US3867762A - Drawing instrument - Google Patents

Abstract

This instrument is a drawing instrument for drafting axonometric projection drawings based on a projection drawn by the multiview projection, with which any of projection drawings, either isometric, dimetric or trimetric, may be produced by the operations of rulers.

Description

United States Patent 1191 Hirano 51 Feb. 25, 1975 1 DRAWING INSTRUMENT [76] Inventor: Akira Hirano, 178 Kashira-machi,

i1lla as11tna K mi wr u 2119191 Japan 221 Filed: July 14,1972

21 Appl. No.: 271,646

[30] Foreign Application Priority Data July 14, 1971 Japan 46-52340 July 14, 1971 46-52337 July 14, 1971 46-52338 July 14, 1971 Japan 46-52339 [52] US. Cl. 33/77 [51] Int. Cl ..B43l13/14 [58] Field of Search ..'33/77, 18 C [56] References Cited UNITED STATES PATENTS 2,454,380 11/1948 Goff 33/79 R FOREIGN PATENTS OR APPLICATIONS 1,008,492 5/1957 Germany 33/77 465,199 9/1928 Germany 33/79 R 761,930 11/1950 Germany 33/77 Primary Examiner-Harry N. Haroian Attorney, Agent, or Firm-Armstrong, Nikaido & Wegner [57] ABSTRACT This instrument is a drawing instrument for drafting axonometric projection drawings based on a projection drawn by the multiview projection, with which any of projection drawings, either isometric, dimetric or trimetric, may be produced by the operations of rulers.

3 Claims, 6 Drawing Figures 8/1972 Heinz 33/77 DRAWING INSTRUMENT BACKGROUND OF THE INVENTION The hitherto considered method of drafting a axonometric projection drawing from the multiview projection drawings, consists of the assumption of a cube 1 having two faces X and Y which intersect at a right angle, and are perpendicular to three straight lines, OX, OY and OZ. The faces X, Y and Z are arranged parallel to thefront, plan and side faces of the body, and the multiview projection drawings including the front view A, plan view B, etc., may be drawn with the ridge XO as the ground line by projecting the beam lines on the projecting faces at a right angle respectively. On the other hand, the piramidal part with the apex O of the cube is cut off, and with this cut face XYZ taken as the new projecting face, the axonometric projection drawing C of the central body is drawn by projecting the beam lines on this face at a right angle thereto. According to a geometrical theory, the lines connecting the corresponding points on the front view A or the plan view B with the corresponding points on the axonometric projection drawing criss-cross the ridges XZ, XY of the cut face, which may, therefore, be regarded as the ground lines. Accordingly, as the planes of the front view and the plan view are turned upward, they are centered on the ground lines of the cut face to the same plane as that of the projecting face of the cut face XYZ, and projecting lines are drawn perpendicular to the respective ground lines from each apex (a, b h) of the front view and plan view, thus the intersections reasonably agree withthe corresponding points of the axonometric projection C.

Accordingly, to draw an axonometric projection drawing, usually the ground line XY and X2 which make a certain intersecting angle K are assumed, as shown in FIG. 6; the front view A and the plan view B, are arranged at certain angles (described later) to the ground lines X2 and XY; and a perpendicular m is drawn from the front view A to the ground line XZ, and another perpendicular 1,, from the plan view B, to the ground line XY; then, by plotting the intersections, the axonometric projection is drawn.

