Dimetria and isometry. Drawing perspective and axonometry of the house How to draw an isometric projection

EXERCISE:

1) According to the given axonometric projections (Figure 6.2 - 6.21), build complex drawings of three models and apply dimensions.

2) Build an isometry of model No. 3 with a cutout of ¼ part.

METHODOLOGICAL INSTRUCTIONS

To complete the task, you need to study the topics “Constructing an isometric projection of a part” and “Cutting one quarter of a part”.

A complex drawing of the model is built in the same way as a complex drawing of geometric bodies, since the model can be mentally divided into separate simple geometric elements, which are prisms, cylinders, truncated cones, etc. We perform the isometry of the model in the following sequence:

1) We draw the coordinate axes at an angle of 120 o.

2) We start drawing the model from the horizontal plane, gradually, as it were, building on one element of the part after another, with thin lines. The length of the model is plotted along the axis X , axis width y , axis height z . All distances parallel to the coordinate axes are plotted in full size, without distortion.

3) We find the centers of the circles, determine in which plane they are located (horizontal, frontal or profile). We determine the direction of the major and minor axes of the ovals and draw them according to the given diameters.

4) We make a cutout of the front quarter (Figure 6.1), directing two secant planes along the axes xz y. Removing part of the model

5) Delete the auxiliary lines that were used in the constructions, outline the contour of the model with a solid main line and hatch the sections.

Figure 6.1 Cutout ¼ part of the model

Figure 6.3 Models No. 1, 2, 3

Figure 6.5 Models No. 1, 2, 3

Figure 6.7 Models No. 1, 2, 3

Figure 6.9 Models No. 1, 2, 3

Figure 6.11 Models No. 1, 2, 3

Figure 6.13 Models No. 1, 2, 3

Figure 6.15 Models No. 1, 2, 3

Figure 6.17 Models No. 1, 2, 3

Figure 6.19 Models No. 1, 2, 3

Figure 6.21 Models No. 1, 2, 3

Graphic Work No. 7

TECHNICAL DRAWING

EXERCISE: make a technical drawing of the model in isometry with a cutout of the front quarter according to the given drawing (Figure 7.3 - 7.22).

METHODOLOGICAL INSTRUCTIONS

The technical drawing is done by hand, without the use of drawing tools. To complete the work, you must study the section "Technical drawing".

When constructing an oval, it must be taken into account that the major axis of the oval is perpendicular to the minor axis. The length of the major axis of the oval is approximately equal to five segments , and the length of the small one is three segments (Fig. 7.1).

	a B C D E F)

Figure 7.1 Construction of ovals in isometry

If the oval is located in a horizontal plane, then the minor axis of the oval coincides with the axis z (Fig. 7.1, a). If the oval is located in the profile plane, then the minor axis of the oval coincides with the axis X (Fig. 7.1, c). If the oval is located in a horizontal plane, then the minor axis of the oval coincides with the axis y (Fig. 7.1, e).

We start drawing a cylinder by drawing axonometric axes. Then we build two bases in the form of ovals and draw generators that are tangent to the ovals (Fig. 7.1, b, d, e).

Hatching is applied based on the specified light direction. In figure 7.2, the light falls from above, from the left, from behind. Horizontal surfaces are the brightest, as they receive the maximum amount of light. Vertical surfaces are darker than horizontal ones. The more the vertical plane is turned away from the light flux, the darker it is.

To give volume to cylindrical and conical surfaces, a gradual transition is made from darker edges to a lighter middle. A light unshaded strip is left in the middle, which is called a “glare” (Fig. 7.2).

Hatching is done with straight lines. Hatching of lighter surfaces is done with a hard pencil with weak pressure (Fig. 7.2). Darker surfaces are hatched with a soft pencil. The darker the surface, the more pressure on the pencil when hatching.

