You will need
- — a sheet of drawing paper;
- — the range;
- a pair of compasses;
- — protractor.
Construct with a ruler and protractor or compass and ruler coordinate axes for rectangular (trigonalidae) isometric projection. In this kind of axonometric projection, all three axes OX, OY, OZ form between them angles of 120°, while the axis OZ is the vertical direction.
For simplicity, draw the isometric projection without distortion on the axes, so as is customary isometric distortion to equate to unity. By the way, the word "isometric" in Greek means "equal size". In fact, when displaying a three-dimensional object on a plane the ratio of the length of any projected line segment parallel to coordinate axis, to the valid length of this part is the same for all three axes of 0.82. Therefore, the linear dimensions of the object in the isometric (when the adopted distortion ratio) increased to 1.22 times. The image is correct.
Start to project the object on a perspective plane with its top face. Measure along axis OZ from the centre of intersection of the axes of the coordinate height of the part. Fine with axis lines X and Y through that point. The same point put half of the cut part length on one axis (e.g. the Y axis). Swipe through the point cut the desired size (width of part) parallel to the other axis (OX).
Now along the other axis (OX) set aside the half-width. Through this point guide cut the desired size (length of part) parallel to the first axis (OY). Two drawn line segment must intersect. Extend the remaining part of the upper face.
If this face has a circular opening, draw it out. In the isometric circle is shown as a ellipse, because we look at it at an angle. The dimensions of the axes of this ellipse calculate based on the diameter of the circle. They are equal: a = 1,22 D and b = 0,71 D. If the circle is on a horizontal plane, the axis a of the ellipse is always horizontal, the axis b is vertical. The distance between the points of the ellipse on the X-axis or Y is always equal to the diameter of the circle D.
Draw three corners of the upper edge of the vertical fin equal to the height of the part. Connect edges through their bottom points.
If the figure has a rectangular hole, draw it out. Aside from the center of the rib top face vertical (parallel to Z-axis) cut the desired length. Through the obtained point to draw a segment of the required size parallel to the top face, and hence the x-axis From the extreme points of this segment, draw a vertical rib desired value. Connect them to the bottom. Swipe from the bottom right point of the diamond is drawn the inner edge of the hole, which should be parallel to the y-axis.
Advice 2 : How to draw in isometric
Construction of isometric projection of the part allows to obtain the most detailed view on the spatial characteristics of the object image. Isometric cutaway of the part in addition to appearance shows the internal structure of the subject.
You will need
- - a set of drawing pencils;
- - the range;
- - triangles;
- - protractor;
- a pair of compasses;
The drawing in the isometric view select a location depicted part or device, which will be visible all the time.
After you select the location, decide what type of isometry you will perform. There are two types of isometry: isometric rectangular and horizontal oblique isometric (or military perspective).
Draw axis thin lines so that the image is located in the center of the sheet. In a rectangular isometric angles between the axes are one hundred and twenty degrees. In a horizontal oblique isometric angles between the X and Y axes are ninety degrees. And between X and Z; Y and Z one hundred and thirty-five degrees.
Begin performing isometric with the upper surface of the depicted items. From the corners of horizontal surfaces swipe down the vertical line and mark on these lines the corresponding linear dimensions from the detail drawing. In the isometric linear dimensions on all three axes remain a multiple of the unit. Sequentially connect the points obtained on the vertical lines. The external contour of the part ready. Follow the images available on the faces of holes, grooves, etc.
Remember that when drawing objects in isometric view the appearance of curvilinear elements will be distorted. A circle in isometric view is depicted as an ellipse. The distance between the points of the ellipse on the axes of isometries is equal to the diameter of the circle, and the axes of the ellipse do not coincide with the axes of the isometric view.
If the item has a hidden cavity or a complex internal structure, complete the isometric projection with the cutout of the part. The neckline can be simple or stepped depending on the complexity of the part.
All steps must be performed using the drawing tools — ruler, pencil, compass and protractor. Use multiple pencils of different hardness. Solid — thin lines, hard-soft — dotted and dash-dotted lines, soft — for main lines. Don't forget to draw and fill in the title block and frame in accordance with GOST. Design isometric can be performed in specialized software such as Compass, AutoCAD.
Advice 3 : How to build isometric projection
All objects of reality exist in three-dimensional space. In the drawings they have to portray in a two dimensional coordinate system, and it does not give the viewer an adequate understanding of how the object looks in reality. Therefore, technical drawing, apply the projection, allowing to transfer the amount. One of them is called isometric.
You will need
- - drawing utensils.
Construction of isometric projections start with the arrangement of the axles. One of them is always vertical, and in the drawings it is usually designated as the Z axis, the Initial point is denoted as O. we Continue the axis OZ down.
The remaining two axes can be defined in two ways, depending on what drawing tools you have. If you have a protractor, set aside from the axis OZ in both sides of the angles equal to 120º. Swipe X and y axes.
If you have only a compass, draw a circle of arbitrary radius with center at point O. let's Continue the axis OZ until its second intersection with the circle and a dot, for example, 1. Spread the legs of the compasses at a distance equal to the radius. Draw a arc with center at point 1. Mark the point of intersection with the circle. They also indicate the directions of the axes X and Y. the left side of the Z-axis moves the X axis to the right - Y.
Construct an isometric projection of a plane figure. The coefficients of distortion in isometric along all axes are accepted 1. To construct a square of side a, put it away from point O of the axes X and Y and make the serifs. Swipe through the resulting points straight lines parallel to both these axes. Square in this projection looks like a parallelogram with angles of 120º and 60º.
To build the triangle, it is necessary to continue the X-axis so that a new part of the beam is located between the axes Z m Y. Divide the side triangle in half and mark the resulting dimension from the point On the X-axis in both directions. On the Y-axis put the height of the triangle. Connect the ends of the segment located on the X-axis, with the resulting point on the y-axis.
In a similar way is constructed in an isometric projection and a trapezoid. On the X-axis in one and the other side of the point About set aside half of the base of this geometric figure, and the Y - axis height. Using the tick marks on the Y-axis guide line parallel to the X-axis, and mark on it in both directions half of the second founding. Connect the resulting points with ticks on the x-axis.
A circle in isometric view looks like an ellipse. It can be constructed as the coefficient of distortion, and without. In the first case, the large diameter is equal to the diameter of the circle, and the small amount of 0.58 from him. When you build without accounting for this factor axis of the ellipse will be equal to, respectively, 1.22 and 0.71 diameter of the original circle.
Flat figures can be located in space both horizontally and vertically. As a basis we can take any axis, principles of construction remain the same as in the first case.
Dimensional object of complex shape, analyze and mentally divide it into more simple, is better every way to present a close to form geometric shapes. It may be necessary to postpone the dimensions are not on the axes, and parallel to them lines. The distance between these lines depend on the shape of the part. For example, one of the axes to postpone the distance from the edge to a recess or protrusion and draw a line parallel to the other two axes. Isometric projection of a fragment in this case is based not on the main grid, and additional.