In this method, however, the intersecting angle K of the axes X2 and XY of the projecting triangle and the way of arranging the front view A and the plan view B, relative to the ground lines XZ and XY are not fully ascertained. First, the intersecting angle K is determined by the conditions, or six factors, to define the cube having X, Y and Z faces, as shown in FIG. 5; that is, the angles )t, p. and 7 which the beam lines make with respective faces of the cube, and the angles a, B and 7 which the bottom sides of the projected figures on respective faces make with the ground lines XY, X2 and YZ. In the next place, referring to FIG. 5, as the three axes OX, CY and OZ which mutually criss-cross are transferred to the projecting face XYZ, then the three straight lines X, O Y and 0,2 which intersect at a point 0, corresponding to the apex O are respectively perpendicular to their opposing sides, according to the geometrical theory. Accordingly, as the plane XYO is turned, and centered on the axis XY, to align with the projecting face XYZ, the apex 0 moves on the aforementioned perpendicular ZO to the point 0 This operation is reproduced on the projecting face XYZ in FIG. 6. The orthocenter 0 of the triangle XYZ is the projected point of the apex 0. If the intersection between the circle with the side XY as its diameter and the perpendicular ZZ from the apex Z is designated 0 then [XO Y is 0 is, therefore, the point transferred from the former apex O of the cube by the rotary motion. Accordingly, since 0 X corresponds to the ground line OX of the Z face of the cube on the plan view B, of the Z face rotated, the side dc of the plan view B, is arranged in parallel to O X with this 0 X as the ground line. A similar operation is carried out with the Y face, so that the projecting point 0 of I the apex O transferred by rotation with XZ as the axis is determined in the triangle XYZ. Then, as X0 corresponds to the ground line X0, the side ab of the front view A is arranged parallel to the straight line X0 After these arrangements are made, projecting lines I and m are drawn to the ground lines XY and XZ, thereby obtaining the respective intersections. In this way, the axonometric projection intended is obtained.

In the usual'method, the front view A and the plan view B should be separated, arranged around the face of the axonometric projection, and inclined at certain angles. Since in the actual multiview projection, the front view and the plan view B are drawn on one sheet of paper in parallel to each other, many inconveniences are involved in separating and arranging them as described above.

The plan view B was drawn in parallel to the front view A on the common plane of axonometric projection, as shown in FIG. 6. As the projecting line 1 of the former plan view B, was drawn, it was fixed to the figure unmodified, on the basis of the assumption that the plan view B was formed by rotating and transferring, on the same surface of the paper, the aforementioned plan view B arranged with an inclination to the main axis XY. Then, it was discovered that the projecting lines I drawn from the FIG. B intersect the projecting lines 1,, drawn from the FIG. B on the same straight line P, and the projecting lines I and 1,, intersect each other as if they were light beams reflecting from the straight line P as the mirror surface with the angle of incidence and reflection at 0 (the substantiation for this is omitted).

The present invention concerns a drawing instrument capable of making the drawing of axonometric projection by way of ruler operations and manipulations while placing the front view A and the plan view arranged vertically, and taking advantage of the aforementioned principle.

SUMMARY OF THE INVENTION The present invention makes it possible to draft the axonometric projection in such a way that with the front view and the plan view arranged vertically, and the straight line P making a predetermined angle with the ground line and the direction of the projecting lines m from the front view known, the projecting lines I can be drawn out from the plan view B at a given angle to the straight line P; these lines are reflected at the straight line P to form the projecting lines 1 and the corresponding points on the axonometric projection are determined by their intersection with the projecting lines from the front view.

The object of the present invention is to provide a drawing instrument, with which it is possible to draft an axonometric projection from a multiview projection drawn side by side by rotating the rulers arranged and oriented of appropriate angles, and combining these rulers with an angular ruler.

Another object of the present invention is to provide a drawing instrument with the third ruler attached in addition to the vertical and horizontal rulers to facilitate the operation of making the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS:

FIG. 1 illustrates a total plan view of one embodiment'of the invention, showing the device in a drafting operation;

FIGS. 2 and 3 respectively illustrate enlarged plan views of the device as arranged and oriented in other embodiments;

FIG. 4 illustrates a plan view showing another application of the drawing instrument of FIG. 3;

FIG. 5 illustrates a perspective view for demonstrating the principle of the axonometric projection; and,

FIG. 6 illustrates another explanatory diagram of the principle of this invention.

DETAILED DESCRIPTION The drawing instrument which has been well known up to present is utilized in making up the drawing instrument of this invention. The drawing instrument 2 (as shown in FIG. 2) of FIG. 1 is shown with the ruler orienting element 5 of the drawing instrument 2 of FIG. 2 being enlarged. To this element 5, is attached ruler element 5A and the horizontal ruler 3 and the vertical ruler 4 are attached at its tip. It is equipped with the angle changing mechanism 7 with which the horizontal ruler 3 is inclined at an appropriate angle by switching the lever 6, and then, the element 5 is clamped and the parallel transfer mechanism 9 connecting the element 5 to the fixed point 8 through links of parallelograms, with which the horizontal ruler 3 and the vertical ruler 4 are transferred in parallel to themselves as shown by the phantom lines in FIG. 1.

