PROTRACTOR FOR THE MEASURING OF SOLID ANGLES TO BE USED WITH ELLIPSE DRAWING PATTERN SETS

Abstract: In order to be able to define two out of the axonometric axial directions, the protractor for measuring solid angles, serving for the determination of the interrelating values of the orthogonal axonometry characteristics, i.e. angular subtenses of the ellipse and the angles of inclination of the axonometry axes, to be drawn with the ellipse drawing pattern with changing angular subtenses, is provided with two pointers of a length surpassing the diameter of the semi-circle, being fixed rotatably in the end points of said diameter, while the third axonometric axial direction is always perpendicular to the diameter of the semi-circle. Along the periphery of the semi-circle there are two angular scales increasing in opposite directions. Said scales are plotted from the centres of rotation in the endpoints of the diameter of the semi-circle as midpoints. The plate is containing a nomogram with three sets of curves for the determination of the angular subtenses of the ellipses indicating the limits of the range of interpretation. The optimum points belonging to each single area defined by the three sets of curves and defining the optimal intersecting axes are marked on the plate. On the semi-circle of the plane there is a plain protractor scale and in the centre of the semi-circle there is a longshaped groove running perpendicularly to the diameter.

Description: Protractor for the measuring of solid angles to be used with ellipse drawing pattern sets Technical field The invention relates to a protractor for the measuring ' of solid angles to be used with ellipse drawing pattern sets, with a parallel chart /nomogram/ arranged on a transparent plate, provided with rotatable pointers for the determination of the orthogonal axonometry charac¬ teristics i. e. of the interrelated values ' of the " angular subtenses of the ellipse and of the angle of inclinat¬ ion of the axonometry axes. In practice, for drawing the circular projections of axonometric and practical perspectives of general position ellipse drawing pattern sets with a graduation- of 5o of th'e angular subtense have been mainly used. In order to be able to perform accurate designing and to enable the suitably quick utilization of the ellipse drawing pattern sets, the following two tasks are of fundamental importance: a/ to choose the drawing patterns corresponding to the required layout from the set staying at our disposal, in the knov/ledge of the inter- secting axes; b/ in case of previously chosen drawing patterns to determine accurately the intersecting axes. It may happen, that the two tasks are to be combined, i. e. the optimal intersecting axes are to be determined for a given position of the intersecting axes. Let us- define the two fundamental tasks in a geo- i metrical sense: a/ in the knov/ledge of the angles enclosed by the datum lines the values of the circular projections of the co-ordinate planes having ' been rounded off for the angular subtenses of the drawing pattern are to be determined, b/ to determine the angles enclosed by the axes of the optimal intersecting axes for known drawing patterns. Background art - For fulfilling both the fundamental tasks complicated trigonometric equations are to be solved. Taking the lenghtiness of said calculations into consideration, in practice tables have been generally used for the determinat ion of the interrelated values. The so-called measuring discs having been used or said purpose are also known. Due to the restricted capacity, limited, reading and surveying possibilities, respectively, of the known solutions the angles of inclination of the axes — similarly to the a f lar subtenses of the drawing patterns — are graduated by 5°, accordingly, only a narrow range o the interrelated values of the angular subtenses of the drawing patterns and the angles of inclination of the axes is contained. As a consequence, presently the choice of the drawing patterns can be ' performed only by means of inaccurate and approximating methods, however, optimum search cannot be performed at all. Disclosure of Invention The main object of the invention is to provide a measur¬ ing device for the simultaneous use with ellipse drawing pattern sets, by means of which the two previously described fundamental tasks can be performed in a simple, O ' - - 5 - quick and accurate manner, furthe on, the conversion of the intersecting axes of a given position into the so-called optimal intersecting axes becomes possible, and in addition to these the tasks set can be solved utmost quickly and with a highgrade security, without performing complicated calculations and using tables. Accordingly, in the sense of the cardinal idea of the invention we are starting from a nomo ram v/ith three sets of curves, where the three sets of curves are defining the angular subtenses of the ellipse. The three sets of curves defining the subtenses of the ellipses and indicating the limits of interpretation ranges there¬ of, are applied ' onto a