axonometric diagram

Chapter 7 Axonometric Drawings §7-1 Basic Knowledge of Axonometric Drawings Since axonometric drawings have a strong sense of three-dimensionality, they are also referred to as three-dimensional drawings. Reading axonometric drawings does not require specialized knowledge; ordinary people can understand them, and they are also easy to draw. As a result, they are widely used in various industries, especially in the mechanical industry for structural designs, schematic diagrams of how machines work, piping diagrams, and user manuals. They are also frequently used in the construction industry for visual renderings of buildings. I. Formation of axonometric projection: The method of projecting an object along with its reference rectangular coordinate system, in a direction that is not parallel to any of the coordinate planes, using parallel projection onto a single projection plane (the axonometric plane) to obtain a figure with a three-dimensional appearance, is called axonometric projection. The resulting figure is known as an axonometric projection diagram, or simply an axonometric drawing. Axonometric axes: The axonometric projection axes OX, OY, OZ. II. Axial angles and axial scaling factors 1. Axial angles: The angles between the two axonometric axes, ∠XOY, ∠XOZ, ∠YOZ. Used to control the shape changes in axonometric projection. 2. Axial scaling factor: The ratio of the length of the projection of a straight line segment on an object that is parallel to the coordinate axes onto the axonometric projection plane, to its actual length, is called the axial scaling factor. The axial scaling factors for the OX, OY, and OZ axes are denoted by p, q, and r respectively. The axial expansion coefficient calculated using mathematical methods is a non-integer, which poses many difficulties in drawing. In practice, simplified axial expansion coefficients are used when creating axonometric drawings. III. Basic properties of axonometric projections (the same as those of parallel projection) 1. Parallelism: If two lines in space are parallel to each other, then their axonometric projections are also parallel to each other. 2. Metricity: For any straight line segment parallel to the coordinate axes, its axonometric projection will be parallel to the corresponding axonometric axes, and its scaling factor will be the same as that of the respective axonometric axis; thus, it can be measured directly. (The origin of axonometry) 3. Proportionality: The ratio of the lengths of two line segments on a straight line is equal to the ratio of their axial projections. IV. Classification of axonometric drawings: Based on the different relative positions of the projection plane with respect to the projection direction, axonometric drawings are divided into two main categories:  Orthographic axonometric drawings: The axonometric projection direction is perpendicular to the axonometric projection plane.  Oblique axonometric projection: The axis of projection is inclined relative to the projection plane. Since the angles between the object’s reference rectangular coordinate axes and the axonometric projection planes vary, the axial scaling factors also differ. Therefore, the above two categories can be further divided into the following three categories:  Isometric or oblique isometric projection, where p=q=r  Ortho-isometric or oblique ortho-isometric projection, where p=q≠r, or p=r≠q, or q=r≠p  Ortho-triangular or oblique triangular projection, where p≠q≠r. **The standard (GB4458.3-84) recommends two types of axonometric projections that are relatively easy to draw:  Isometric axonometric projection  Oblique ortho-isometric projection §7-2 Isometric Axonometric Projection I. Angles between axes and axial scaling factors in isometric projection 1. Angles between axes: ∠XOY=∠XOZ=∠YOZ=120° 2. Axial scaling factors: The calculated axial scaling factors are p1=q1=r1=0.82; the simplified values are p=q=r=1 II. Points to note when drawing isometric axonometric projections 1. The edges of a solid that are parallel to the three coordinate axes will be parallel to the corresponding axonometric axes in the projection, allowing for direct measurement. 2. Edges that are not parallel to the three coordinate axes in three-dimensional space are also not parallel to any of the axonometric axes in axonometric drawings, and their lengths cannot be measured directly. 3. Edges that are parallel to each other in three dimensions remain parallel to each other in axonometric drawings as well. 4. Axonometric drawings usually show only the visible contour lines; the invisible contour lines are drawn only when necessary. III. Isometric drawing of planar solids – the coordinate method. Examples: triangular pyramid, hexagonal prism. Drawing steps: 1. Select coordinate axes and the coordinate origin on the planar solid ； 2. Draw the axonometric axes ； 3. Projections of various points on the bottom surface ； 4. Determine the projections of the other points based on the height ； 5. Connect the adjacent points on the same side in sequence, thicken the lines to complete the shape. IV. Isometric Drawing of Spherical Solids (I) Isometric drawing of a circle – ellipse; Rhombus method – similar to the four-center method: 1. Draw coordinate axes through the center of the circle, and then construct a square tangent to the circle with sides parallel to the coordinate axes ； 2. Draw the axonometric axes; measure the radius directly along the axis from point O. Draw lines parallel to the axonometric axes through the four intersection points on the axis, thereby obtaining the axonometric diagram of the square tangent to the circle – a rhombus ； 3. As the diagonals of a rhombus, connect the two endpoints of the shorter diagonal (O1, O2) with the four intersection points mentioned earlier; this yields the two intersection points O3, O4 on the longer diagonal ； 4. Draw arcs with centers at O1, O2, O3, and O4 respectively to obtain an approximate ellipse. (II) Methods for isometric projection of common solids – Examples: cylinders, cones. 