The standard line 10 is marked at the tip of the vertical ruler 4. Its root end is pivotally mounted for rotation on the pivot 11 of the ruler element 5A. It is clamped with a fixing means 12, inclined at a certain angle q to the horizontal ruler 3.

The horizontal ruler 3 is extended from the element 5A, and the auxiliary ruler 13 is attached to it on the same line in a linear fashion. An angular ruler 14 is located at a definite point on the surface of this auxiliary ruler, making a certain angle p to the-ruler surface. This angular ruler 14 may be located so as to rotate along with the auxiliary ruler so that it may be brought down normally and maintained flush with the auxiliary ruler, and thus is used by drawing it out to the angle p and holding it. Alternatively, as shown in the drawing, the same purpose may be served by detachably providing a triangular ruler 15 with one of its base angles p. In this instance, the stopper 16 by which thetriangular ruler 15 is held in place on the horizontal ruler 3 is provided, so that the projecting line may be drawn at the angle of p-from a definite point on the auxiliary ruler 3.

In the following, the drafting procedure is described for this drafting from the front view and plan view of FIG. 1 drawn by the first quarter drawing method:

1. First, after slackening the lever 6 of the drawing instrument 2, the standard line P making a certain angle t with the central line T of the front view A is drawn.

2. With the horizontal ruler 3 put to 12 point of the front view A, the projecting line m is drawn along the auxiliary ruler I3.

3. The ruler face of the vertical ruler 4 is put to h point of the plan view B, and simultaneously, the standard line 10 of the vertical ruler 4 is brought in line with the standard line P. I

4. The vertical ruler 4 is securely held in that position, and the triangular ruler I5 is placed on the auxiliary ruler 13, with one end of the triangular ruler l5 touched on the stopper l6.

5. The projecting line 1,, is drawn at an angle of p along the ruler face of the triangular ruler l5.

6. The intersection b between the projecting line 1,, and the projecting line m is the desired point on the view of axonometric projection. Other points are determined in the same way to draw up the projection draw- Referring to FIG. 6, the projecting angle a agrees with LO1XY, with its actual angle a, given by LO2XY, while the projecting angle ,8 agrees with L OIXY, with its actual angle b given by L O3XZ.

The angle at which the projecting line I from the plan view B is reflected at the standard line P, designated 26, is identical with the angle of rotation of the plan view B to the plan view B.

Assuming that the intersecting angle between the projecting lines I and m is r, and the intersecting angle between the projecting line I and the central line T is s, then r= a and s b as geometrically proven. There exists a relation, 4) a 0, and p agrees with 4ZXY.

In the case of equiangular projection, a 45, b 4 31 4Z Y= Qf b9r 0=. "1 41= s P 60, and q 90. Accordingly, the purpose may be served by use of a triangular ruler 15 with its interior angles 90, 60 and 30.

The drafting of the axonometric projection drawing can be accomplished by the drafting procedure mentioned above. The projection drawing C may be drawn from the front view A and the plan view B drawn by the third quarter drawing method in the same way as in FIG. 3.

The angles p, q and t employed in the drafting performed as described above are preliminarily given as the drafting conditions, that is, conditions defined by the angles k, v and p. that the beam line makes with the X, Y and Z faces of the cube and the angles a, B and y which the axonometrical projection drawing of a solid body'makes with the ground line.

Since in the case of an equiangular projection drawing, the angle q which the vertical ruler 4 makes with the horizontal ruler 3 is a right angle, an ordinary drawing instrument manufactured with both rulers fixed at a right angle may be put to this use.

In FIG. 2, the standard line 17 is drawn at the tip of the vertical ruler 4 at an angle of (b which the standard line P makes with the ruler face, or desirably at 4) 60 which is assigned for the equiangular projection drawing, and the standard line 17 is aligned with the standard line P, while the horizontal ruler 3 is put to the front view, and simultaneously, the projecting line m is drawn, whereby the auxiliary ruler is omitted.

