How to construct a top view based on two given ones. The order of constructing images in drawings

The presentation shows algorithms for constructing the missing species based on two given ones. Three cases are considered: when there is no front view, or top view, or left view. Construction of the missing view in the drawing is carried out using external or internal coordination.

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Constructing a missing view in a drawing based on two given

Drawings of geometric bodies are classified as projection drawing, and drawings of parts are classified as technical. Therefore, images on projection drawings are called projections, and on technical drawings they are called views. In drawing, quite often there are problems related to the construction of a third one using two given types. The drawing may not have a left, top or front view - main view. In all 3 cases, the work to construct the missing species is carried out using a single algorithm.

Algorithm for constructing a missing type of part based on two given ones. Based on the drawing, the geometric shape and symmetry of the parts are analyzed and the missing type is determined. Mentally imagine a visual image of the part. (It’s better to draw it to make your future work easier).

Based on the created visual image, the outline of the missing species is determined and its graphic composition is analyzed. Construct the missing view in the drawing using external or internal coordination. Build: An overall rectangle and draw the axis of symmetry (if the image is symmetrical); Visible outlines of the part (either from reference points or through connection lines); Invisible outlines. Apply dimensions. Trace the drawing.

Algorithm for constructing a missing part view using external coordination Left view Top view Front view Return to algorithm

1. Construct an overall rectangle of the missing type using a constant straight line, and draw the axes of symmetry 2nd action Selecting a type

2. Construct visible outlines of the image of the part on the missing view using communication lines 3rd action Selecting a view 1st action

3. Construct invisible outlines of the image of the part using projection communication lines Selecting type 2 action

1. Construct an overall rectangle of the missing type using a constant straight line, and draw the axes of symmetry 2nd action Selecting a type

2. Construct visible outlines of the image of the part on the missing view using communication lines 3rd action Selecting a view 1st action

3. Construct invisible outlines of the image of the part using projection communication lines Selecting type 2 action

Algorithm for constructing a missing part view using internal coordination Left view Top view Front view Return to algorithm

2. Construct the visible outlines of the image of the missing view from the reference point: Lower geometric body; Upper geometric body. 3rd action Select type 1st action

3. Construct invisible outlines of the image of the missing type of part using projection communication lines from reference points. Selecting type 2 action

1. Construct an overall rectangle and draw axes of symmetry in it: draw projection connection lines from one of the specified views, defining one of the dimensions of the overall rectangle; select a reference point; measuring on a second given view a second size of the overall rectangle; construct an overall rectangle of the missing type from the reference point; draw the axis of symmetry 2nd action Select the view

1. Construct an overall rectangle and draw axes of symmetry in it: draw projection connection lines from one of the specified views, defining one of the dimensions of the overall rectangle; select a reference point; measuring on a second given view a second size of the overall rectangle; construct an overall rectangle of the missing type from the reference point; draw the axis of symmetry 2nd action Select the view

2. Construct the visible outlines of the image of the missing view from the reference point: Lower geometric body; Upper geometric body 3 action Select type 1 action

3. Construct invisible outlines of the image of the missing part view using projection communication lines from reference points. Select view 2 action

Having completed the layout of the drawing and completed two specified projections of the part, they proceed to the next stage of work - constructing the third projection of the part.

Two specified projections can be: frontal and horizontal, frontal and profile. In both cases, the construction is performed in the same way.

In Fig. Figure 2 shows the construction of a profile projection based on given frontal and horizontal projections.

The construction was made using the method of rectangular (orthogonal) projection, i.e. all three images (projections) were constructed without violating the projection connection, but the coordinate axes and projection connection lines are absent in the drawing. To ensure that the projection connection is not disrupted when constructing images, it is necessary to apply a crossbar or triangle in the direction of the corresponding projection connection simultaneously to two projections on which at the moment carry out construction.

Based on two given projections, in this case frontal and horizontal, a profile is constructed by transferring dimensions in height from the frontal projection, and in width from the horizontal projection. To do this, first determine the location of the profile dimensional rectangle, draw the axis of symmetry and carry out the construction in the following order. Size A from frontal projection (part height) and size G from the horizontal projection (width of the part) is used when constructing an overall rectangle. The base of the model is a parallelepiped with a width G (already built) and height V , which is built on a profile projection, taken from the frontal one. To do this, to the front projection in height V apply a crossbar, and draw a thin horizontal line on the profile within the overall rectangle. The lower base of the model on the profile projection is constructed.

