Building axonometric projections

5.5.1. General. Orthogonal projections of the object give a complete picture of its form and sizes. However, the apparent disadvantage of such images is their small clarity - the shape is composed of several images performed on different planes of projections. Only as a result of the experience develops the ability to imagine the form of the object - "read the drawings".

Difficulties in reading images in orthogonal projections led to the occurrence of another method, which was to combine the simplicity and accuracy of orthogonal projections with the visibility of the image - the method of axonometric projections.

Axonometric projectionthey call a visual image obtained as a result of parallel projection of the subject together with the axes of rectangular coordinates, to which it is attributed to the space on any plane.

The rules for performing axonometric projections are established GOST 2.317-69.

Axonometry (from the Greek Axon - axis, Metreo - measure) - the construction process based on the reproduction of the size of the subject in the directions of its three axes - lengths, widths, heights. As a result, a volume image is obtained, perceived as a tangible thing (Fig. 56b), unlike several flat images that do not give a shape of the subject (Fig. 56a).

Fig. 56. Visual image of axonometry

IN practical work Axonometric images are used for different purposes, therefore, various types were created. Common for all types of axonometry is that the basis of the image of any subject is accepted by this or that location of the axes OX, OY, OZ, in the direction of which determines the size of the subject - length, width, height.

Depending on the direction of the projection rays in relation to the picture plane, the axonometric projections are divided into:

but) rectangular- Projecting rays perpendicular to the art plane (Fig. 57a);

b) kosholny- Projecting rays are tilted to the picture plane (Fig. 57b).

Fig. 57. Rectangular and rowing axonometry

Depending on the position of the subject and axes of the coordinates relative to the planes of projections, as well as, depending on the direction of projection, the measurement unit is projected in the general case with distortion. The dimensions of projected items are distorted.

The ratio of the length of the axonometric unit to its true magnitude is called coefficientdistortion for this axis.

Axonometric projections are called: isometricif the distortion coefficients on all axes are equal ( x \u003d y \u003d z); dimectricif the distortion coefficients are equal to two axes ( x \u003d Z.);trimetric If the distortion coefficients are different.

For axonometric images of items, there are five types of axonometric projections set by GOST 2.317 - 69:

rectangular – isometricand dimectric;

kosholny– frontal dimectric, frontal isometric, horizontal isometric.

Having orthogonal projections of any subject, you can build its axonometric image.

Always need to choose from all kinds best view This image is the one that provides good visibility and simplicity of constructing axonometry.

5.5.2. General procedure for constructing. The general procedure for constructing any type of axonometry comes down to the following:

a) choose the axes of the coordinates on the orthogonal projection of the part;

b) build these axes in aksonometric projection;

c) build axonometry of the full image of the subject, and then its elements;

d) cause contours of the section of the part and remove the image of the clipped part;

e) dreamed of the remaining part and affix the dimensions.

5.5.3. Rectangular isometric projection. This type of axonometric projection is widespread due to the good visibility of images and simplicity of constructions. In rectangular isometric axonometric axes OX, OY, OZ Located at angles 120 0 one to the other. Axis Oz. Vertical. Axis OX. and Oy. It is convenient to build, laying out the corners of 30 0 using the coal from the horizontal. The position of the axes can also be determined by postponing from the beginning of the coordinates in both directions of five arbitrary equal units. Through fifth divisions, vertical lines are carried out and lay the same units on them. The actual distortion coefficients over the axes are 0.82. To simplify the construction, a given coefficient is applied equal to 1. In this case, when building axonometric images of measuring objects, parallel to the directions of axonometric axes, lay off without abbreviations. The location of the axonometric axes and the construction of the cube rectangular isometric, in the visible face of which the circles are inscribed, are shown in Fig. 58, a, b.

Fig. 58. Location of rectangular isometry axes

The circle inscribed in the rectangular isometry of squares - three visible graves of the cube, are ellipses. The large axis of the ellipse is equal to 1.22 D., and small - 0.71 D.where D.- diameter of the image of the circle. The large axes of ellipses are perpendicular to the corresponding axonometric axes, and small axes coincide with these axes and with a direction perpendicular to the plane of the cube face (in Fig. 58b - thickened strokes).

When building rectangular axonometry of circles lying in coordinate or parallel planes are guided by the rule: the large axis of the ellipse is perpendicular to the coordinate axis, which is absent in the circumference plane.

Knowing the size of the axes of the ellipse and the projection of diameters parallel to the coordinate axes, it is possible to build an ellipse on all points, connecting them with a pantal.

The construction of the oval in the four points - the ends of the conjugate diameters of the ellipse located on the axonometric axes are shown in Fig. 59.

Fig. 59. Building ovala

Through the point ABOUT The intersections of the conjugate diameters of the ellipse are carried out horizontal and vertical straight lines and describe the circumference with a radius equal to half of the conjugate diameters AB \u003d SD. This circle will cross the vertical line at the points. 1 and 2 (centers of two arcs). From the point 1, 2 conduct arc circles with radius R \u003d 2-A (2-D)or R \u003d 1-C (1-B). Radius OE Do serfs on a horizontal direct and get two more centers of mating arcs 3 and 4 . Next join centers 1 and 2 With centers 3 and 4 lines that in the intersection with arcs radius R. Give points of conjugation K, N, P, M.Extreme arcs are conducted from the centers 3 and 4 radius R 1 \u003d 3rd (4-n).

The construction of a rectangular isometric detail given by its projections is made in the following order (Fig. 60, 61).

1. Choose axis coordinates X, Y, Z on orthogonal projections.

2. Build axonometric axes in isometry.

3. Build the base of the part - parallelepiped. To do this, from the beginning of the coordinates along the axis H. Put segments OA and OV, respectively, equal to segments O 1 A 1 and O 1 in 1taken from horizontal projection details and get points BUT and INThrough which spend straight, parallel axes Y., and laid segments equal to half of the width of the parallelepiped.

Get points C, D, J, Vwhich are isometric projections of the lower rectangle vertices, and connect them with straight, parallel axis H.. From the beginning of the coordinates ABOUT along the axis Z. Decoration cut Oo 1.equal to the height of the parallelepiped O 2 O 2'; Through the point O 1. Conduct axes X 1, y 1 And build an isometry of the upper rectangle. The vertices of rectangles are connected by straight, parallel axis Z..

4. Build axonometry of the cylinder. Along the axis Z. from O 1. Decoration cut O 1 O 2, Equal cut O 2 'О 2'. cylinder height, and through the point O 2. Conduct axes X 2,Y 2.. The upper and lower base of the cylinder are circles located in horizontal planes. X 1 O 1 y 1 and X 2 O 2 y 2; Build their axonometric images - ellipses. Essaying forming cylinders spend on both ellipses (parallel to the axis Z.). The construction of ellipses for the cylindrical opening is performed similarly.

5. Build an isometric image of the ribbon rib. From the point O 1. along the axis X 1 Decoration cut O 1 E \u003d O 1 E 1. Through the point E. spend a straight parallel axis Y.and put off in both directions segments equal to half the width of the rib E 1 to 1 and E 1 F 1. From the points obtained K, E, F parallel to axis X 1 spend direct to meet with ellipse (points P, N, M). Next, spend straight, parallel axis Z. (line intersection of the rib planes with the surface of the cylinder), and segments are laid on them RT, MQ. and NS.equal to cuts P 2 T 2, M 2 Q 2, I. N 2 S 2. Points Q, S, T Connect and drive around the lecture K, T. and F, Q. Connect straight.

