4th topic
4.1. Combined simplest shapes. Dimensioning
Embedded Files
Picture 4.1. Complex prisms
Overview
Overview
As described in the previous topics, primary bodies include the cylinder, cone, sphere, prism, and pyramid. The world of geometric bodies is very wide, but most of them are combinations of different primary bodies. The main classes are polyhedrons and shapes of rotation.
In volumetric modelling, commands for editing (rounding, trimming, etc.) offer great possibilities, making it possible, for example, to form rather complex shapes from a prism (Pic. 4.1).
The intersection of polyhedrons
The intersection of polyhedrons
The type of intersection depends on the type of intersecting solids and how they intersect. Two intersecting solids may be of the same type (e.g., prism and prism, Pic. 4.2, 4.3 and 4.4) or different types (e.g., prism and pyramid, Pic. 4.5).
The line of intersection between two prisms is a closed figure composed of some lines meeting at the vertices. The two solids may intersect in different ways. The axes of the solids may be parallel, inclined, or perpendicular to each other.
Turn around prisms and define the prisms' intersection lines!
Picture 4.2. Simple shapes and their combinations.
Picture 4.3. The intersection of two prisms: main views and sample of a roof.
Picture 4.4. Intersection of two prisms: main views and detail of a wooden construction.
The intersection of cylinders and a cone
The intersection of cylinders and a cone
Lines of sections of cylinders are ellipses, but in pictorial views, you can see straight lines (Pic. 4.6). Intersections must be represented on multiview drawings correctly and clearly. For example, when a cone and cylinder intersect (Pic. 4.7), the type of intersection that results will depend on their sizes and on the angle of intersection relative to their axes. The line of intersection is determined using auxiliary views and cutting planes.
Picture 4.6. Intersection of cylindrs: main views and sample of models
Picture 4.7. Intersection of cylinder and cone: main views and sample of models
Picture 4.8. Intersection of cylinders and a prism: main views and detail of model.
The intersection of prism and cylinder
The intersection of prism and cylinder
Intersecting shapes with coincident axes are shown in the example of a fastener part. The intersection line of the two shapes is very well represented in all projections. (Pic. 4.8).
Picture 4.9. Simple shapes and their combination.
Constructive Solid Geometry (CSG)
Constructive Solid Geometry (CSG)
Constructive solid geometry (CSG, previously known as computational binary solid geometry), a technique used in solid modelling, allows a modeller to create a complex surface or object using Boolean operators to combine simpler objects, making it possible to generate visually complex objects with only a few primitive ones.
Each primitive is defined as a combination of volumes.
Typical standard primitives are the cone, cylinder, sphere, torus, right-angle wedge, and swept solids.
Boolean operations are union (U), intersection ( ౧) and difference (-), which are also used in mathematics as addition or subtraction.
In the animated picture 4.9, you can see the result of Boolean operations using a cube, sphere, and cylinders.
The same principles of modelling are applied to building projects when CAD and BIM are used. The next example will show you how we can use CSG when modelling houses (Pic. 4.10).
Picture 4.10: a) House modelling example; b) Roofs' examples.
Photos of different roofs for comparison with previously described examples of intersections of different shapes.
Dimensioning
Dimensioning
The process of adding size information to a drawing is known as dimensioning the drawing. Once the shape of a part is defined with orthographic drawings, size information is added in the form of dimensions.
A dimension is a numerical value expressed in appropriate units of measurement and used to define the size, location, orientation, form or other geometric characteristics of a part.
Rules of Dimensioning
1. Dimensions are used to define the length, width, height, diameter of circles (Ø), and radius of arcs (R).
2. Positioning dimensions define the centre of the circles and other key features.
3. The size and position of each element are determined only once.
4. The dimension of an element in a view showing its characteristic form should include a size mark Ø or ☐.
5. There must be at least 10 mm between the object and the first row of dimensions. Consecutive rows of dimensions must be equal and separated by at least 7 mm.
6. Dimensions are placed outside of views, except in the case of large circles.
7. Sizes are placed as they increase, and measurement lines must not intersect each other or distance lines.
8. The dimensions of several identical elements should be shown only once.
Pictures 4.11. Examples of dimensions
a) Datum Plane Dimensioning - Continuous
b) Cylindrical dimensions
c) Arcs dimensions
d) Angle dimensioning using Coordinates and Angular methods
Arrangement and indication of dimensions
Arrangement and indication of dimensions
Chain dimensioning (Pic. 4.12, a) is a dimensioning system that shows dimensions from point to point or a series of adjacent dimensions in one horizontal row. When chain dimensioning is used, the location of one feature is based on the location of the previous feature. Chain dimensioning is used when it is important that two features are located at a certain distance from each other, for example, two fixed holes with two fixed pins that must be a certain distance from each other.
Parallel Dimensioning (Pic. 4.12, b) is needed when a number of dimensions is measured in the same direction from a common surface or line. The dimension lines are parallel to each other and equally spaced.
Combined Dimensioning (Pic. 4.12, c) combines chain and parallel dimensioning in the same drawing.
Progressive Dimensioning (Pic. 4.12, d) is used when a dimension has to be established from data. Overall dimensions are placed outside smaller dimensions, and this dimension is shown using a common reference line.
Dimensioning by Coordinates (Pic. 4.12, e) can be used in place of other dimensioning styles, to make a drawing easier to read. This method is used when a number of holes of different sizes have to be dimensioned.
Equidistant Dimensioning (Pic. 4.12, f) uses the product of the spacing and the dimension value. A point is said to be equidistant from a set of objects if the distance between the point and each object in the set is equal.
Repeated Dimensions (Pic. 4.12, f) are used when certain features or elements of the same size are repeated a number of times in a drawing, to avoid the repetition of the same dimension everywhere. The product of a number of repeated features and the dimension value may be indicated at only one such feature.
Picture 4.12. Examples of indications of dimensions
a) Chain dimensioning
b) Parallel Dimensioning
c) Combined Dimensioning
d) Progressive Dimensioning
e) Dimensioning by Coordinates
f) Equidistant and Repeated Dimensioning
Page updated
Report abuse