transparent plate, within a semi¬ circular area. In the end points of the diameter of the semicircle a pointer each with a length surpassing the diameter of the semicircle have been fixed in a rotatable manner, whereas along the periphery of the semicircle two angular scales increasing in opposite directions have been arranged, which are plotted from the end points of the diameter of the semicircles as centres. The so- called optimum points defining the optimal intersecting axes and belonging to each single area being confined by the curves of the three sets of curves are marked on the plate. In such a manner, by the proper setting of the pointers two of the axonometric axial directions can be defined in seconds. In accordance with the invention, on the transparent plate of the protractor for measuring of solid angles serving for the determination of the orthogonal axono- etry characteristics, — the angular subtenses of the ellipses and the angles of inclination of the axonometry axes — and thereby for facilitating the use of the ellipse drawing pattern sets, in order to be able to determine two of the axonometric axial directions, two pointers with a length surpassing the diameter of the semicircle are arranged in a r ' otatable manner in the end points of the diameter of the semicircle, while the straight line lying perpendicularly to -the diameter of the semicircle is always representing the third axial direction; in addition to this, along the periphery of the semicircle there are two angular scales increasing in opposite directions, having been plotted from the end points of the diameter of the semicircle 'as centres; at least, the three sets of curves of the nomogram defining the angular subtenses of the ellipse ' and delimiting the interpretation range thereof are arranged on the area of the semicircle, furtheron, the so-called optimum points defining the optimal intersecting axes and belonging to each single area being confined by the curves of the set of curves are marked on the plate. At a preferred embodiment of the protractor for measur¬ ing of solid angles the angular scales on the periphery of the semicircle are marked at each grade in the range between 0° and 90°, while the zone confining sets of curves of the angular subtenses of the ellipse are angular values within the range between 10° and 80°, v/ith a 5° graduation in compliance with the usual graduat ion of the angular subtense of the ellipse drawing patter sets, as a consequence, on the measuring device angular subtense zones with a graduation of 5 are formed. At an other preferred embodiment of the invention a plain protractor with a graduation of 1 is also arranged, the centre of v/hich being identical v/ith the centre of the semicircle. The embodiment is also to be considered as advantageous, at v/hich in the centre of the semicircle, in the directio C.'.'.PI normal to the diameter, on the side lying opposite to the calibrated semicircle, a markin groove, pre¬ ferably of a longitudinal shape, is formed. The main advantages resulting from the developed charac- ter and the shape of the protractor for measuring the ■ solid angle in accordance with the invention, are as follows: - the quick determination of the angular subtenses of the drawing pattern belonging to the intersecting axes of optional position; - determination of the most advantageous position of the intersecting axes for preselected design patterns; . - conversion of intersecting axes of a given position into optimal intersecting axes; - • accuracy of designing to be performed by means of the ellipse drawing pattern can be well estimated in advance; - - accurate measuring results may be obtained instead of the approximating values; - direct angular measurement becomes possible, accordingly, the use of a separate protractor becomes superfluous; - the dimensions of the device for measuring of solid angles are favourable, production is relatively simple, accordingly, it is not expensive, Brief Description of Drawings The invention will be described in detail by means of a preferable embodiment by the aid of the accompanying drawings, v/herein figure 1 is showing the plan view of the protractor f°r measuring of solid angles v/ith a part of the set of curves, figure 2 is showing the sectional side-view of the " device according to the invention as illustrated in figure 1, in the enviroment of the centres of rotation A and B, figures 5 to 5 are showing schematically the single steps of the deteimination of the angular subtenses of the drawing pattern, if the intersecting ' axes are kncwn, . figure 6 is showing the spatial arrangement of the ellipsesalong the axes k, 1 and with the angular- subtenses X , A and^ having been determined .by means of the protractor for measuring of solid angles, figures 7 to 9 are showing schematically the single steps of.the determination of the optimal inter¬ secting axes of axonometry in case of given angular subtenses, figure 10 is showing the ellipses with the given aagula subtenses " , A and _μ- along the axes k + , l 0 p aaά m opt. , Best Mode