6. Build cutout parts specified detailFor which two secant planes are carried out: one through the axis Z. and H., and the other - through the axis Z. and Y..

The first securing plane will reduce the lower rectangle of parallelepiped on the axis H. (section OA), top - on the axis X 1and rib - along the lines En and Es, cylinders - by forming, top base of the cylinder - along the axis X 2.

Similarly, the second securing plane will reduce the upper and lower rectangles on the axes Y. and Y 1., and cylinders - by forming, top base of the cylinder - along the axis Y 2..

Flat figures obtained from the section are shaded. To determine the direction of the hatching, it is necessary to postpone equal segments from the origin of the coordinates, and then the ends are connected.

Fig. 60. Building three projections Details

Fig. 61. Performance of rectangular isometric details

Shell lines for cross section located in the plane Xoz., will be parallel to the segment 1-2 , and for the section lying in the plane Zoy.- parallel to the segment 2-3 . Delete all invisible lines and drive out the contour lines. Isometric projection is used in cases where it is necessary to construct circles in two or three planes parallel to the coordinate axes.

5.5.4. Rectangular dimectric projection. Axonometric images built by rectangular dimetry have the best visibility, but the construction of images is more complicated than in isometric. The location of the axonometric axes in dimethics the following: axis Oz. directed vertically, and axis Oh. and Oy. Make up with a horizontal line conducted through the origin of the coordinates (point ABOUT), angles, respectively, 7º10' and 41º25'. The position of the axes can also be determined by postponing from the beginning of the coordinates in both directions of eight equal segments; Through the eighth divisions, one segment is deposited on the left vertical, and on the right - seven sections on the right. Connecting the obtained points with the start of coordinates, determine the direction of the axes OHand OU (Fig. 62).

Fig. 62. Location of axes in rectangular dimetry

Distortion coefficients on the axes OH, Oz. equal to 0.94, and along the axis OY.- 0.47. To simplify in practice, enjoy the distortion coefficients: on the axes OX. and Oz. The coefficient is 1, along the axis OY.– 0,5.

The construction of a rectangular dymetry of a cube with circles, inscribed in three visible, its face is shown in Fig. 62b. The circle inscribed in the face is the ellipses of two types. The axis of the ellipse, located in the face, which is parallel coordinate plane Xoz., equal: Large axis - 1.06 D.; Small - 0.94 D.where D.- Diameter of the circle, inscribed on the edge of the cube. In two other ellipses, large axis are equal to 1.06 D., and small - 0.35 D..

To simplify construction, it is possible to replace the ellipses of ovals. In fig. 63 Receptions of the construction of four centered ovals that replace the ellipses are given. Oval in the front edge of the cube (rhombus) is constructed as follows. From the middle of each side of the rhombus (Fig. 63a), perpendicular to the intersection with diagonals is carried out. Points received 1-2-3-4 will be centers of mating arcs. Dougteings of the arcs are in the middle of the sides of the rhombus. Building can be performed in another way. From the middle of the vertical sides (points N. and M.) Conduct horizontal straight lines before crossing the diagonals of the rhombus. The intersection points will be the desired centers. From the centers 4 and 2 Conduct arc radius R.and from the centers 3 and 1 - Radius R 1.

Fig. 63. Building a circle in a rectangular dimetry

Oval, replacing two other ellipses, are performed as follows (Fig. 63b). Straight LP. and MN.conducted through the mid-opposite sides of the parallelogram intersect at the point S.. Through the point S. Conduct horizontal and vertical lines. Straight LN.connecting the middle of the adjacent sides of the parallelogram, divide in half, and through its middle they are carried out perpendicular before crossing it with the vertical line at the point 1 .

on the vertical straight line lay the segment S-2 \u003d S-1. Little 2-M. and 1-N. crossed horizontal straight at points 3 and 4 . Points received 1 , 2, 3 and 4 There are centers oval. Straight 1-3 and 2-4 Determine the point of conjugation T. and Q..

from the centers 1 and 2 Describe arches of circles TLN. and QPM.and from the centers 3 and 4 - Dougie. Mt. and NQ.. The principle of constructing a rectangular dimension of the part (Fig. 64) is similar to the principle of constructing a rectangular isometric shown in Fig. 61.

Choosing one or another view of a rectangular axonometric projection, it should be borne in mind that in a rectangular isometric, the rotation of the side of the subject is the same and therefore the image is sometimes not visual. In addition, often diagonal in terms of the edge of the object in the image merge into one line (Fig. 65b). These disadvantages are absent on images performed in a rectangular dimension (Fig. 65B).

Fig. 64. Building part in a rectangular dimetry

Fig. 65. Comparison different species Axonometry

5.5.5. Kosomgol Frontal isometric projection.

Axonometric axes are located as follows. Axis Oz. - vertical, axis OH- horizontal, axis OU relatively horizontal direct is located above an angle of 45 0 (30 0, 60 0) (Fig. 66a). On all axes, the sizes are postponed without abbreviations in a true magnitude. In fig. 66b shows the front isometry of the cube.

Fig. 66. Construction of the Kosholnaya Frontal Isometric

Circles located in planes parallel to the frontal plane are depicted in a large value. The circles located in planes parallel to horizontal and profile planes are depicted in the form of ellipses.

Fig. 67. Detail in Kosholnaya Frontal Isometric

The direction of the axes of ellipses coincides with the diagonals of the edges of the Cuba. For planes Hoy and ZoY. The magnitude of the large axis is 1.3 D., and small - 0.54 D. (D.- circle diameter).

An example of frontal isometric part is shown in Fig. 67.

Consider rice. 92. It is given a frontal dimeric projection of the cube with the circles inscribed in its face.

Circles located on planes perpendicular to the x and z axes are depicted by ellipses. The front edge of the cube, perpendicular to the axis y, is projected without distortion, and the circle located on it is depicted without distortion, i.e. is described by a circulation. Therefore, the front dimethrical projection is convenient for the image of objects with curvilinear outlines, the sub-windows shown in Fig. 93.

Construction of a frontal dimectric projection flat details with a cylindrical hole. Frontal dimethrical projection of a flat part with a cylindrical hole is performed as follows.

1. Build the outline of the front edge of the part, using the circulation (Fig. 94, a).

2. Through the centers of the circle and arc parallel to the axis, they spend direct, on which half of the thickness of the part are laying. Receive centers of circles and arcs located on the back surface of the part (Fig. 94, b). From these centers, circle and arc are carried out, the radii of which should be equal to the radius of the circle and the arc of the front face.

3. Conductance to arcs. Remove the extra lines and drive the visible circuit (Fig. 94, B).

Isometric projections of circles. The square in isometric projection is projected into the rhombus. Circles inscribed in squares, for example, located on the edges of the cube (Fig. 95), are depicted in an isometric projection by ellipses. In practice, the ellipses are replaced by ovals, which are drawn by four arcs of circles.

Building an oval inscribed in rhombus.

1. Construct a rhombus with a party equal to the diameter of the circle depicted (Fig. 96, a). To do this, through the point o, the isometric axes x and y and on them on the point o, segments are laid out of the radius of the image of the circle. Through points A, W, C and D spend straight parallel to the axes; Get rhombus. The big axis of the oval is located on a large diagonal of rhombus.