Figure 7.2

Option 1

Illustration 7.3 Enclosure

Option 2

Figure 7.4 Rack

Option 3

Figure 7.5 Support

Option 4

Figure 7.6 Rack

Option 5

Figure 7.7 Lid

Option 6

Figure 7.8 Lid

Option 7

Figure 7.9 Lid

Option 8

Figure 7.10 Enclosure

Option 9

Figure 7.11 Support

Option 10

Figure 7.12 Support

Option 11

Figure 7.13 Lid

Option 12

Figure 7.14 Support

Option 13

Illustration 7.15 Enclosure

Option 14

Figure 7.16 Support

Option 15

Figure 7.17 Flange

Option 16

Figure 7.18 Stop

Option 17

Illustration 7.19 Enclosure

Option 18

Figure 7.20 Box

Option 19

Figure 7.21 Support

Option 20

Figure 7.22 Enclosure

Graphic Work No. 8

SIMPLE CUT

EXERCISE:

1) Based on two projections of the model (Figure 8.1 - 8.20), build a third projection using the cuts indicated in the diagram, apply dimensions.

2) Perform an isometry of the model with a cutout of the front quarter.

METHODOLOGICAL INSTRUCTIONS

To complete the work, you need to study the topic "Simple cuts". The rules for making cuts are as follows:

1) The position of the cutting plane is indicated in the drawing by an open line and arrows indicating the direction of view. The arrows are applied at a distance of 2 - 3 mm from the outer end of the stroke of the section line. An inscription is made above the cut, which contains two letters that indicate the cutting plane, written through a dash and underlined with a thin line, for example, “ A-A ».

2) If the cutting plane coincides with the plane of symmetry of the object and the cut is located in a projection connection with the view, then when performing horizontal, frontal and profile cuts, the position of the cutting plane is not marked on the drawing and the cut is not accompanied by an inscription.

3) On one image, it is allowed to connect part of the view and part of the section. Hidden contour lines on the connected parts of the view and section are usually not shown.

4) If the part is symmetrical, then in the drawing half of the view and half of the section are separated by a dash-dotted line, which is the axis of symmetry. Part of the incision is located on right or from below from the axis of symmetry.

Option 1

	b)

Figure 820 Scheme for performing cuts (a) and two projections of the model (b)

Graphic Work No. 9

Instruction

Construct with a ruler and protractor or a compass and ruler for a rectangular (orogonal) isometric projection. In this type of axonometric projection, all three axes - OX, OY, OZ - are angles of 120 ° to each other, while the OZ axis has a vertical orientation.

For simplicity, draw an isometric projection without distortion along the axes, since it is customary to equate the isometric distortion factor to one. By the way, “isometric” itself means “equal size”. In fact, when displaying a three-dimensional object on a plane, the ratio of the length of any projected segment parallel to the coordinate axis to the actual length of this segment is 0.82 for all three axes. Therefore, the linear dimensions of the object in isometry (with the accepted distortion coefficient) increase by 1.22 times. In this case, the image remains correct.

Start projecting the object onto the axonometric plane from its top face. Measure along the OZ axis from the center of intersection of the coordinate axes the height of the part. Draw thin lines for the X and Y axes through this point. From the same point, set aside half the length of the part along one axis (for example, along the Y axis). Draw a segment of the required size (part width) through the found point parallel to the other axis (OX).

Now, along the other axis (OX), set aside half the width. Through this point, draw a segment of the desired size (part length) parallel to the first axis (OY). The two drawn line segments must intersect. Complete the rest of the top face.

If this face has a round hole, draw it. In isometry, a circle is shown as an ellipse because we are looking at it from an angle. Calculate the dimensions of the axes of this ellipse based on the diameter of the circle. They are equal: a = 1.22D and b = 0.71D. If the circle is located on a horizontal plane, the a-axis of the ellipse is always horizontal, the b-axis is always vertical. In this case, the distance between the points of the ellipse on the X or Y axis is always equal to the diameter of the circle D.

Draw from the three corners of the top face vertical edges equal to the height of the part. Connect the edges through their bottom points.