On the base of the model there is a quadrangular prism with two inclined faces. Its upper base is located at a height A from the lower base of the part and is already constructed as the height of the overall rectangle. It remains to construct the width of the upper and lower bases. They are the same size and equal in size d , which is taken on a horizontal projection. To do this, measure half the distance on a horizontal projection d and lay it down on the profile projection in both directions from the axis of symmetry. Two vertical lines are drawn through the constructed points, limiting the image of this prism. The prism standing on the base of the part is built.

The part has two slots: left and right. On the frontal projection they are depicted by lines of an invisible contour, and on the horizontal projection by a line of a visible contour. To construct them on a horizontal projection, half the distance is measured from the center line e and, accordingly, are laid on the lower base of the profile projection. Two thin lines are drawn upward from the constructed points, parallel to the axis of symmetry. They will limit the distance along the width of the slot. Its height (distance b ) are built according to the frontal projection, for which to the highest point of the distance b apply a crossbar and at this height, on the profile projection, draw a thin horizontal line limiting the slot from above.

You will need

• - a set of pencils for drawing of different hardness;
• - ruler;
• - square;
• - compass;
• - eraser.

Instructions

Sources:

• projection construction

Projection is strongly associated with exact sciences- geometry and drawing. However, this does not prevent it from occurring all the time in seemingly non-scientific and everyday things: the shadow of an object that falls on a flat surface in sunlight, sleepers railway, any map and any drawing is already nothing else? like a projection. Of course, creating maps and drawings requires an in-depth study of the subject, but the simplest projections can be created independently, armed only with a ruler and a pencil.

You will need

• * pencil;
• * ruler;
• * sheet of paper.

Instructions

The first method of constructing a projection is by central projection and is especially suitable for depicting objects on a plane when it is necessary to reduce or increase their actual size (Fig. a). The central design algorithm is as follows: we denote the design plane (P") and the design center (S). To project ABC into the plane P", we draw through the center point S and points A, B and C AS, SB and SC. Their intersection with the plane P" forms points A", B" and C", when connected by straight lines we obtain the central projection ABC.

The second method differs from the one described above only in that the straight lines with the help of which the vertices of the triangle ABC are projected into the P plane are not, but parallel to the designated design direction (S). Nuance: the design direction cannot be parallel to the P plane. When connecting projection points A"B"C" we get a parallel projection.

Despite its simplicity, the skill of constructing such simple projections helps to develop spatial thinking and can easily be a step in the descriptive.

Video on the topic

One of the most fascinating tasks in descriptive geometry is the construction of the third kind given two. It requires a thoughtful approach and pedantic measurement of distances, so it is not always given the first time. However, if you carefully follow the recommended sequence of actions, it is quite possible to construct the third view, even without spatial imagination.

You will need

• - a sheet of paper;
• - pencil;
• - ruler or compass.

Instructions

First of all, try the two available kind m determine the shape of individual parts of the depicted object. If the top view shows a triangle, then it can be a prism, cone of revolution, triangular or. The shape of a quadrangle can be taken by a cylinder, or a triangular prism or other objects. An image in the shape of a circle can represent a sphere, cone, cylinder, or other surface of revolution. Anyway, try to imagine general shape the subject as a whole.

Draw the boundaries of the planes for ease of transferring lines. Start with the most convenient and understandable element. Take any point that you definitely "see" on both kind x and move it to the third view. To do this, lower the perpendicular to the boundaries of the planes and continue it on the next plane. Please note that when switching from kind on the left in the top view (or vice versa), you must use a compass or measure the distance using a ruler. So in place of your third kind two lines intersect. This will be the projection of the selected point onto the third view. In the same way, you can do as many points as you like until it becomes clear to you general view details.

Check the correctness of the construction. To do this, measure the dimensions of those parts of the part that are completely (for example, a standing cylinder will be the same “height” in the left view and the front view). In order to make sure that you don’t mind, try from the position of an observer from above and count (at least approximately) how many boundaries of holes and surfaces should be visible. Every straight line, every point must have a reflection on everyone kind X. If the part is symmetrical, do not forget to mark the axis of symmetry and check the equality of both parts.

Delete all auxiliary lines, check that all invisible lines are marked with a dotted line.

To depict a particular object, first its individual elements are depicted in the form of simple figures, and then their projection is performed. The construction of projection is quite often used in descriptive geometry.

You will need

• - pencil;
• - compass;
• - ruler;
• - reference book “Descriptive Geometry”;
• - rubber.

Instructions

Carefully read the conditions of the task: for example, the frontal projection F2 is given. The point F belonging to it is located on the side of the cylinder. It requires the construction of three projections F. Mentally imagine how it all should look, then start building the image.

A cylinder of rotation can be represented as a rotating rectangle, one of the sides of which is taken as the axis of rotation. Second rectangle - opposite axis rotation - lateral surface cylinder. The rest represent the bottom and top of the cylinder.

