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Processing of simple objects
Processing of simple objects
A sectional view or section is a look inside an object. Sections are used to clarify the interior construction of a part that can not be clearly described using hidden lines in exterior views. By making an imaginary cut through the object and removing a portion, the interior features may be seen more clearly.
Horizontal, vertical, and inclined cutting planes are used to create these cuts (Pic. 3.1: a, b, c).
a) using a vertical cutting plane
b) using a horizontal cutting plane
c) using an inclined cutting plane
Picture. 3.1. Using cutting planes
Picture. 3.2. Parallel cross-sections
A cross-section is what you get when you cut straight through a shape (Pic. 3.2). Parallel cross-sections are cross-sections repeated in parallel across a solid.
Auxiliary planes are used to make a drawing of this shape if it is necessary to obtain views that are not shown in orthogonal projections and add dimensions to them. The cutting plane to be used should first be selected. The resulting section should be a simple geometric shape that is easy to construct.
Cross-sections of prism
Cross-sections of prism
A regular prism is a prism whose base is a regular polygon. The true face of the section will be a triangle or a polygon. The view and size of the section will depend on the cutting plane, its angle of inclination and height (see the video).
Cross-sections of pyramid
Cross-sections of pyramid
A regular pyramid is a pyramid whose base is a regular polygon, while the projection of the vertex coincides with the centre of a circle that is inscribed in or circumscribed around the base. The true face of a section will be a triangle or a polygon. The view and size of the section of the prism will depend on the cutting plane, its angle of inclination and height (see the video).
Cross-sections of cone
Cross-sections of cone
A cone has a circle as a base, and the vertex is above the centre of the base and its section. The true face of the section through the apex of the cone will be a triangle. The true edge of a section drawn parallel to the base will be a circle. The true face of a section drawn parallel to the generatrix will be a parabola.
If the plane intersects the cone through the generatrix and the base on one side of the axis of the cone, then the view of the true face of the section will be a hyperbola.
The true face of any other area passing through two opposite generatrices will be an ellipse (see the video).
Dimensions of truncated shapes
Dimensions of truncated shapes
When a simple shape is changed or processed (Fig. 3.3, a), the drawings of orthogonal projections of the shape change, and heights and angles must be shown (Pic. 3.3,b).
Picture 3.3: a) polyhedrons with their parameters,
b) truncated polyhedrons with dimensions
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