If the shape has a rectangular hole, draw it. Set aside a vertical (parallel to the Z axis) segment of the desired length from the center of the edge of the upper face. Through the resulting point, draw a segment of the required size parallel to the upper face, and hence the X axis. From the extreme points of this segment, draw vertical edges of the desired size. Connect their bottom points. From the lower right point of the drawn rhombus, draw the inner edge of the hole, which should be parallel to the Y axis.

Image of circles in isometric projection

Consider how circles are depicted in isometric projection. To do this, let's draw a cube with circles inscribed in its faces (Fig. 3.16). Circles located respectively in planes perpendicular to the axes x, y, z are shown in isometry as three identical ellipses.

Rice. 3.16.

To simplify the work, ellipses are replaced by ovals outlined by arcs of circles, they are built like this (Fig. 3.17). A rhombus is drawn, into which an oval should fit, depicting a given circle in an isometric projection. To do this, on the axes lay off from the point ABOUT in four directions, segments equal to the radius of the depicted circle (Fig. 3.17, A). Through the received points a, b, c, d draw straight lines forming a rhombus. Its sides are equal to the diameter of the circle being drawn.

Rice. 3.17.

From the vertices of obtuse angles (points A And IN) describe between points A And b, and With And d arc radius R, equal to the length of the straight lines Wa or Вb(Fig. 3.17, b).

points WITH and D lying at the intersection of the diagonal of the rhombus with straight lines Wa And Bb, are the centers of small arcs conjugating large ones.

Small arcs are described by radius R, equal to the segment Sa (Db).

Construction of isometric projections of parts

Consider the construction of an isometric projection of a part, two types of which are given in Fig. 3.18, A.

Construction is carried out in the following order. First, draw the original shape of the part - a square. Then they build ovals depicting an arc (Fig. 3.18, b) and circles (Fig. 3.18, c).

Rice. 3.18.

To do this, find a point on a vertically located plane ABOUT, through which isometric axes pass X And z. By this construction, a rhombus is obtained, in which half of the oval is inscribed (Fig. 3.18, b). Ovals on parallel planes are built by transferring the centers of arcs to a segment equal to the distance between these planes. Double circles in Fig. 3.18 shows the centers of these arcs.

on the same axes X And z construct a rhombus with a side equal to the diameter of the circle d. An oval is entered into the rhombus (Fig. 3.18, c).

They find the center of the circle on a horizontally located face, draw isometric axes, build a rhombus into which an oval is entered (Fig. 3.18, G).

The concept of a dimetric rectangular projection

The location of the axes of the dimetric projection and the way they are constructed are shown in fig. 3.19. Axis z swipe vertically, axis X- at an angle of about 7 ° to the horizontal, and the axis at forms an angle of approximately 41 ° with the horizontal (Fig. 3.19, A). You can build axes using a ruler and a compass. For this, from the point ABOUT lay horizontally to the right and left of eight equal divisions (Fig. 3.19, b). From the extreme points, perpendiculars are restored. Their height is: for the perpendicular to the axis X - one division, for perpendicular to the axis at- seven divisions. The extreme points of the perpendiculars are connected to point O.

Rice. 3.19.

When drawing a dimetric projection, as well as when constructing a frontal one, the dimensions along the axis at are reduced by 2 times, and along the axes X And z put off without cuts.

On fig. 3.20 shows the dimetric projection of a cube with circles inscribed in its faces. As can be seen from this figure, circles in the dimetric projection are depicted as ellipses.

Rice. 3.20.

technical drawing

Technical drawing - this is a visual image, made according to the rules of axonometric projections by hand, by eye. It is used in cases where you need to quickly and clearly show the shape of an object on paper. This is usually necessary in design, invention and rationalization, as well as in teaching the reading of drawings, when, with the help of a technical drawing, it is necessary to explain the shape of the part shown in the drawing.

Performing a technical drawing, they adhere to the rules for constructing axonometric projections: the axes are placed at the same angles, the dimensions along the axes are also reduced, the shape of the ellipses and the sequence of construction are observed.