2. Enjoy the rhombus. To do this, from the tops of blunt angles (points A and B) describe arcs with a radius R, equal to the distance from the top of the stupid angle (points A and B) to the points A, B or C, D, respectively. Through points B and A, B and B spend straight (Fig. 96, b); The intersection of these straight lines with a larger diagonal of rhombus gives points C and D, which will be small arc centers; Radius R 1 small arc is equal to CA (DB). The arcs of this radius mate large arches oval. So build oval, lying in the plane perpendicular to the z axis (oval 1 in Fig. 95). Ovals located in planes perpendicular to the x axes (oval 3) and y (oval 2) are built in the same way as oval 1., only the construction of oval 3 leads on the axes of y and z (Fig. 97, a), and ovala 2 (see Fig. 95) - on the X and Z axes (Fig. 97, b).

Construction of an isometric projection of part with a cylindrical hole.

How to apply the considered construction buildings?

An isometric projection of the part is given (Fig. 98, a). It is necessary to portray a through cylindrical hole drilled perpendicular to the front face.

Construction performs as follows.

1. Find the position of the center of the hole on the front edge of the part. Through the found center, isometric axes are carried out. (To determine their direction, it is convenient to use the image of the cube in Fig. 95.) On the axes from the center there are segments equal to the radius of the image of the circle (Fig. 98, a).

2. Build a rhombus, the side of which is equal to the diameter of the image depicted; Conduct a large diagonal of rhombus (Fig. 98, b).

3. describe large arcs oval; Find centers for small arcs (Fig. 98, c).

4. Conduct small arcs (Fig. 98, d).

5. Build the same oval on the back edge of the part and conduct tangents to both ovals (Fig. 98, e).

Answer the questions

1. What figures are depicted in the frontal dim-tricary projection of the circle located on planes perpendicular to the axes x and y?

2. Is the circumference distorted in the front dimeric projection if its plane is perpendicular to the axis of the axis?

3. As an image of what parts is conveniently used by the front dimeric projection?

4. What figures are the circumference of the circumference, located on the planes perpendicular to the x, y, z?

5. What figures in practice are replaced by ellipses depicting circles in isometric projection?

6. What elements is the oval?

7. What is equal to the diameters of the circles depicted by ovals included in the rhombus in Fig. 95, if the parties of these rhombuses are 40 mm?

Tasks to § 13 and 14

Exercise 42.

In fig. 99 Axis were carried out to build three rhombuses depicting squares in an isometric projection. Consider rice. 95 And record, on what edge of the cube - the upper, right side or left side will be located each rhombus, built on the axes, data in Fig. 99. Which axis (x, y or z) will be perpendicular to the plane of each rhombus?

Building axonometric projections begin with axonometric axes.

Position of the axes. The axes of the front di metric projection are located, as shown in Fig. 85, a: axis X - horizontally, the z axis is vertically, the axis y is at an angle of 45 ° to the horizontal line.

The angle of 45 ° can be constructed using an drawing kit with angle 45, 45 and 90 °, as shown in Fig. 85, b.

The position of the axes of isometric projection is shown in Fig. 85, the city of the axis x and y are at an angle of 30 ° to the horizontal line (an angle of 120 ° between the axes). The construction of the axes is conveniently carried out with the help of a kit with angle 30, 60 and 90 ° (Fig. 85, e).

To construct an isometric projection axis with a circulation, it is necessary to carry out an axis Z, describe from an arc point of an arbitrary radius; without changing the circular solution, from the point of intersection of the arc and the z axis, to make serifs on the arc, connect the points obtained with the point O.

When constructing a frontal dimectric projection along the X and Z axes (and in parallel), actual dimensions are laid out; According to the axis (and in parallel), the sizes are reduced by 2 times, from here and the name "dimethium", which in Greeting means "Double Measure".

When building an isometric projection along the x, y, z axes, and in parallel, the actual sizes of the subject, hence the name "isometry", which in Greetly means "equal measurements" is delayed.

In fig. 85, in and e shown the construction of axonometric axes on paper rated into the cage. In this case, to obtain an angle of 45 °, they are diagonal in square cells (Fig. 85, B). The tilt of the axis is 30 ° (Fig. 85, g) is obtained by the ratio of lengths of segments 3: 5 (3 and 5 cells).

Construction of frontal dimectric and isometric projections. Construct frontal dimethric and isometric projections of the part, three species of which are shown in Fig. 86.

The procedure for building projections Next (Fig. 87):

1. Conduct axes. Built the front edge of the part, laying the real values \u200b\u200bof the height - along the z axis, lengths along the x axis (Fig. 87, a).

2. From the vertices of the resulting figure parallel to the axis V, ribs are carried out. Details thickness are laid along: for frontal di metric projection - abbreviated 2 times; For isometric - valid (Fig. 87, b).

3. Through the points obtained, direct, parallel to the edges of the front face (Fig. 87, B).

4. Remove unnecessary lines, apply the visible contour and cause dimensions (Fig. 87, d).

Compare the left and right speakers in Fig. 87. What is general and what is the difference in these constructions on them?

From the comparison of these drawings and the text given to them, it can be concluded that the order of constructing frontal dimectric and isometric projections is generally the same. The difference lies in the location of the axes and the length of the segments laid down along the axis y.

In some cases, the construction of axonometric projections is more convenient to start with the construction of the foundation figure. Therefore, we consider how flat geometric shapes are depicted in axonometry located horizontally.

Construction of the axonometric system projection is shown in Fig. 88, a and b.

Along the axis x, the side of the square A is placed, along the y axis - half of the side A / 2 for the frontal dimectric projection and side A for isometric projection. Cuts of segments are connected straight.

The construction of the axonometric projection of the triangle is shown in Fig. 89, a and b.

Symmetrically point O (the beginning of the axes of the coordinate) along the axis x lay down half of the side of the triangle A / 2, and along the axis y is its height H (for the front dimeric projection half of the height H / 2). The obtained points are connected by the sections of the straight lines.

Building an axonometric projection of the correct hexagon is shown in Fig. 90.

On the x axis to the right and left from the point about the segments, equal to the side of the hexagon. On the axis, the point of S / 2, equal to half the distance between the opposite sides of the hexagon (for the front dimethrical projection, is lowered). From the points M and N, obtained on the axis y, are carried out to the right and left parallel to the axes x segments equal to half the hexagon side. The obtained points are connected by the sections of the straight lines.

Answer the questions

1. How are the axis of frontal dimectric and isometric projections? How are they built?

The standard establishes the following types obtained on the main planes of projections (Fig. 1.2): front view (main), top view, view of the left, view on the right, bottom view, rear view.

For the main species, the one that gives the most complete picture of the form and size of the subject.

The number of images should be the smallest, but ensuring a complete picture of the form and sizes of the subject.

If the main types are located in the projection connection, their names are not denoted. For best use Drawing fields The species are allowed outside the projection link (Fig.2.2). In this case, the view image is accompanied by the designation by type:

1) indicates the direction of the view

2) above the image of the species appreciate BUT as in fig. 2.1.

The species are designated by the capital letters of the Russian alphabet with a font, 1 ... 2 sizes exceeding the font of dimensional numbers.

Figure 2.1 shows the item for which you need to perform four types. If these types are located in the projection connection, then they will take a lot of space on the drawing field. Can be located required species So, as shown in Fig. 2.1. The drawing format is reduced, but the projection bond is broken, so you need to designate the view on the right ().

2.2. Mixed species.

The local species is called an image of a separate limited space of the subject.

It can be limited to the cliff line (Fig.2.3 a) or not limited (Fig.2.3b).

In general, local species are drawn up in the same way as the main types.

2.3. Additional types.

If any part of the subject is impossible to show on the main types without distortion of form and sizes, then apply additional types.

An additional view is the image of the visible part of the surface of the object obtained on the plane, not parallel to any of the main planes of projections.