1. Select coordinate axes and the coordinate origin (usually, the center of the base circle is chosen as the origin) ； 2. Draw the axonometric axes and determine the center of the base circle ； 3. Determine the center of the top circle based on the height, and draw its axonometric projection – an ellipse ； 4. Draw the visible parts of the axonometric projection of the circular base, and outline its two sides ； 5. Erase excess lines, darken the lines, and complete the graphic. (III) Method of drawing an isometric projection with rounded corners 1. Draw an isometric projection of a rectangular prism ； 2. Measure the radius of the corner, R, on the edge with the corner; from this measurement point, draw a perpendicular line to the edge line, and find their intersection point ； 3. With the obtained intersection point as the center, draw an arc with a radius equal to the distance from the intersection point to the foot of the perpendicular. Isometric projection with predefined rounded corners ； 4. Use the offset method (based on height relationships) to draw the arc on the other side ； 5. Erase excess lines, darken the lines, and complete the graphic. V. Methods for drawing isometric views of composite solids 1. Stacking method: Suitable for composite solids with a stacked structure. According to the stacking relationship of each basic shape, draw its axonometric diagram by stacking them one by one. 2. Cutting method: Suitable for cutting-type assemblies. First, draw the complete shape, then cut away the unwanted parts one by one. 3. Comprehensive method: Applicable to comprehensive combinations. Combine the above methods. VI. Methods of drawing orthographic projections of intersections and intersections of solids 1. Method of drawing orthographic projections of intersections: The coordinate method is commonly used, with the height of the element lines being utilized to determine the points on the intersection line. 2. Method of drawing an isometric projection of intersecting lines ① Coordinate method: Using the coordinates of the points on the intersecting lines in the projection diagram, the positions of these points are determined in the axonometric diagram, and then connected to form a smooth curve. ② Auxiliary plane method (not covered) §7-3 Oblique axonometric projection I. Axial angles and axial scaling factors in oblique axonometric projection 1. Axial angles: ∠XOZ=90°, ∠XOY=∠YOZ=135° 2. Axial scaling factors: p=r=1, q=0.5 II. Projection properties of oblique axonometric projection 1. Surfaces on an object that are parallel to the XOZ coordinate plane appear in their true shape in the oblique axonometric projection. 2. In oblique isometric projection, the thickness of an object is reduced by half. III. Method of drawing oblique isometric drawings 1. Determine a rectangular coordinate system in the view ； 2. Draw the previous shape — copy the original main view ； 3. At all turning points in this diagram, draw parallel lines along the OY axis; on these lines, mark a distance equal to 1/2 of the object’s thickness, and then draw the visible contour lines behind it ； 4. Erase excess lines, darken the strokes, and complete the graphic. §7-4 Axonometric Cross-Sections In axonometric drawings, in order to clearly show the invisible internal structures of an object, cross-sectional drawing techniques are often used, which we call axonometric cross-sections. I. Position of the cut in axonometric drawings: When making a cut in an axonometric drawing, it is generally not done by removing half of the object, but rather by removing one-quarter of it. That is, the object is cut using two mutually perpendicular cutting planes that are parallel to the coordinate planes. In this way, the inner and outer shapes of the object can be fully displayed. II. Direction of cross-hatching lines in axonometric drawings: In axonometric drawings, major cross-hatching lines are always represented by thin solid lines that are parallel to each other at equal intervals, but the directions of adjacent cross-hatches differ. III. How to draw axonometric sectional views Method 1: Draw the outer shape first, then the section (for beginners) 1. First, draw the complete outer shape of the composite body ； 2. Draw the cross-section profile at the selected cutting position ； 3. Draw the visible internal shape after cutting ； 4. Erase the cut-off part ； 5. Draw the cross-hatching ； 6. Thicken the line. Method 2: Draw the cross-section first, then the outer shape (for those who are skilled). 1. First, draw the shape of the cross-section ； 2. Then, based on their relationship to the cross-section, draw the shapes of the other parts ； 3. Draw the cross-hatching ； 4. Thicken all internal and external contour lines visible after sectioning.