Due to the fact that the surface of the cylinder of rotation when constructing given projections is made in the form of a horizontally projecting surface, the projection of point F1 must necessarily coincide with point P.

Draw the projection of point F2: since F is on the front surface of the cylinder of rotation, point F2 will be point F1 projected onto the lower base.

Construct the third projection of point F using the ordinate axis: place F3 on it (this projection point will be located to the right of the z3 axis).

Video on the topic

Please note

When constructing image projections, follow the basic rules used in descriptive geometry. Otherwise, projections will not be possible.

Useful advice

To construct an isometric image, use the top base of the rotation cylinder. To do this, first construct an ellipse (it will be located in the x"O"y plane). After that, draw tangent lines and the lower half-ellipse. Then draw a coordinate polyline and use it to construct a projection of point F, that is, point F."

Sources:

• Construction of projections of points belonging to a cylinder and a cone
• how to construct a cylinder projection

Horizontals - isohypses (lines of equal heights) - lines that connect on earth's surface points that have the same height marks. The construction of contour lines is used to compile topographic and geographical maps. Contour lines are constructed based on measurements with theodolites. The places where the cutting planes exit outward are projected onto horizontal plane.

Instructions

The level surface for measuring horizontal lines in Russia is considered to be the zero of the Kronstadt water gauge. It is from this that the horizontal lines are counted, which makes it possible to connect with each other separate plans and maps drawn up by various organizations. Horizontal lines determine not only landform, but also the relief of water basins. Isobats (water contours) connect points of equal depth.

To indicate the relief, general symbols are used, which are contour (scale), non-scale and explanatory. In addition, there are additional elements that accompany conventional signs. They include all kinds of inscriptions, rivers, and color schemes for the cards.

There are two ways to construct a horizontal line on a plan between two points: graphical and analytical. To graphically plot the horizontal line on the plan, take graph paper.

Draw several horizontal parallel lines at equal distances on the paper. The number of lines is determined by the number of required sections between two points. The distance between the lines is assumed to be equal to the specified distance between the horizontal lines.

Draw two vertical parallel lines at a distance, equal to the distance between given points. Mark these points on them, taking into account their height (altitude). Connect the dots with a slanted line. The points where the line intersects the horizontal lines are the points where the cutting planes exit outward.

Transfer the segments obtained as a result of intersection to horizontal straight line connecting two given points, by the orthogonal projection method. Connect the resulting points with a smooth line.

To construct contour lines using the analytical method, formulas derived from the characteristics are used. In addition to these methods, today they are used to construct contour lines. computer programs, such as "Archicad" and "Architerra".

Video on the topic

Sources:

• the horizontal is like in 2019

When creating an architectural project or developing an interior design, it is very important to imagine how the object will look in space. You can use axonometric projection, but it is good for small items or details. The advantage of frontal perspective is that it gives an idea not only of appearance object, but allows you to visually imagine the ratio of sizes depending on the distance.

You will need

• - a sheet of paper;
• - pencil;
• - ruler.

Instructions

The principles of constructing a frontal perspective are the same for a piece of Whatman paper and a graphic editor. So do it on a sheet of paper. If the item is small, A4 format will be sufficient. For frontal perspective or interior, take a sheet. Lay it horizontally.

For a technical drawing or drawing, select a scale. Take as a standard some clearly distinguishable parameter - for example, a building or the width of a room. Draw an arbitrary segment corresponding to this line on the sheet and calculate the ratio.

This one will become the base of the picture plane, so place it at the bottom of the sheet. Designate the end points, for example, as A and B. For a picture, you don’t need to measure anything with a ruler, but determine the ratio of the parts of the object. The sheet must be larger than the picture plane in order to

“Construction Problems” - All problems that can be solved with a compass and ruler can be solved with origami. The process of solving a construction problem using a compass and ruler is divided into 4 stages: Analysis Construction Proof Research. Results of control sections. Methods for identifying the level logical thinking students.

“Two Captains Kaverin” - V.A. Kaverin. The image of Captain Ivan Lvovich Tatarinov recalls several historical analogies. By an absurd accident, Sanya's father is accused of murder and arrested. And returning to Polyarny, Sanya also finds Katya at Dr. Pavlov’s. The expedition did not return. The boys walk to Moscow.

“Building graphs” - Solution key: Construct on a plane a set of points given by the equation: From the drawing we can easily read the answer. Parallel translation along the x-axis. Symmetrical display relative to the ordinate axis. Find all values ​​of the parameter a for each of which the system. Tasks elective course. Let us plot the graphs of the function with a dotted line in one coordinate system.