If an additional species is performed in a projection connection with the corresponding image (Fig.2.4 a), then it is not denoted.

If the image of an additional species is made to free space (Fig.2.4 b), i.e. The projection bond is broken, the direction of the view is indicated by the arrow located perpendicularly depicted part of the part and is indicated by the letter of the Russian alphabet, and the letter remains parallel to the main inscription drawing, and does not rotate behind the arrow.

If necessary, the image of an additional species can be rotated, then the letter is set to the letter and the rotation sign (this is a circle of 5 ... 6mm with an arrow between the sash angle 90 °) (Fig.2.4 V).

Additional view most often performed as a local.

3. Crashes.

The incision is called an image of an object mentally dissected by one or several planes. The section shows what lies in the secant plane and what is located behind it.

In this case, a part of the object located between the observer and the securing plane is mentally removed, as a result of which all the surface closed by this part becomes visible.

3.1. Building cuts.

Figure 3.1 shows three types of items (without incision). On the main form interior surfaces: Rectangular grooves and cylindrical stepped hole are shown by dashed lines.

In fig. 3.2 Discalled the incision obtained as follows.

The securing plane, parallel to the frontal plane of projections, the subject mentally dissected along its axis passing through the rectangular groove and the cylindrical stepped hole located in the center of the subject .. Then mentally removed the front half of the item between the observer and the securing plane. So, as the subject is symmetrical, it makes no sense to give a complete cut. It is performed on the right, and left leaves the bottom.

The view and incision are separated by a barcompuncture line. The context shows what happened in the securing plane and what is behind it.

When considering the drawing, you can see the following:

1) bar lines, which are mainly indicated by rectangular grooves and a cylindrical stepped hole, are circled with solid main lines on the cut, since they are as a result of mental dissection of the subject visible;

2) On the context, which held along the main species, the solid main line indicating the slice disappeared at all, since the front half of the subject is not depicted. The slice on the depicted half of the subject is not designated, since it is not recommended to show the invisible elements of the subject with bar lines on the cuts;

3) A flat figure, which is in the securing plane, is selected on the section of the hatch, the hatching is applied only in the place where the securing plane dishes the material of the subject. For this reason, the rear surface of the cylindrical stepped hole is not shaded, as well as the rectangular groove (with the mental dissection of the subject, the securing plane of these surfaces has not affected);

4) as a cylindrical stepper opening, a solid main line depicting on the front plane of the projections is a horizontal plane formed by a change in diameters;

5) The incision placed on the site of the main image does not change the images of the top view and on the left.

When performing cuts in the drawings, you must be guided by the following rules:

1) On the drawing only useful cuts ("useful" are called cuts chosen for reasons of necessity and sufficiency);

2) Invisible internal outlines depicted by dashed lines, circuit with solid main lines;

3) figure section included in the incision, stroke;

4) The mental dissection of the subject should only apply to this section and not affect the change in other images of the same subject;

5) on all images, the bar lines are cleaned, since the inner circuit is well read on the cut.

3.2 Designation of cuts

In order to know where the subject has the form shown in the image of the section, the location where the secant plane passed, and the incision itself is denoted. The line indicating the securing plane is called the cross section line. It is depicted open line.

At the same time choose the initial letters of the alphabet ( A B C D E etc.). Over the cut, obtained using this sectional plane, perform an inscription by type A-A. . Two pair letters through a dash (Fig. 3.3).

Letters in the lines of the section and the letters denoting the incision should be bigger sizethan figures of dimensional numbers on the same drawing (on one or two font numbers)

In cases where the secant plane coincides with the plane of the symmetry of this item and the corresponding images are located on the same sheet in the immediate projection bond and are not divided by any other images, it is recommended that you not to mark the position of the securing plane and the image of the cut is not accompanied by the inscription.

Figure 3.3 shows the drawing of the subject on which two cuts are made.

1. In the main form, the incision is made by the plane, the location of which coincides with the symmetry plane for this item. It passes along the horizontal axis on top view. Therefore, this incision is not indicated.

2. Singing plane A-A. It does not coincide with the plane of symmetry of this part, therefore the corresponding section is indicated.

The letter designation of the secant planes and cuts are parallel to the main inscription regardless of the angle of inclination of the secular plane.

3.3 String materials in cuts and sections.

In cuts and sections, the figure obtained in the secant plane, stroke.

GOST 2.306-68 Sets graphic designation different materials (Fig.3.4)

Metal hatching is applied with thin lines at an angle of 45 ° to the line contour lines, or to its axis, or to the drawing frame lines, and the distance between the lines should be the same.

The hatching at all cuts and sections for this subject is the same in direction and step (the distance between the strokes).

3.4. Classification of cuts.

Cuts have several classifications:

1. Classification, depending on the number of sequential planes;

2. Classification, depending on the position of the securing plane relative to the planes of projections;

3. Classification, depending on the position of the secant planes relative to each other.

Fig. 3.5

3.4.1 Simple cuts

Simple is called an incision made by one secular plane.

The position of the secular plane can be different: vertical, horizontal, inclined. It is chosen depending on the form of the subject, internal organization which you need to show.

Depending on the position of the securing plane relative to the horizontal plane of projections, the cuts are divided into vertical, horizontal and inclined.

The vertical is a sectional case with a securing plane perpendicular to the horizontal plane of projections.

The vertically located secant plane can be parallel to the frontal plane of the projections or profile, forming the front (Fig. 3.6) or profile cuts (Fig. 3.7).

A horizontal section is a section of a section under a securing plane parallel to the horizontal plane of projections (Fig.3.8).

An inclined section is called a section with a securing plane component with one of the main planes of projections an angle is different from the direct (Fig.3.9).

1. According to the axonometric image of the part and the specified dimensions, draw three of its species - the main, top and left. Visual image does not overcool.

7.2. Task 2.

2. Perform the necessary cuts.

3. Build surface intersection lines.

4. Apply the dimensional lines and put the dimensional numbers.

5. Perform the drawing stroke and fill the main inscription.

7.3. Task 3.

1. Size overdue the given two types of items and build the third appearance.

2. Perform the necessary cuts.

3. Build surface intersection lines.

4. Apply the dimensional lines and put the dimensional numbers.

5. Perform the drawing stroke and fill the main inscription.

For all tasks, kinds are drawn only in the projection connection.

7.1. Task 1.

Consider examples of tasks.

Task1. . By visual image, build three types of details and perform the necessary cuts.

7.2 Task 2.

Task2. . For two species, build the third appearance and perform the necessary cuts.

Task 2. III stage.

1. Perform the necessary cuts. The number of cuts should be minimal, but sufficient to read the inner contour.

1. Singing plane BUT Opens internal coastal surfaces. This plane is parallel to the frontal plane of projections, so the cut A-A. Combined with the main type.

2. On the form of the left, the local section is shown opening the cylindrical opening æ32.

3. Dimensions are applied on those images where the surface is read better, i.e. Diameter, length, etc., for example, æ52 and length 114.

4. Remote lines as possible not to cross. If the main species is selected correctly, then the greatest number sizes will be on the main form.

Check:

1. To make each item of the part there is a sufficient amount of sizes.
2. So that all the protrusions and holes are tied with dimensions to other parts items (size 55, 46, and 50).
3. Dimensions.
4. Run the drawing stroke by removing all the lines of the invisible contour. Fill the main inscription.

7.3. Task 3.

Build three types of details and perform the necessary cuts.

8. Information about surfaces.

Building lines belonging to surfaces.

Surfaces.

In order to build surface crossing lines, you need to be able to build not only surfaces, but also points located on them. This section discusses the most common surfaces.