To perform an isometric projection of any part, you need to know the rules for constructing isometric projections of flat and volumetric geometric shapes.

Rules for constructing isometric projections of geometric shapes. The construction of any flat figure should begin with the axes of isometric projections.

When constructing an isometric projection of a square (Fig. 109), from the point O along the axonometric axes, half the length of the side of the square is laid in both directions. Through the resulting serifs, straight lines are drawn parallel to the axes.

When constructing an isometric projection of a triangle (Fig. 110), segments equal to half the side of the triangle are laid along the X axis from point 0 to both sides. On the Y-axis from the point O, the height of the triangle is plotted. Connect the resulting serifs with straight line segments.

Rice. 109. Rectangular and isometric projections of a square

Rice. 110. Rectangular and isometric projections of a triangle

When constructing an isometric projection of a hexagon (Fig. 111), from the point O, along one of the axes, lay off (in both directions) the radius of the circumscribed circle, and along the other - H / 2. Through the obtained serifs, straight lines are drawn parallel to one of the axes, and the length of the side of the hexagon is laid on them. Connect the resulting serifs with straight line segments.

Rice. 111. Rectangular and isometric projections of a hexagon

Rice. 112. Rectangular and isometric projections of a circle

When constructing an isometric projection of a circle (Fig. 112), segments equal to its radius are plotted along the coordinate axes from the point O. Through the resulting serifs, straight lines are drawn parallel to the axes, obtaining an axonometric projection of the square. From vertices 1, 3, arcs CD and KL are drawn with a radius of 3C. Connect points 2 with 4, 3 with C and 3 with D. At the intersections of straight lines, the centers a and b of small arcs are obtained, after drawing which they get an oval that replaces the axonometric projection of the circle.

Using the described constructions, it is possible to perform axonometric projections of simple geometric bodies (Table 10).

10. Isometric projections of simple geometric bodies

Methods for constructing an isometric projection of a part:

1. The method of constructing an isometric projection of a part from a shaping face is used for parts whose shape has a flat face, called a shaping face; the width (thickness) of the part is the same throughout, there are no grooves, holes and other elements on the side surfaces. The sequence for constructing an isometric projection is as follows:

1) construction of isometric projection axes;

2) construction of an isometric projection of the shaping face;

3) construction of projections of the remaining faces by means of the image of the edges of the model;

Rice. 113. Building an isometric projection of a part, starting from a shaping face

4) stroke of the isometric projection (Fig. 113).

1. The method of constructing an isometric projection based on the sequential removal of volumes is used in cases where the displayed form is obtained as a result of the removal of any volumes from the original form (Fig. 114).
2. The method of constructing an isometric projection based on a sequential increment (adding) of volumes is used to perform an isometric image of a part, the shape of which is obtained from several volumes connected in a certain way to each other (Fig. 115).
3. Combined method of constructing an isometric projection. An isometric projection of a part, the shape of which was obtained as a result of a combination of various shaping methods, is performed using a combined construction method (Fig. 116).

An axonometric projection of a part can be performed with an image (Fig. 117, a) and without an image (Fig. 117, b) of invisible parts of the form.

Rice. 114. Construction of an isometric projection of a part based on sequential removal of volumes

Rice. 115 Construction of an isometric projection of a part based on a sequential increment of volumes

Rice. 116. Using a combined method of constructing an isometric projection of a part

Rice. 117. Variants of the image of isometric projections of the part: a - with the image of invisible parts;
b - without the image of invisible parts

5.5.1. General provisions. Orthogonal projections of an object give a complete picture of its shape and dimensions. However, the obvious disadvantage of such images is their low visibility - the figurative form is composed of several images made on different projection planes. Only as a result of experience does the ability to imagine the shape of an object develop - “to read the drawings”.

Difficulties in reading images in orthogonal projections led to the emergence of another method that was supposed to combine the simplicity and accuracy of orthogonal projections with the clarity of the image, the method of axonometric projections.

Axonometric projection called a visual image resulting from the parallel projection of an object, along with the axes of rectangular coordinates to which it is referred in space, onto any plane.