“Constructing graphs of functions” - Topic: Constructing graphs of functions. Graph of the function y = sinx. Draw a graph of the function y=sin(x) +cos(x). Completed by: Filippova Natalya Vasilievna mathematics teacher Beloyarsk secondary secondary school No. 1. Tangent line. Plotting a graph of the function y = sinx. Algebra.

“Linear Equation in Two Variables” - Definition: An algorithm for proving that a given pair of numbers is a solution to an equation: An equality containing two variables is called an equation in two variables. Give examples. -Which equation with two variables is called linear? -What is an equation with two variables called? Linear equation with two variables.

“Two Frosts” - Well, how did you cope with the woodcutter? And when we got there, I felt even worse. The other one answers: - Why not have fun! Well, I think we’ll get there, and then I’ll grab you. Live as long as I do, and you’ll know that an ax keeps you warmer than a fur coat. How can we have fun - freezing people? Two frosts. The older brother, Frost - Blue Nose, chuckles and pats his mitten against his mitten.

Date____

Grade: 9 ""

Topic: Construction of the third type of object based on two data

Goal: to teach how to construct the third type of object based on two data

Tasks:

Consolidate knowledge about the types in the drawing;

Develop spatial understanding and thinking, the ability to analyze the geometric shape of an object and skills in working with drawing tools;

To educate: hard work, accuracy, creative attitude to work, independence

Lesson type: combined

Lesson methods: explanatory - illustrative, practical

Form of organization: collective, individual

Lesson progress

Org moment

Repetition

2 . Test

Post new

First of all, you need to find out the shape of individual parts of the surface of the depicted object. To do this, both given images must be viewed simultaneously. It is useful to keep in mind which surfaces correspond to the most common images: triangle, quadrilateral, circle, hexagon, etc.

In the top view, a triangular prism, triangular and quadrangular pyramids, a cone of rotation, etc. can be depicted in the shape of a triangle.

Let's analyze the construction of the left view based on the data from the main view and the top view

The shape of many objects is complicated by various cuts, cuts, and intersections of surface components. Then you first need to determine the shape of the intersection lines, and you need to build them at individual points, introducing designations for the projections of points, which after completing the construction can be removed from the drawing.

In Fig. a left view of an object is constructed, the surface of which is formed by the surface of a vertical cylinder of rotation, with a T-shaped cutout in its upper part and a cylindrical hole with a frontally projecting surface. The plane of the lower base and the frontal plane of symmetry F are taken as the base planes. The image of the L-shaped cutout in the view on the left is constructed using the cutout contour points A B, C, D and E, and the intersection line cylindrical surfaces- using points K, L, M and symmetrical ones. When constructing the third type, the symmetry of the object relative to the plane F was taken into account.

Consolidation

Work using cards (build using two given third view)

Bottom line

Construction of the third type by measurement.

Opens (Fig.9) (technical drawing closed.

If the part is not very complex and for some reason it is impossible to make a projection connection with the top view, the third view is plotted using a ruler. If the part is simple and you can visualize it in your mind, there is no need to create a technical drawing.

Question: Who will build the top view of this part?

The student is called at will and builds a left view of part 9 on the IAD.

A technical drawing of the part is opened for verification.

Summary: This method cannot always be applied. For example, if there was no projection relationship between the front view and the top view, would we be able to construct the cut line? No. Therefore, I still recommend that you adhere to the projection connection in all three views.

4.Now let's return to our original task. In the lessons we will use the “constant line” method to construct a drawing.

You have images of two types of parts printed on paper on your table.

Task 1: Glue the first task into your notebook so that there is space left for constructing the third type. Place the notebook horizontally. Draw a constant straight line. Build a third view.

Students work in a notebook.

The one who completed the task first completes it on the IAD.

There are several solutions to this problem.

Question: Who will find another solution?

Students take turns coming to the board and offering

your decisions. Are opening (Fig. 6, 5, 4, 3, 2)

5. Exercises for the eyes.

To give our eyes a rest, let’s do some gymnastics for them.

Hold a pencil at arm's length in front of you. Without taking your eyes off it, bring it to the bridge of your nose, move it straight away from you (several times), then at arm's length, following the pencil, move it to the right - to the left.

6. Task2:We pasted the second task into the notebook. We built a third type based on two types of parts.

Opens(Fig. 10) Technical drawing closed.

The first one to complete it in a notebook draws it on the board.

In case of difficulty, the technical drawing of the part is opened or for verification after completing the task.

7. Homework:

A. D. Botvinnikov Section 13.4. At the end of the exercise paragraph: Fig. 112, 113,114.

Paste task 3 into your notebook.(Fig. 11) Based on two types of parts, construct a third one.