of Carrying out the Invention With reference to figures 1 and 2, the protractor for measuring of solid angles consists of the semicircular transparent plate 1 having been shaped with rounded corners. On the plate 1, in the end points of the dia- • meter of the semicircle the pointers 2, 3 are fixed - preferably by riveting - rotatably around the centres of rotations A and B, lying in a distance "a", in such a manner, that they should not interfere with each other v/hile rotating. The pointers 2, 3 are made of . a flat transparent material and their lengths surpasses the length of the diameter of said semicircle. The pointer 2 represents the axoncmctry-axis "k", while the pointer 3 represents the axonometry axis "m", by aβanβ of the • measuring hairline theoretically intersecting the centres of rotation A and B, respectively. Alon the periphery two angular scales 8 are to be found increasing - in opposite directions. These have been 'plotted in such a manner, that alternately now the angles of rotation of the pointer 3 around the fulcrum A, now the angle of rotation of the pointer 2 around the fulcrum B were plotted onto the periphery of the semi- circle. The semicircular periphery of the plate.1 was marked with the usual scale 9 of a plain protractor. ' The basic diameter "a of the circular arch was also plotted, while in the centre a long-shaped marking groove 10 lying perpendicularly to said basic diameter was formed, In the middle of the semicircular arch there is a long- shaped radial marking groove 11 to be found. The area of the semicircle contains the confining curves 4 of the- angular subtensesX - having been indicated with a dashed line -, the confining curves.5 of the angular subtenses A - indicated with a continuous line - and the confining curves 6 of the angular subtensesis. - indicated with a dotted line in the figurei The cαifi ing curves 4 and 6 of the angular subtenses of the axonometry axes defined by the pointers 2 and • 3, respectively, marked with "k" and "m" are formed by semicircles, and the magnitude of the radii of the semicircle corresponds to the second power of the cosines of the angular subtenses * X and J t respectively, while their centres are lying on the straight line interconnect- ing the centres of rotation /fulcrum/ B and A of the pointers 2, 3. One of the end points of the semicircles is always lying in the belonging centre of rotation A or B. The set of curves confining the aone of angular subtenses. of he drawing pattern of the shortened axonometry axis indicated with "1" and represented by the normal dropped to the midpoint of the line AB consists of semiellipses with a changing angular subtense A , and the end points o .the major axis of said ellipse are simultaneously forming the centres of rotation A and B. On the plate 1 the so-called optimum points 7 are also indicated. Said points are " yielding the most advantageous optimal position of the intersecting axeβ of all the thre interrelated angular subtenses, ' i. e. the optimum points " are " forming the centres of the polygons defined by the sets of curves 4, 5 and 6. The single steps of the application of the protractor for measuring of solid angles in accordance with the invention may be well followed in figures 3 to 5, supposed, that in the ' knowledge of the intersecting axes the determination of the angular subtenses of the drawing pattern is wanted. As a first step we are determining the angular values ϋ( and h of the plotted axonometry intersecting axes in such a manner, that the origin 0. of the protractor for measuring of solid angles is fitted onto the midpoint of the intersecting axes and the angular values d and 9> are read on the scale of the plain protractor /see figure 3/. As a second step the angular values <X and β> having been determined and read off in the previously described manner are to be set on the angular scale 8 by means of the measuring hairlines of the pointers 2, 3. In this case the hairlines of the pointers 2, 3 are defining the point of intersection P /see figure 4/. The third step: the angular subtense values * X , aud it- OIV. belonging to the point of intersection P correspond to the values having been marked in the angular subtense zones defined by the set of curves 4, 5 and 6. In case, if the poin of intersection P lied on the curve/s/ confining the zones, the measuring results ' correspond to the values of the zones of the angular. subtenses of the optimum point 7 lying nearest to the intersection point P /see " figure 5/. . The ellipses with the angular subtenses " X , and i- having been obtained as a result of the measuring process, are spatially illustrated in figure 6 and are "stringed" onto the predetermined axonometry axes k, 1 and m, respectively. I case, if we wish to determine the optimal intersect- . ing axes of axono-oetry from the given angular subtense, we act, as follows: In the first step we are searching for the optimum point ' belonging to the given angular subtenses X., Λa ^ by means of the set of curves of the plane 1, which will simultaneously represent