25, the outer 3,322,340 4. 3 rotated for moving the micrometer 43 along the slot 18 end of the scaled stock 26 of which is embraced by a by a knurled knob 65 on the shaft 59, and for micromatic collar 27 which is secured to the member 24, as indicated adjustment a smaller knurled knob 66 is provided on the in FIGURES 1 and 4, and has an integral bracket 28 outer end of the shaft 59. which supports a vernier dial 29. The stock 26 of the It will be observed, by reference to all of the illustra micrometer 25 has a stem 30 extending axially therefrom 5 tions in which the micrometers 25 and 43 are shown, and the outer end of the stem 30 is milled to form a that the former is always in axial alignment with the shoulder 31 and a head 32, as shown in FIGURE 5, vertical line 19 on the protractor plate 10 and the latter defining spindle 33 for a bearing 34. A fitting 35 is is positioned so that its longitudinal axis is tangential to pressed on the bearing 34 to provide a rotative association the curvature of the protractor scale 12, or at an angle between the stem 30 and the fitting 35 so that the latter O of approximately 30 degrees from the horizontal line 20, is restrained from rotation by a pin 36 thereon extending as shown in FIGURES 8, 9 and 10, and 60 degrees, as through the slot 23 of the plate 10 when the stock 26 of shown in FIGURES 13, 14 and 15, and such angle is the micrometer 25 is extended and retracted in the opera maintained constant regardless of the rotative position of tion thereof.