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

Axonometry (from the Greek axon - axis, metreo - measure) is a construction process based on reproducing the dimensions of an object in the directions of its three axes - length, width, height. As a result, a three-dimensional image is obtained, perceived as a tangible thing (Fig. 56b), in contrast to several flat images that do not give a figurative form of an object (Fig. 56a).

Rice. 56. Visual representation of axonometry

In practical work, axonometric images are used for various purposes, so various types of them have been created. Common to all types of axonometry is that one or another arrangement of axes is taken as the basis for the image of any object. OX, OY, OZ, in the direction of which the dimensions of the object are determined - length, width, height.

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

A) rectangular- projecting rays are perpendicular to the picture plane (Fig. 57a);

b) oblique- projecting rays are inclined to the picture plane (Fig. 57b).

Rice. 57. Rectangular and oblique axonometry

Depending on the position of the object and the coordinate axes relative to the projection planes, as well as depending on the projection direction, the units of measurement are generally projected with distortion. The dimensions of the projected objects are also distorted.

The ratio of the length of an axonometric unit to its true value is called coefficient distortion for this axis.

Axonometric projections are called: isometric, if the distortion coefficients along all axes are equal ( x=y=z); dimetric, if the distortion coefficients are equal along the two axes ( x=z);trimetric, if the distortion coefficients are different.

For axonometric images of objects, five types of axonometric projections are used, established by GOST 2.317 - 69:

rectangular – isometric And dimetric;

oblique– frontal dimetric, frontalisometric, horizontal isometric.

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

It is always necessary to choose from all views the best view of a given image - the one that provides good visibility and ease of constructing axonometry.

5.5.2. General order of construction. The general procedure for constructing any type of axonometry is as follows:

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

b) build these axes in axonometric projection;

c) build an axonometry of the complete image of the object, and then its elements;

d) apply the contours of the section of the part and remove the image of the cut-off part;

e) circle the rest and put down the dimensions.

5.5.3. Rectangular isometric view. This type of axonometric projection is widely used due to the good visibility of images and the simplicity of construction. In rectangular isometry, axonometric axes OX, OY, OZ located at angles of 120 0 to one another. Axis oz vertical. axes OX And OY it is convenient to build, setting aside angles of 30 0 from the horizontal with the help of a square. The position of the axes can also be determined by setting aside five arbitrary equal units from the origin in both directions. Through the fifth division, vertical lines are drawn down and 3 of the same units are laid on them. The actual distortion coefficients along the axes are 0.82. To simplify the construction, a reduced coefficient of 1 is used. In this case, when constructing axonometric images, the measurements of objects parallel to the directions of the axonometric axes are postponed without reductions. The location of axonometric axes and the construction of a rectangular isometry of a cube, in the visible faces of which circles are inscribed, are shown in Fig. 58, a, b.

Rice. 58. The location of the axes of rectangular isometry

The circles inscribed in the rectangular isometry of the squares - the three visible faces of the cube - are ellipses. The major axis of the ellipse is 1.22 D, and small - 0.71 D, Where D is the diameter of the depicted circle. The major axes of the ellipses are perpendicular to the corresponding axonometric axes, while the minor axes coincide with these axes and with the direction perpendicular to the plane of the cube's face (thick strokes in Fig. 58b).

When constructing a rectangular axonometry of circles lying in coordinate or parallel planes, they are guided by the rule: the major axis of the ellipse is perpendicular to the coordinate axis, which is absent in the plane of the circle.

Knowing the dimensions of the axes of the ellipse and the projection of diameters parallel to the coordinate axes, it is possible to build an ellipse at all points, connecting them using a pattern.