8.1. Prism.

A trigger prism is given (Fig. 8.1) truncated by the front-scale-pro-drug plane (2GPs, 1 algorithm, module No. 3). S. Ç L \u003d. T (1234.)

Since the prism is projected relatively P 1. The horizontal projection of the intersection line is already in the drawing, it coincides with the main projection of a given prism.

The sequential plane is projected relatively P 2. It means that the front projection of the crossing line is in the drawing, it coincides with the front projection of this plane.

The profile projection of the intersection line is built on two specified projections.

8.2. Pyramid

A truncated triangular pyramid F (S, ABC) (Fig. 8.2).

This pyramid F. intersects planes S, D. and G. .

2 GPZ, 2 algorithm (module No. 3).

F. Ç S \u003d 123.

S. ^ P 2. Þ S 2 \u003d 1 2 2 2 3 2

1 1 2 1 3 1 and 1 3 2 3 3 3 F. .

F. Ç D \u003d 345.

D. ^ P 2. Þ \u003d 3 2 4 2 5 2

3 1 4 1 5 1 and 3 3 4 3 5 3 are built on surface accessories F. .

F. Ç r \u003d 456

G. ÇP 2. Þ g 2 \u003d 4 2 5 6

4 1 5 1 6 1 and 4 3 5 3 6 3 are built on surface accessories F. .

8.3. Bodies bounded by surfaces of rotation.

The rotation bodies call geometric shapes, bounded by the surfaces of rotation (ball, ellipsoid of rotation, ring) or the surface of rotation and one or several planes (rotation cone, rotation cylinder, etc.). Images on the planes of projections parallel to the axis of rotation are limited to outlaw lines. These outlaw lines are the boundary of the visible and invisible part. geometric tel. Therefore, when constructing projections of lines belonging to the surfaces of rotation, it is necessary to build points located on essays.

8.3.1. Cylinder rotation.

P 1. The cylinder will be projected into this plane in the form of a circle, and into two other planes of projections in the form of rectangles whose width is equal to the diameter of this circle. Such a cylinder is projection to P 1. .

If the axis of rotation is perpendicular P 2. , then on P 2. It will be projected in the form of a circle, and on P 1. and P 3. In the form of rectangles.

Similar argument with the position of the rotation axis perpendicular P 3. (Fig.8.3).

Cylinder F. Crosses with planes R, S, L. and G. (Fig.8.3).

2 GPZ, 1 Algorithm (Module No. 3)

F. ^ P 3.

R, S, L, G. ^ P 2.

F. Ç R. = but (6 5 and)

F. ^ P 3. Þ F 3 \u003d a 3 (6 3 \u003d 5 3 and \u003d)

a 2. and A 1. are built on surface accessories F. .

F. Ç S \u003d b (5 4 3)

F. Ç S \u003d C (2 3) Reasoning is similar to the previous one.

F G \u003d D (12 and

Tasks in Figures 8.4, 8.5, 8.6 are solved similarly to the task in Fig.8.3, since the cylinder

everywhere profile - projection, and holes - surfaces projection relative to

P 1. - 2GPZ, 1 algorithm (module No. 3).

If both cylinders have the same diameters (Fig. 8.7), then there will be two ellipses of the intersection lines (Monta Theorem, Module No. 3). If the axis of rotation of these cylinders lie in the plane parallel to one of the planes of projections, the ellipsees will be projected into this plane in the form of intersecting lines.

8.3.2. Prokius

Tasks in Figures 8.8, 8.9, 8.10, 8.11, 8.12 -2 GPZ (Module No. 3) are solved by 2 algorithms, since the surface of the cone cannot be projected, and the split planes are frontal-projection everywhere.

Figure 8.13 shows the rotation cone (body) crossed by two frontal-projection planes G. and L. . The intersection lines build 2 algorithm.

In Figure 8.14, the surface of the rotation cone intersects with the surface of the profile-projection cylinder.

2 GPZ, 2 solutions algorithm (module No. 3), that is, the profile projection of the intersection line is in the drawing, it coincides with the profile projection of the cylinder. Two other projections of the crossing line are built by affiliation to the rotation cone.

Fig.8.14.

8.3.3. Sphere.

The surface of the sphere intersects with a plane and with all the surfaces of rotation with it, around the circles. If these circles are parallel to the planes of projections, then they are projected into the circumference of the natural value, and if not parallel, then in the form of an ellipse.

If the axis of rotation of the surfaces intersect and are parallel to one of the planes of projections, then all the crossing lines - circles are projected into this plane as segments of straight lines.

In fig. 8.15 - sphere, G. - plane, L. - cylinder, F. - frustum.

S. Ç G \u003d but - circle;

S. Ç L \u003d B. - circle;

S. Ç f \u003d with - Circle.

Since the axis of rotation of all intersecting surfaces is parallel P 2. , then all lines of intersection - circles on P 2. They are projected into straight lines.

On the P 1. : Circle "but" is projected into a true magnitude as parallel to it; circle "B" projected into the cut straight, as parallel P 3. ; circle "from" is projected in the form of an ellipse, which is built according to belonging the sphere.

First, the points are built 1, 7 and 4, which determine the small and large axis of the ellipse. Then builds the point 5 as lying at the equator sphere.

For other points (arbitrary), circles (parallels) are carried out on the surface of the sphere and by affiliation, they define horizontal projections of the points lying on them.

9. Examples of tasks.

Task 4. Wire three types of details with the necessary cuts and apply the sizes.

Task 5. Build three types of details and perform the necessary cuts.

10. Askonometry

10.1. Brief theoretical information about axonometric projections

A comprehensive drawing compiled from two or three projections, possessing the properties of reversibility, simplicity, etc., at the same time has a significant drawback: he lacks visibility. Therefore, wanting to give a more visible idea of \u200b\u200bthe subject, along with the complex drawing, the axonometric, widely used in the description of the designs of products, in the operating manuals, in the assembly schemes, for explanations of the drawings of machines, mechanisms and their parts.

Compare two images - orthogonal drawing and axonometric one and the same model. What picture is easier to read the form? Of course on the axonometric image. (Fig.10.1)

The essence of axonometric projection is that geometric figure Together with the axes of rectangular coordinates, to which it is attributed in space, parallel to some plane of projections, called the axonometric plane of projections, or art plane.

If you postpone the coordinates on the axes x, Y. and z. section l (LX, LY, LZ) and disroach on the plane P ¢ , then we get axonometric axes and on them segments l "X, L" Y, L "Z (Fig.10.2)

lX, LY, LZ - Natural scales.

l \u003d LX \u003d LY \u003d LZ

l "X, L" Y, L "Z - Aksonometric scales.

The resulting set of projections on P ¢ is called axonometry.

The ratio of the length of axonometric scale segments to the length of natural scale segments is called an indicator or a distortion coefficient along the axes that are designated KX, KY, KZ.

Types of axonometric images depend:

1. From the direction of projection rays (they can be perpendicular P" - Then the axonometry will be called orthogonal (rectangular) or arranged at an angle of not 90 ° - row angular axonometry).

2. From the position of the coordinate axes to the axonometric plane.

Three cases are possible here: when all three axes of coordinates make up with the axonometric plane of projections sharp corners (equal and unequal) and when one or two axis is parallel to it.

In the first case, only rectangular projection is applied, (S. ^ P ") In the second and third - only rowing projection (S P ") .

If the axes are coordinates Oh, oy, oz Not parallel to the axonometric plane of projections P" , Will they be projected on her in full size? Of course not. The image of direct in the general case is always less than a natural value.