FIG. 3 presents another embodiment of this invention, in which while the vertical ruler 4 is fixed perpendicular to the horizontal ruler 3 as in FIG. 2, the auxiliary ruler 13 is rotatably attached at its root end on the opposite side of the horizontal ruler 3. Angular ruler 14 is slidably located along auxiliary ruler 13 with reference to stopper 20. When the auxiliary ruler l4 and the horizontal ruler 3 are arranged on the same straight line, that is at the orientation angle of this drawing instrument may be used for drafting an equiangular projection drawing. Then, when element 5 is reversed by 180, and the auxiliary ruler is inclined at an angle of 6 as shown in FIG. 4, a reduced drawing from the original one may be produced. That is, when the horizontal line a b of the original drawing D is arranged parallel to the auxiliary ruler l3, and the standard line 18 on the auxiliary ruler 13 is transferred from a to b and from a to d,, the triangular ruler 19 is placed on the horizontal ruler 3, and then, the points corresponding to those on the vertical and horizontal lines are plotted, thereby drafting the reduced drawing E from the FIG. A. This may be proven as follows. Perpendiculars are drawn respectively from points b and a to the straight line D passing through a of the figure D and parallel to the ruler, aand their intersections are designated b and d Then, the horizontal distance a b on the FIG. E corresponding to the horizontal distance a b on the original FIG. D is:

a b a b a b cos 0.

Similarly, the vertical distance a d on the FIG. E corresponding to the vertical distance a d on the original FIG. D is:

z z 11 111 11 d, cos 0 Accordingly, the FIG. E is reduced from the original figure D in dimension for each side by cos 0,. It is also possible to draft the enlarged figure D with the figure E as the original by turning the element 5 by 180.

1 claim:

1. A drawing instrument for use in drafting the anonometric projection drawing from the multiview projection drawing, comprised of the following components;

a. a parallel transferring mechanism with which a ruler orienting and arranging means is transferred parallel to itself and the angle changing mechanism with which the ruler arranging means angle is altered;

b. a horizontal ruler attached to the arranging means of the drawing instrument;

0. a vertical ruler attached to the arranging means of the drawing instrument at a right angle to the horizontal ruler and provided with the standard line extending traversely thereof near the free end and making an angle of inclination of to the ruler edge face, said vertical ruler having a stopper member located thereon near the arranging means;

d. an auxiliary rulerpivotally mounted on an end of said arranging means for independent rotation relative to said vertical and horizontal rulers, the position of said pivotal mounting being at a location'on said arranging means remote from said attachment of said horizontal and vertical rulers such that they extend in substantially opposite directions;

e. an angular ruler arranged to sliding engage said horizontal ruler and said stopper for drawing a line at a certain angle from a definite point on the ruler face and located adjacent to said auxiliary ruler and slidable therealong.

2. A drawing instrument, as defined in claim 1, wherein the angular ruler is a triangular ruler with its base and legs at predetermined angles, and adapted to function with the stopper.

3. A drawing instrument, as defined in claim 2, wherein the triangular ruler has interior angles of 30, 60 and

Claims (3)

1. A drawing instrument for use in drafting the anonometric projection drawing from the multiview projection drawing, comprised of the following components; a. a parallel transferring mechanism with which a ruler orienting and arranging means is transferred parallel to itself and the angle changing mechanism with which the ruler arranging means angle is altered; b. a horizontal ruler attached to the arranging means of the drawing instrument; c. a vertical ruler attached to the arranging means of the drawing instrument at a right angle to the horizontal ruler and provided with the standard line extending traversely thereof near the free end and making an angle of inclination of 75* to the ruler edge face, said vertical ruler having a stopper member located thereon near the arranging means; d. an auxiliary ruler pivotally mounted on an end of said arranging means for independent rotation relative to said vertical and horizontal rulers, the position of said pivotal mounting being at a location on said arranging means remote from said attachment of said horizontal and vertical rulers such that they extend in substantially opposite directions; e. an angular ruler arranged to sliding engage said horizontal ruler and said stopper for drawing a line at a certain angle from a definite point on the ruler face and located adjacent to said auxiliary ruler and slidable therealong.

2. A drawing instrument, as defined in claim 1, wherein the angular ruler is a triangular ruler with its base and legs at predetermined angles, and adapted to function with the stopper.

3. A drawing instrument, as defined in claim 2, wherein the triangular ruler has interior angles of 30*, 60* and 90*.

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