the point of intersection P of the pointers 2 and 3 /see figure 7/. In course of the second step the hairline of the pointers 2, 3 are superimposed in the point of section P by rotation. By means of the pointer 2 the angular value &. , by means of the pointer 3 the angular value can be read on the angular scale 8 /see figure 8/. In course of the third step, on the plain protractor 9 we determine the angle of inclination C of the axonometry axis "k", i. e. the. angle of inclination & of the axonometry axis "m" for the axonometry axis "1" having been marked by the aid of the marking grooves 10, 11. In such a manner the optical intersecting axes can be easily drawn /see figure 9/. The intersecting axes k . , 1 QΏ + and m , plotted for the angular subtenses * , j^ and a, in the previously described manner with ellipses thereon are illustrated spatially in figure 10. The conversion of the intersecting axes of an optional .position into optimal intersecting axes may be also " performed by the aid of the protractor for measuring the solid angle according to the invention. First of ■ all, the values of the angular subtenses of the drav/ing pattern for the intersecting axes are to be determined, hereafter, by using the optimum points, the most advan¬ tageous, i. e. optimal position of the intersecting axes may be determined in accordance v/ith the figures 7 to 9 * The aim of the protractor for measuring the solid angle in accordance with the invention has been to facilitate the use of the ellipse drawing pattern sets. These type of ellipse -drawing pattern sets are produced by every • firm of world-wide reputation trading in this line, while the majority of th technical illustrators, designers and mechanical designers permanently use said drawing pattern sets. The protractor for measuring of solid angles according to the invention yields new possibilities for the utilization with an increased efficiency, it may be the centre of interest not only for the technicians working with drav/ing pattern, sets, but also for those, who are buying a set for the first time. In practice it may represent an indispensable instrument of labour, since - as it becomes obvious from the aforesaid - handling • is absolutely easy, rate of v/ork can be considerably accelerated, simultaneously yielding highly accurate results. It should be mentioned that the accumulated value of the protractor for measuring of the solid angles is far greater than that of the measuring devices and tables of values having been ur.od up to now. / ^J : EA * OMPI

Claims: Claims: 1. Protractor for measuring of solid angles, to be used with ellipse drawing pattern sets, with a parallel.chart arranged on a transparent plate, provided ' v/ith rotatable pointers for the determination of the orthogonal axonometry characteristics, i. e. of the interrelated values of the angular subtenses of the ellipse and the angles of inclination of the axonometry axes, c h a r a c t e r i z e d in that a semicircle is plotted onto the transparent plate /I/, the pointers /2, 3/ of the length surpassing- the diameter of the semi¬ circle are fixed rotatably around the centres of rotation /A, B/ in the end points of the diameter /a/ of the semi¬ circle, along the periphery of the semicircle there are two angular scales /8/ increasing in opposite directions having been ' plotted from the centres of rotation /A, B/ as midpoints, furtheron the area of the semicircle contains the sets of curves /4, 5, 6/ of the nomogram defining the angular subtenses / ~-< , , A, / of the ellipse in the single zones, at least the optimum points /7/ belonging to each single are confined by the three sets of curves /4, 5, 6/ and defining the optimal intersecting axes are marked in the plate /l/. 2. Protractor for measuring of solid angles as claimed in claim 1, c h a r a c t e r i z e d in that the angular scales /8/ having been plotted on the periphery of the semicircle are marked v/ith a graduation of 1° within the range between 0° and 90°, v/hile the set of curves /4, 5, 6/ confining the angular subtenses of the ellipse are graduated by 5° in the range of the angular values betv/een 10° and 80°. 3. Protractor for measuring solid angles as claimed in claim 1 or 2, c h a r a c t e r i z e d in that the rotatable pointers /I, 2/ arc made of a transparent flat material and are provided v/ith hairlines theoretically intersecting the centres of rotation /A, B/. 4. Protractor for measuring of solid angles as claimed in claims 1 to 3, c h a r a c t e r i z e d in that it is provided with a plain protractor scale /9/ with a graduation of 1°, having the same centre as the . semicircle. 5. Protractor for measuring of solid angles as claimed in any of the claims 1 to 4, c h a r a c ¬ t e r i z e d , in that in the centre of the semicircle, on the side lying opposite to the scaled semicircular arch, there is a long-shaped marking groove /10/ running perpendicularly to the diameter.

Inventors: NAGY B
Applicants: NAGY B, NOVEX FOREIGN TRADE CO LTD
Application year: 1981
Main classification: B43L11
IPC codes: B43L11