Consider the orthogonal drawing of the point BUT And its axonometric image.

The position of the point is determined by the three coordinates - X a, y a, z a obtained by measuring the units of natural broken OA X - A X A 1 - A 1 A (Fig.10.3).

A " - Home Aksonometric Projection BUT ;

BUT - Secondary point projection BUT (projection of the projection point).

Distortion coefficients on the axes X ", y" and z " There will be:

k X. = ; k y. = ; k y. =

In orthogonal axonometry, these indicators are equal to cosine angles of inclination axes of coordinates to the axonometric plane, and therefore they are always less than one.

They are binding to formula

k 2 x + k 2 y + k 2 z \u003d 2 (i)

In Koomgol Aksonometry, distortion indicators are related to the formula

k x + k y + k z \u003d 2 + ctg A (III)

those. Any of them may be less equal to or more units (here A is an angle of inclination of the projection rays to the axonometric plane). Both formulas are a conclusion from the Polka theorem.

Polka Theorem: Axonometric axis on the drawing plane (n ¢) and the scale on them can be selected perfectly arbitrarily.

(Consequently, the axonometric system ( O "X" Y "Z") In the general case, it is determined by five independent parameters: three axonometric scales and two angles between axonometric axes).

The angles of inclination of natural axes of coordinates to the axonometric plane of projections and the direction of projection can be selected arbitrarily, therefore, possibly a variety of types of orthogonal and rowing axonometry.

They are divided into three groups:

1. All three distortion indicators are equal to (k x \u003d k y \u003d k z). This type of axonometry is called isometric . 3K 2 \u003d 2; k \u003d "0.82 - theoretical distortion coefficient. According to GOST 2.317-70, it is possible to use K \u003d 1 - the reduced distortion coefficient.

2. Two of any indicator are equal (for example, KX \u003d KY KZ). This type of axonometry is called dimethrey . k x \u003d k z; k y \u003d 1/2 2k x 2; k x 2 + k z 2 + k y 2/4 \u003d 2; k \u003d "0.94; k x \u003d 0.94; ky \u003d 0.47; KZ \u003d 0.94 - Theoretical distortion coefficients. According to GOST 2.317-70, distortion coefficients may be reduced - k x \u003d 1; k y \u003d 0.5; k z \u003d 1.

3. 3. All three indicators are different (k x ¹ k y ¹ k z). This type of axonometry is called tRIMETRY .

In practice, several species are used both rectangular and rowing axonometry with the most simple ratios between distortion indicators.

From GOST2.317-70 and various types of axonometric projections, we consider orthogonal isometrics and dimetry, as well as a rowing dimethry, as the most frequently used.

10.2.1. Rectangular isometry

In isometry, all axes are tilted in an axonometric plane under the same and the same angle, therefore the angle between the axes (120 °) and the distortion coefficient will be the same. Select scale 1: 0.82 \u003d 1.22; M 1,22: 1.

For convenience, the construction is used by the shown coefficients and then natural dimensions are deposited on all axes and lines. Images are thus becoming more, but it does not affect the clarity.

The choice of the type of axonometry depends on the form of the image portable. The easiest way to build a rectangular isometric, so such images are more common. However, in the image of details, including quadrangular prisms and pyramids, their clarity decreases. In these cases, it is better to perform a rectangular dimethry.

Koomgol Dimetry should be chosen for parts having a large length at low height and width (type shaft) or when one side of the part contains the greatest number Important features.

In axonometric projections, all properties of parallel projections are preserved.

Consider the construction flat Figure AVDE .

First of all, we will construct axes in axonometry. Fig.10.4 presents two ways to build axonometric axes in isometry. Figure 10.4. but The construction of the axes is shown using a circulation, and in Fig.10.4 b. - Building with equal segments.

Fig.10.5.

Figure ASDE Lies in the horizontal plane of projections, which is limited by the axes OH and OY. (Fig.10.5a). We build this figure in axonometry (Fig.10.5b).

Each point lying in the plane of projections, how much does coordinate have? Two.

Point lying in the horizontal plane - coordinates H. and Y. .

Consider the construction tA . What coordinates will begin to build? With coordinate X A. .

To do this, measure the orthogonal drawing OA H. and put on the axis X " , get a point And x " . And x and 1 which axis is parallel? Axis Y. . So from t. And x " We carry out a straight parallel axis Y. "and put the coordinate on it Y A. . Point received BUT" and will be aksonometric projection tA .

Similarly, all other points are built. Point FROM Lies on the axis OY. So it has one coordinate.

In Figure 10.6, a five-marched pyramid is given, in which the base is the same pentagon Assd. What needs to be completed to get a pyramid? It is necessary to complete the point S. which is its vertex.

Point S. - the point of space, so it has three coordinates X s, y s and z s . First, a secondary projection is built S (s 1), And then all three sizes are transferred from an orthogonal drawing. Connection S " C. A ", b", c ", d" and E. ", We will get an axonometric image of a bulk figure - pyramid.

10.2.2. Isometric circumference

The circumference is projected onto the plane of the projections in a natural value, when they are parallel to this plane. And since all the planes are inclined to the axonometric plane, the circles lying on them will be projected onto this plane in the form of ellipses. In all types of axonometry, the ellipses are replaced by ovals.

In the image of oval, it is necessary, first of all, pay attention to the construction of a large and small axis. It is necessary to start with the definition of the position of the small axis, and the large axis is always perpendicular to it.

There is a rule: the small axis coincides with the perpendicular to this plane, and the large axis is perpendicular to it or the direction of the small axis coincides with the axis that does not exist in this plane, and the big one is perpendicular to it (Fig.10.7)

The large axis of the ellipse is perpendicular to the coordinate axis, which is absent in the circumference plane.

The large axis of the ellipse is 1.22 'D OCD; The small axis of the ellipse is 0.71 'D OCD.

Figure 10.8 in the plane of the circle there is no axis Z. Z. ".

Figure 10.9 in the plane of the circle there is no axis H. , so the large axis perpendicular to the axis H. ".

And now we consider how the oval is drawn in one of the planes, for example, in a horizontal plane XY. . There are many ways to build an oval, get acquainted with one of them.

The sequence of building an oval is as follows (Fig.10.10):

1. The position of a small and large axis is determined.

2. Through the intersection point of a small and large axis carrying the line parallel to the axes X " and Y " .

3. On these lines, as well as on a small axis, from the center radius equal to the radius of a given circumference, postpone points 1 and 2, 3 and 4, 5 and 6 .

4. Connect a point 3 and 5, 4 and 6 and celebrate the intersection points with a large axis of the ellipse ( 01 and 02 ). From the point 5 , radius 5-3 and from the point 6 , radius 6-4 , carry out arcs between points 3 and 2 and points 4 and 1 .

5. Radius 01-3 We carry out an arc connecting points 3 and 1 and radius 02-4 - Points 2 and 4 . Evals are also built in other planes (Fig.11).

For simplicity of building a visual image of the axis surface Z. may coincide with the height of the surface, and the axis X. and Y. with axes of horizontal projection.

To build a point BUT belonging to the surface need to build it three coordinates X a, y a and Z A. . The point on the surface of the cylinder and other surfaces is built in the same way (Fig.10.13).

Large axis oval perpendicular to the axis Y. ".

When constructing axonometry, details limited to several surfaces should be followed by the following sequence:

Option 1.