Axonometric view of pipes: just make sure to get the direction right

I use software for automatic extraction; I haven’t drawn by hand in many years now and have completely forgotten how. None of the friends I know from those large complexes can draw by hand either. Haha! Either strive to evolve on your own, or accelerate degeneration by replacing one thing with another! ;P

The axonometric diagram commonly referred to in everyday language usually means an isometric diagram. By setting it to isometric snap in CAD, anyone can draw. It’s not that complicated.

Well, thank you all. I’ve just started working; I’m involved in simulation design, and I’ve never drawn axonometric diagrams before. I have to start drawing them tomorrow in order to prepare the stress analysis reports, hehe

Yes, in CAD: Tools -- Sketch Settings -- Snapping and Grids -- Grid Snapping -- set it to isometric snapping. Then you can use F5 to switch between different directions! Determine the north direction

I’ve already experienced it! It’s not as difficult as I thought.

Just pay attention to the markings and directions; the markings aren’t very convenient, so manual adjustments are required

Use 3D software to create it; PDMS or PDS can be used, and then it can be extracted – this is the simplest approach. Actually, it can also be drawn using CAD, just as the person on floor 7 said. As long as you keep the right direction, it’s actually not difficult.

I’ve really never drawn axonometric diagrams before; it’s been very enlightening. I need to study this properly*~~

The figure obtained by projecting an object, along with the rectangular coordinate system that defines it, onto a projection plane in a direction that is not parallel to any of the coordinate planes, using the method of parallel projection, is called an axonometric diagram. 　　Axonometric projection is a type of one-sided parallel projection; it is able to reflect the shapes of the front, side, and horizontal surfaces of a solid at the same time, thereby giving a strong sense of three-dimensionality. It is commonly used as an auxiliary drawing in engineering design and industrial production. 　　In engineering, the orthographic projection method is generally used to create projection drawings of objects. That is, the multiple orthogonal projection, which can fully and accurately reflect the shape and size of an object; it has good quality and is simple to draw, but it lacks a strong sense of three-dimensionality, and only those with certain skills in interpreting such drawings can understand it. Sometimes, in engineering, a type of diagram with a stronger sense of three-dimensionality is also used to represent objects, namely axonometric drawings. An axonometric drawing is a three-dimensional image created using axonometric projection; it resembles how people perceive things visually, but it cannot accurately reflect the true shape and size of an object. Moreover, drawing such diagrams is more complex than drawing orthographic projections. Therefore, in production, it is used as an auxiliary diagram to help people understand orthographic views. 　　In drawing instruction, axonometric drawings are also one of the means to develop spatial reasoning skills. Drawing axonometric diagrams can help people visualize the shape of objects and develop spatial imagination. 　Axonometric drawings can be divided into two main categories depending on the direction of the projection rays and the position of the axonometric projection planes: 　　Orthographic axonometric drawing: The direction of the projection rays is perpendicular to the axonometric projection plane. 　　Oblique axonometry: The direction of the projection rays is inclined relative to the axonometric projection planes. 　　Based on different axial expansion coefficients, each category can be further divided into three types: 1. Orthographic projection. Isometric projection (abbreviated as isometric): p1=q1=r1. 　　Orthographic projection (abbreviated as ortho-projection): p1=r1≠q1. 　　Orthographic projection (abbreviated as ortho-projection): p1≠q1≠r1. 　　2. Oblique axonometry Oblique isometric projection (abbreviated as oblique isometry): p1=q1=r1. 　　Oblique axonometric projection (abbreviated as oblique projection): p1=r1≠q1. 　　Oblique three-view projection (abbreviated as oblique three-view): p1≠q1≠r1. 　　Since computer-aided drawing has greatly simplified the creation of axonometric drawings, the classification of such drawings is no longer as important as it used to be. However, two types of axonometric drawings are commonly used in engineering: isometric and oblique axonometrics.