Understanding the Dihedral System in Technical Drawing
Understanding the Dihedral System
The Dihedral System uses orthogonal projection onto two planes perpendicular to each other. To represent it on a plane (vertical plane), it is rotated perpendicularly (horizontal) 90 degrees around the intersection line (ground line). In addition to these two planes, a third plane perpendicular to the preceding ones (profile plane) is generally considered. Its representation is made by projecting onto the vertical plane around the line of intersection.
Dimension line: A segment topped by small lines or dots on both ends, indicating the extent of the referenced object.
Concept of Dimension and Distance
- Height (Cota) of a point is the distance between that point and the horizontal plane. It is the same as the distance between the vertical projection of the point and the ground line.
- Offset (Withdrawal) is the distance from the point to the vertical plane, i.e., the distance between the horizontal projection of the point and the ground line.
General Positions of a Point in the First Quadrant
The multiple positions a point may have in the first quadrant are reduced to six general positions.
Dihedral System Description
Also called dual projection, or Monge, it is a cylindrical projection system in which only orthogonal projection is used.
Its basic elements are:
- Vertical Plane
- Ground Line
- Horizontal Plane
Each of the planes, when intersecting with the former, is divided into two half-planes separated by the aforementioned ground line. This leaves the space divided into four dihedral angles, called the first, second, third, and fourth quadrants.
1st Quadrant | 2nd Quadrant
3rd Quadrant | 4th Quadrant
To represent the two projections in space on a plane (in our case, on paper), the dihedral system requires that both projections are positioned on a single plane. The plane of the drawing is achieved by a simple rotation around the ground line.
Tracing a Line
The points where a line intersects the planes of projection are called the traces of the line.
Elevation and Plan
The vertical projections of bodies are called elevations and determine two of their dimensions: height and width. The horizontal projections are known as plans and also define two dimensions of the body: depth and width.
Representations and Hidden Views of a Solid
To differentiate the parts of a drawing that are in front from those that are behind, the former (visible parts) are always drawn with a continuous line. The parts at the back of the body (hidden parts) are drawn with a dashed line.
The Profile or Side View
The main views of the body are:
- Elevation or main view: This is the most important face of a body, or the one that contains the most data. It is, therefore, the view that determines the position of the others. It is obtained by looking at the body from the front.
- Plan or top view: Once the elevation is drawn, the plan is obtained by observing the object from above. It is situated below the elevation.
Often, the information provided by the plan and elevation of a body regarding its shape and volume is not enough to know exactly what it is like. For this reason, a third projection, the side view or profile of the figure, is necessary.
- Profile or side view: This is the third representation that can be made of a solid for its accurate determination. It is obtained by looking at the object from one of its sides, and the drawing is located next to the elevation.