You will need
- - base diameter
- - the height of the cone
Build X and Y axis at an angle of 120°. Vertically upward from their intersection guide axis Z.
Build on the axes of the rhombus whose side is equal to the base diameter of the cone.
Fill in the auxiliary rhombus oval.
Aside from the center of the ellipse the height of the cone parallel to the axis Z.
Swipe from the top of the cone tangent to the ellipse at the base.
Determine the visibility of lines in the drawing. Visible lines are solid, invisible, dotted line, axial - dash-dotted line.
If you need to build a cone you have to build another subsidiary rhombus on the height of cut and re-enter it in the oval. This is true for the cone, cut by a plane parallel to the base of the cone. If the cut plane is positioned at an angle, then the build will be different.
Auxiliary building complete solid pencil, so they will be less noticeable. Visible lines are constructed of a cone circle with a soft pencil.
Advice 2: How to build a truncated cone
The need to build various geometric solids regularly occurs in the manufacture of various sheet metal products paper plastics and in many other situations. To create a three-dimensional truncated cone, a prism or a cylinder is possible only after you run the scan. This can be done both by the classical method using ruler and compass, and in some computer programs.
You will need
- - parameters of a truncated cone;
- - the range;
- a pair of compasses;
- - a sheet of paper;
- - computer programs such as AutoCAD or Autodesk.
To build a direct scan of a truncated cone , you must know some of its parameters. The job must be specified as the minimum radius of the top and bottom of the base and height. There may be other options. For example, instead of height can be specified the angle of inclination of the generatrix to the lower base. Sometimes, given the length, height and one radius. In this case, you need to calculate the dimensions that allow you to build scan most convenient way.
Start with a classic build on a piece of paper. Using the compass, draw the bottom base. The specified or calculated its radius label as r'. Calculate circumference by the formula P=2nr'. This length is equal to the length of the arc bounding the lateral surface of the complete or a truncated cone. The full length of the generatrix of the cone, denote as R'.
Sector angle, the arc length of which you already found, compute exactly the same as full cone. It is the ratio of the radius of the circle base to the image, multiplied by 360°. That is, α=r'/R'*360°. Draw scan the lateral surface of the complete cone. It will continue the base radius to the length of R' and mark the centre of the sector. Using the protractor set aside from it calculated the angle α, connect this point with the centre of the sector and continue straight. Draw an arc of radius R' between these lines.
Calculate the length of the generatrix of the truncated cone R". If it is set in the condition, then set it from the points of intersection R' and the lower base, that is, from the ends of already drafted sector. Plotting points connect the arc. Its radius is equal to the difference R' and R" and the angle is the same α at the vertex of the sector. Angle and the upper part forming a full cone you no longer need, side scan you have prepared. Left to draw only the upper base. To the drawing looked better, continue one of the lines bounding the lateral surface, the size of r and draw the circle.
Computer programs allow you to drill much faster and with less effort than the classic build. However, the principle remains the same. In AutoCAD, fastest way to perform a full scan of the cone. Performs the same calculations as in the classical method, only you can make them using the built-in calculator.
Draw an isosceles triangle, one of whose sides is equal to twice the radius of the lower base of the cone, and the side — forming a complete cone.
Draw a circle with a radius equal to the generatrix of the cone. Cut off from her arc, any subsidiary having direct and using the Trim command. The extra line remove.
Find the menu "Properties". You will find the boxes in which you can enter the parameters of the angle, start angle and end angle. In the first enter a zero value, and what to write in the second — calculate with built-in calculator or enter the already known parameter. When using a built-in calculator 360° dial using the keypad.
Using the mouse, specify the base radius. Don't forget that it starts with the middle of the already drawn triangle and ends at the lower vertex. Enter the icon "/" from the keyboard and specify the length of the generatrix. You will have a window with parameters of the full cone. Press "Enter".
In exactly the same way, calculate and draw the lateral surface is full of small cone that forms in which is the difference between the generatrix of existing full cone and the part that will be clipped. The angle thus calculated is not necessary, it already is. Put the drawings on top of one another, aligning the angle of the line and restricting it. The point of intersection of the upper arc forming and connect auxiliary line.
Build both bases. They represent a circle. The diameter of the first base of an existing triangle. The diameter of the second auxiliary line between the points of intersection of the upper arc forming. Extra auxiliary lines clean.
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.