1. The item mentally divided into elementary geometric shapes.

2. Draws out the axonometry of each surface, the construction lines are preserved.

3. Cutout 1/4 details are built to show the internal configuration of the part.

4. The hatching of GOST 2.317-70 is applied.

Consider an example of constructing axonometry details, the outer contour of which consists of several prisms, and inside the parts of the cylindrical holes of different diameters.

Option 2. (Fig. 10.5)

1. The secondary projection of the details on the plane of the projections P.

2. The heights of all points are postponed.

3. Cutout 1/4 part of the part is built.

4. The hatching is applied.

For this detail, the option 1 will be more convenient for construction.

10.3. Steps of a visual image of the part.

1. The part fits into the surface of the quadrangular prism, the dimensions of which are equal to the dimensional size of the part. This surface is called wrapping.

An isometric image of this surface is performed. The wrapping surface is based on overall dimensions (Fig.10.15 but).

Fig. 10.15 but

2. The protrusions located on the top of the part on the axis are cut out of this surface. H. and the prism is built with a height of 34mm, one of which will be the top plane of the wrap surface (Fig.10.15 b.).

Fig. 10.15 b.

3. The lower prism is cut out of the remaining prism with the bases of 45 '35 and 11mm height (Fig.10.15 in).

Fig. 10.15 in

4. Two are built cylindrical holeswhose axes lie on the axis Z. . The top base of the large cylinder lies on the top base of the part, the second below is 26 mm. The lower base of the large cylinder and the upper base is small lie in the same plane. The lower base of the small cylinder is based on the lower base of the part (Fig.10.15 g.).

Fig. 10.15 g.

5. A 1/4 part of the part is performed to open the inner circuit of it. The incision is performed by two mutually perpendicular planes, that is, along the axes H. and Y. (Fig.10.15 d.).

Fig.10.15 d.

6. The cross sections and the entire remaining part of the part are performed, and the carved part is cleaned. Invisible lines are erased, and cross sections are shaded. The hatching density should be the same as on an orthogonal drawing. The direction of the stroke lines is shown in Fig. 10.15 e. accordance with GOST 2.317-69.

The lines of hatching will be lines parallel to the diagonals of the squares lying in each coordinate plane, which are parallel to the axonometric axes.

Fig.10.15 e.

7. There is a feature of hatching of stiffness ribs in axonometry. According to the rules

GOST 2.305-68 In the longitudinal section, the riffness edge on the orthogonal drawing is not

heatshits, and in axonometry is shaded. It is Fig.10.16 an example is shown.

stiffery hatchings.

10.4 Various Dimetry.

Rectangular dimectric projection can be obtained by turning and tilt the coordinate axes relative P ¢ so that the distortions of the axes X " and Z " accepted equal importance, and along the axis Y " - twice the smaller. Distortion indicators " k X. "And" k Z. "Will be 0.94, and" k y. "- 0,47.

In practice, enjoy the indicators given, i.e. By the axes X. "I. Z " put out natural sizes, and along the axis Y. "- 2 times less natural.

Axis Z " usually have vertically, axis X " - at an angle of 7 ° 10 ¢ to the horizontal line, and the axis Y " - Corner 41 ° 25 ¢ to the same line (Fig.12.17).

1. The secondary projection of a truncated pyramid is being built.

2. Point heights are built 1,2,3 and 4.

The easiest way to build the axis H. ¢ By posting on the horizontal line 8 equal parts and down the vertical line 1 the same part.

To build an axis Y " At an angle of 41 ° 25 ¢, it is necessary to postpone 8 parts on the horizontal line, and on the vertical 7 of the same parts (Fig.10.17).

Figure 10.18 shows a truncated quadrangular pyramid. To build it in axonometry it was easier, the axis Z. must coincide with a height, then the top of the base Abcd. will lie on the axes H. and Y (A. and with î h. , IN and D. Î y.). How many coordinates have points 1 and? Two. What kind? H. and Z. .

These coordinates are deposited in full size. The obtained points 1 ¢ and 3 are connected to the points A ¢ and C ¢.

Points 2 I. 4 have two z coordinates and Y. . Since they have the same height, the coordinate Z. postponed on axis Z " . Through the resulting point 0 ¢ A line is carried out parallel to the axis Y. which on both sides of the point is deposited 0 1 4 1 Reduced twice.

Points received 2 ¢ and 4 ¢ Connect with points IN ¢ and D " .

10.4.1. Construction of circles in a rectangular dimension.

Circles lying on coordinate planes in a rectangular dimetry, as well as in isometric, will be depicted in the form of ellipses. Ellipses located on the planes between the axes X " and Y ", y" and Z " The above dimension will have a large axis equal to 1.06d, and a small - 0.35d, and in the plane between the axes X " and Z " - Large axis, too, 1.06d, and a small 0.95d (Fig.10.19).

Ellipses are replaced by four-price ovals, as in isometric.

10.5.Kusomurgol Dimetric Projection (Frontal)

If you place the coordinate axis H. and Y. parallel to the P ¢ plane, then the distortions of these axes will become equal to one (K \u003d T \u003d 1). An indicator of distortion on the axis Y. Usually taken equal to 0.5. Axonometric axes X. "I. Z " make a straight angle, axis Y " Typically spend as a bisector of this angle. Axis H. can be directed as right from the axis Z. "And left.

It is preferable to use the right system, as it is more convenient to depict objects in disseminated. In this type of axonometry, it is good to draw parts having a form of a cylinder or cone.

For convenience, this detail axis Y. It is necessary to combine with the axis of rotation of the surfaces of the cylinders. Then all circles will be depicted in a natural value, and the length of each surface will be reduced twice (Fig.10.21).

11.Rart sections.

When performing drawings of parts of machines, there is often inclined cross sections.

When solving such tasks, it is necessary first of all to understand: how the secant plane should be located and which surfaces are involved in the section so that the item is read better. Consider examples.

The tetrahedral pyramid is given, which disseminates the inclined frontal-projecty plane A-A. (Fig. 11.1). The cross section will be a quadrilateral.

First we build it on P 1. and on P 2. . The frontal projection coincides with the projection of the plane, and the horizontal projection of the quadrilateral is to build a pyramid belonging.

Then we build a natural amount of section. For this introduced an additional plane of projections P 4 parallel to a given sectional plane A-A. , I project a quadrilateral, and then combine it with the drawing plane.

This fourth main task of converting a comprehensive drawing (Module No. 4, p.15 or Problem No. 117 from the working notebook according to the design geometry).

The constructions are performed in the following sequence (Fig. 11.2):

1. 1.N. free place Drawing We carry out axial line, parallel plane A-A. .

2. 2. Mindings of the intersection of the edges of the pyramid with a plane carry out the projection rays perpendicular to the securing plane. Points 1 and 3 They will lie on the line located perpendicular to the axial.

3. 3. Interior between points 2 and 4 It is transferred from a horizontal projection.

4. Similarly, the true value of the cross section of the rotation surface is the ellipse.

Distance between points 1 and 5 -Golly axis ellipse. The small axis of the ellipse must be built by dividing the large axis in half ( 3-3 ).

Distance between points 2-2, 3-3, 4-4 Torn from a horizontal projection.

Consider more complex examplecomprising multifaceted surfaces and rotational surfaces (Fig. 11.3)

The tetrahedral prism is given. It contains two holes: prismatic, located horizontally and cylindrical, whose axis coincides with the height of the prism.

The sequential plane is frontally projecting, so the frontal projection of the cross section coincides with the projection of this plane.

The quadrangular prism is projected to the horizontal plane of projections, which means the horizontal projection of the section is also in the drawing, it coincides with the horizontal projection of the prism.