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

Rice. 59. Building an oval

Through the dot ABOUT the intersections of the conjugate diameters of the ellipse draw a horizontal and vertical line and from it describe a circle with a radius equal to half the conjugate diameters AB=SD. This circle will intersect the vertical line at points 1 And 2 (centers of two arcs). From points 1, 2 draw arcs of circles with a radius R=2-A (2-D) or R=1-C (1-B). Radius OE make serifs on a horizontal line and get two more centers of mating arcs 3 And 4 . Next, connect the centers 1 And 2 with centers 3 And 4 lines that intersect with arcs of radius R give conjugation points K, N, P, M. Extreme arcs are drawn from the centers 3 And 4 radius R 1 =3-M (4-N).

The construction of a rectangular isometry of a part given by its projections is carried out in the following order (Fig. 60, 61).

1. Choose the coordinate axes X, Y, Z on orthogonal projections.

2. Build axonometric axes in isometry.

3. Build the base of the part - a parallelepiped. To do this, from the origin along the axis X postpone segments OA And OV, respectively equal to the segments O 1 A 1 And About 1 in 1 taken from the horizontal projection of the part, and get points A And IN through which straight lines are drawn parallel to the axes Y, and set aside segments equal to half the width of the parallelepiped.

Get points C, D, J, V, which are isometric projections of the vertices of the lower rectangle, and connect them with straight lines parallel to the axis X. From origin ABOUT along the axis Z postpone cut OO 1, equal to the height of the parallelepiped O 2 O 2´; through a point About 1 spend axis X 1 , Y 1 and build an isometry of the upper rectangle. The vertices of the rectangles are connected by straight lines parallel to the axis Z.

4. Build a perspective view of the cylinder. Axis Z from About 1 postpone cut About 1 About 2, equal to the segment O 2 ´O 2 ´´, i.e. the height of the cylinder, and through the point About 2 spend axis x2,Y2. The upper and lower bases 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. Sketchy generators of the cylinder are drawn tangent to both ellipses (parallel to the axis Z). The construction of ellipses for a cylindrical hole is performed in a similar way.

5. Build an isometric image of the stiffener. from point About 1 along the axis X 1 postpone cut O 1 E \u003d O 1 E 1. Through the dot E draw a line parallel to the axis Y, and lay on both sides segments equal to half the width of the rib E 1 K 1 And E 1 F 1. From the received points K, E, F parallel to axis X 1 draw straight lines until they meet the ellipse (points P, N, M). Next, draw straight lines parallel to the axis Z(lines of intersection of the planes of the rib with the surface of the cylinder), and segments are laid on them RT, MQ And NS, equal to the segments P 2 T 2, M 2 Q 2, And N 2 S 2. points Q, S, T connect and circle around the pattern, and the points K, T And F, Q connect with straight lines.

6. A cutout of a part of a given part is built, for which two cutting planes are drawn: one through the axes Z And X, and the other through the axes Z And Y.

The first cutting plane will cut the bottom rectangle of the box along the axis X(line segment OA), upper - along the axis X 1, and the edge - along the lines EN And ES, cylinders - along the generators, the upper base of the cylinder - along the axis X 2.

Similarly, the second cutting plane will cut the upper and lower rectangles along the axes Y And Y 1, and the cylinders - along the generators, the upper base of the cylinder - along the axis Y2.

Plane figures obtained from the section are shaded. To determine the direction of hatching, it is necessary to set aside equal segments from the origin of coordinates on axonometric axes, and then connect their ends.

Rice. 60. Construction of three projections of the part

Rice. 61. Making a rectangular isometry of a part

Hatching lines for a section located in a plane XOZ, will be parallel to the segment 1-2 , and for a section lying in the plane ZOY, are parallel to the segment 2-3 . Delete all invisible lines and stroke the contour lines. Isometric projection is used in cases where it is necessary to build circles in two or three planes parallel to the coordinate axes.

5.5.4. Rectangular dimetric projection. Axonometric images built with rectangular dimetry have the best clarity, but the construction of images is more difficult than in isometry. The location of axonometric axes in dimetry is as follows: axis oz directed vertically, and the axis OH And OY make up with a horizontal line drawn through the origin (point ABOUT), the angles are 7º10´ and 41º25´ respectively. The position of the axes can also be determined by setting aside eight equal segments from the origin in both directions; through the eighth divisions, lines are drawn down and one segment is laid on the left vertical, and seven segments on the right. By connecting the obtained points with the origin, determine the direction of the axes OH And OU(Fig. 62).

Rice. 62. Arrangement of axes in rectangular dimetry

Axial distortion coefficients OH, oz are equal to 0.94, and along the axis OY- 0.47. To simplify in practice, they use the given distortion coefficients: along the axes OX And oz coefficient is 1, along the axis OY– 0,5.

The construction of a rectangular dimetry of a cube with circles inscribed in its three visible faces is shown in fig. 62b. The circles inscribed in the faces are ellipses of two types. Axes of an ellipse located in a face that is parallel to the coordinate plane XOZ, are equal: the major axis is 1.06 D; small - 0.94 D, Where D is the diameter of the circle inscribed in the face of the cube. In the other two ellipses, the major axes are 1.06 D, and small - 0.35 D.

To simplify the constructions, you can replace the ellipses with ovals. On fig. 63 shows the techniques for constructing four center ovals that replace ellipses. An oval in the front face of a cube (rhombus) is constructed as follows. From the middle of each side of the rhombus (Fig. 63a), perpendiculars are drawn to the intersection with the diagonals. Received points 1-2-3-4 will be the centers of the mating arcs. The junction points of the arcs are in the middle of the sides of the rhombus. The construction can be done in another way. From the midpoints of the vertical sides (points N And M) draw horizontal straight lines until they intersect with the diagonals of the rhombus. The points of intersection will be the desired centers. From centers 4 And 2 draw arcs with a radius R, and from the centers 3 And 1 - radius R1.

Rice. 63. Construction of a circle in rectangular dimetry

An oval replacing the other two ellipses is performed as follows (Fig. 63b). Direct LP And MN, drawn through the midpoints of opposite sides of the parallelogram, intersect at a point S. Through the dot S draw horizontal and vertical lines. direct LN, connecting the midpoints of adjacent sides of the parallelogram, is divided in half, and a perpendicular is drawn through its midpoint until it intersects with a vertical line at a point 1 .

a segment is drawn on a vertical line S-2 = S-1.Straight 2-M And 1-N intersect a horizontal line at points 3 And 4 . Received points 1 , 2, 3 And 4 will be the centers of the oval. Direct 1-3 And 2-4 define junction points T And Q.

from centers 1 And 2 describe arcs of circles TLN And QPM, and from the centers 3 And 4 – arcs MT And NQ. The principle of constructing a rectangular dimetry of a part (Fig. 64) is similar to the principle of constructing a rectangular isometry shown in fig. 61.

When choosing one or another type of rectangular axonometric projection, it should be borne in mind that in rectangular isometry the rotation of the sides of the object is the same and therefore the image is sometimes not visual. In addition, the diagonal edges of the object in the image often merge into one line (Fig. 65b). These shortcomings are absent in the images made in rectangular dimetry (Fig. 65c).

Rice. 64. Building a part in rectangular dimetry

Rice. 65. Comparison of different types of axonometry

5.5.5. Oblique frontal isometric view.

Axonometric axes are arranged as follows. Axis oz- vertical, axis OH– horizontal, axis OU relative to the horizontal line is located above an angle of 45 0 (30 0, 60 0) (Fig. 66a). On all axes, the dimensions are set aside without abbreviations, in the true size. On fig. 66b shows a frontal isometry of the cube.

Rice. 66. Construction of an oblique frontal isometry

Circles located in planes parallel to the frontal plane are depicted in full size. Circles located in planes parallel to the horizontal and profile planes are depicted as ellipses.

Rice. 67. Detail in oblique frontal isometry

The direction of the axes of the ellipses coincides with the diagonals of the faces of the cube. For planes XOY And ZOY the magnitude of the major axis is 1.3 D, and small - 0.54 D (D is the diameter of the circle).

An example of the frontal isometry of the part is shown in fig. 67.