The natural amount of section in which both prisms and a cylinder fall on the plane parallel to the secular plane. A-A. (Fig. 11.3).

Sequence of inclined section:

1. The secting axis is carried out, parallel to the securing plane, on the free field of the drawing.

2. The cross section of the outer prism is being built: it is transferred from the front projection length, and the distance between points from the horizontal.

3. The cylinder cross section is built - part of the ellipse. First, characteristic points are built, which determine the length of a small and large axis ( 5 4 , 2 4 -2 4 ) and points that limit the ellipse (1 4 -1 4 ) then additional points (4 4 -4 4 and 3 4 -3 4).

4. The cross section of the prismatic opening is being built.

5. The hatching at an angle of 45 ° to the main inscription is applied, if it does not coincide with the loop lines, and if coincides, the hatching angle can be 30 ° or 60 °. The density of hatching in the section is the same as on an orthogonal drawing.

The inclined section can be rotated. In this case, the designation is accompanied by a sign. It is also allowed to show half the shape of the inclined section, if it is symmetrical. A similar arrangement of the inclined section is shown in Fig.13.4. Designations of points in constructing the inclined section can not be set.

Figure 11.5 is given a visual image of a given figure with a cross section of a plane. A-A. .

Control questions

1. What do they call the view?

2. How do the image of the object be obtained on the plane?

3. How are the names are awarded species on the main planes of projections?

4. What is called the main type?

5. What is called an additional view?

6. What is called local species?

7. What is called incision?

8. What designations and inscriptions are installed for cuts?

9. What is the difference between simple cuts from complex?

10. What is the conventionality when performing broken cuts?

11. What incision is called local?

12. Under what conditions is allowed to combine half of the species and half of the cut?

13. What is called cross section?

14. How do cross sections in the drawings?

15. What is called a remote element?

16. How to simplify the repetitive elements on the drawing?

17. How conditionally reduce the image of the items of large length in the drawing?

18. What is the difference between axonometric projections from orthogonal?

19. What is the principle of the formation of axonometric projections?

20. What are the types of axonometric projections?

21. What are the features of isometric?

22. What are the features of dimethics?

Bibliographic list

1. Suvorov, S.G. Machino-building drawing in matters and answers: (Directory) / S.G. Svorov, N.S. Svorov. - 2nd ed. Pererab. and add. - M.: Mechanical Engineering, 1992.-366c.

2. Fedorenko V.A. Handbook of Machine-Building Drawing / V.A. Fedorenko, A.I.Shoshin, - Publishing House. From the 14th Ed.1981g.-M.: Alliance, 2007.-416c.

3. Hisposy, S.K. Environmental graphics: textbook for media. specialist. studies. Vehicles for specials. tehn Profile / S.K.Bogolyubov. - 3rd ed., Act. and additional-m.: Mechanical engineering, 2000.-351c.

4. High-profol, I.S.Technic drawing e. Studies. For start. prof. Education / I.S.Vyshnepolsky.-4th ed., Pererab. and add.; Graph M.- M.: Higher. Shk.: Academy, 2000.-219c.

5. Levitsky, V.S. Machino-building drawing and automation of drawings: studies. For athmps / V.S.levitsky. - 6th ed., Pererab. and add.; Graph M.-M.: Higher. Shk., 2004.-435c.

6. Pavlova, A.A. Designed geometry: studies. For universities / A.A. Pavlova-2nd ed., Pererab. and add.; Griff Mo.- M.: Vlados, 2005.-301c.

7. GOST 2.305-68 *. Images: species, cuts, sections / unified system of design documentation. - M.: Standards Publishing House, 1968.

8. GOST 2.307-68. Drawing and limit deviations / Unified system

design documentation. - M.: Standards Publishing House, 1968.

What is dimymium

Dimetry is one of the types of axonometric projection. Thanks to the axonometry at one volume image, you can consider the object at once in three dimensions. Since the distortion coefficients of all sizes in the 2nd axes are the same, this projection And the name of the dimethium was called.

Rectangular dimetry

At the location of the z axis, "vertically, the axis x" and y "is formed from a horizontal segment of 7 degrees 10 minutes and 41 degrees 25 minutes. In a rectangular dimensioner, the distortion coefficient along the Y axis will be 0.47, and along the x and z axes and z Twice more, that is, 0.94.

To make the construction of approximately the axonometric axes of the usual dimetry, it is necessary to accept that TG 7 degrees 10 minutes is 1/8, and TG 41 degrees 25 minutes is 7/8.

How to build dimethria

To begin with, it is necessary to draw the axis to depict object in dimension. In any rectangular dymetry, the angles between the axes x and z are equal to 97 degrees of 10 minutes, and between the axes y and z - 131 degrees 25 minutes and between Y and x - 127 degrees 50 minutes.

Now it is required to apply the axis on orthogonal projections of the displayed object, given the selected position of the subject for drawing in a dimeric projection. After completing the transfer to the volumetric emigration overall dimensions Items, you can proceed to the drawing of minor elements on the surface of the subject.

It is worth remembering that the circumference in each plane of dimming is depicted with appropriate ellipses. In a dymetrical projection without distortion on the X and Z axes, the large axis of our ellipse in all 3-planes of the projection will be 1.06 diameters of the drawn circle. A small axis of the ellipse in the Hoz plane is 0.95 diameters, and in the zoy and xy plane - 0.35 diameters. In a dymetrical projection with a distortion along the axes x and z, the large axis of the ellipse is equal to the diameter of the circle in all planes. In the xz plane, the small axis of the ellipse is 0.9 diameters, and the zoy and xy planes are 0.33 diameters.

To get more detailed image, you need to make cutout through parts on dimming. SHASTRIKHE When drawing out the cutout, a parallel diagonal of the projection of the selected square on the required plane should be applied.

What is isometry

Isometric is one of the types of axonometric projection, where the distances of single segments on all 3-axes are the same. Isometric projection is actively used in machine-building drawings to display appearance Objects, as well as in a variety of computer games.

In mathematics, isometry is known as the transformation of the metric space, which retains the distance.

Rectangular isometry

In rectangular (orthogonal) isometric axonometric axes create an angles that are 120 degrees. The z axis is in a vertical position.

How to draw isometric

The construction of an isometric object makes it possible to obtain the most expressive idea of \u200b\u200bthe spatial properties of the image of the object.

Before starting building a drawing in an isometric projection, you must select this location of the item depicted, so that its spatial properties are maximally visible.

Now you need to decide on the type of isometry that you will draw. There are two types of it: rectangular and horizontal rhopoly.

Draw the axis with light thin lines so that the image works in the center of the sheet. As previously stated, the corners in the rectangular form of isometric projection should be 120 degrees.

Start drawing isometry from exactly the top surface of the object image. From the angles of the resulting horizontal surface, you need to spend two vertical straight lines and put on them the corresponding linear dimensions of the subject. In an isometric projection, all linear dimensions for all three axes will remain multiple units. Then it is sequentially required to connect the created points on the vertical direct. As a result, it turns out the outer contour of the subject.

It should be borne in mind that in the image of any item in an isometric projection, the visibility of curvilinear details will be distorted. The circle should be depicted with an ellipse. The segment between the dots of the circle (ellipse) along the axes of isometric projection should be equal to the diameter of the circle, and the axis of the ellipse will not coincide with the axes of isometric projection.

If the displayed object has hidden cavities of whether complex elements, try to perform a shastchik. It can be simple or stepped, it all depends the complexity of the elements.

Remember that all construction should perform strictly with the use of drawing tools. Apply a few pencils with different species hardness.