4- The Theory of Projection

The theory of projection KCEC1101 CAD

Projection Methods Projections Perspective or Central Projections

Linear Perspectives

Aerial Perspectives

Parallel Projections

Oblique Projections

Orthographic Projections

Projection Method Perspective or Central Projections Linear Perspectives

Aerial Perspectives

Projection Methods Parallel Projections Oblique Projections

Axonometric Projections

Orthographic Projections Multiview Projections

The attributes of each projection method

Projection theory

Line of Sight (LOS) A LOS is an imaginary ray of light between an observer's eye and an object.

Projection theory In perspective projection, all LOS start at a single point

Projection theory In parallel projection, all LOS are parallel and no start point (infinitive viewpoint)

Projection theory • A plane of projection is an imaginary flat plane upon which the image created by LOS is projected.

Multiview projection planes 1. The frontal plane of projection is the plane onto which the front view of multiview is projected.

Multiview projection planes 2. The top view is projected onto the horizontal plane of projection, which is a plane suspended above and parallel to the top object.

Multiview projection planes 3. The right side is projected onto the right profile plane of projection, which is a plane that is parallel to the right side of the object.

Advantage of multiview drawing It produce the true dimensions !!! Distorted angle

Distorted dimension

Multiview drawing

The six principal of views 1.

The front view

2.

The top view

3.

The right side view

4.

The left side view

5.

The rear view

6.

The bottom view

The six perpendicular plane of views

Conventional view placement Conventionally, the standard views used in a three-view drawing are the top, front, and right side view. Because the other three principal views are mirror image and do not add to the knowledge about the object.

Projection dimensions The width dimension is common to the front and top views. The height dimension is common to the front and side views. The depth dimension is common to the top and side views.

Projection arrangement

The arrangement of views may vary as long as the dimension alignment is correct.

First-Angle Projection First angle projection is the standard in Europe and Asia.

Third-Angle Projection Third angle projection is the standard projection for the United States and Canada.

Profile plane

The difference between first and third angle projection is the placement of the object and the projection plane The principal projection planes and quadrants used to create first- and third- angle projection drawings

Pictorial comparison between first- third angle projection techniques

First angle projection

The dihedral angles

First angles projection box

First angle projection First angles projection box

Box unfolding

First angle projection

Box unfolding

Box unfolded show relative position of view Placement of 1st angle of view

Third angle projection

The dihedral angles

Third angles projection box

Third angle projection 3rd angles projection box

Box unfolding

Third angle projection Box unfolding

Placement of 3rd angle of view

Box unfolded show relative position of view

The rule of orthographic projection principles 1. 2. 3. 4. 5. 6. 7.

Alignment of features Distances in related views True length and size Foreshortening Configuration of planes Parallel features Edge views

Rule 1: Alignment of features Every point or feature in one view must be aligned on a parallel projector •

•

For example, the hole in the block is an example of a feature shown in one view and aligned on parallel projectors in the adjacent view Adjacent views are two orthographic view placed next to each other such that the dimension they share in common is aligned, using parallel projectors. hole feature

Rule 2: Distances in related views Distances between any two points of the feature in related views must be equal •

•

For example, the distance between surface 1 and surface 2 is the same in the top view as it is in the right side view. Two views that are adjacent to the same view are called related views

Rule 3: True length and size

For example edge 1-2 in the top and right side view is a normal edge (or true-length line)

Features are true length or true size when the lines of sight (LOS) are perpendicular to the feature

An inclined line is parallel to a plane of projection, but inclined to the adjacent planes, it appears foreshortened in the adjacent planes.

For example line 3-4 is inclined and foreshortened in the top and right side view, but true length in the front view, because it is parallel to the frontal plane of projection

Rule 4: Foreshortening Features are foreshortening when the line of sight are not perpendicular to the features •

For example oblique line 1-2 is not parallel to any of the principal planes of projection of the glass box.

•

An oblique line is not parallel to any principal plane of projection

Rule 5: Configuration of planes

Oblique surface

Areas that are the same feature will always be similar in configuration from one view to the next, unless viewed on edge

Incline surface

Surface B and C are an example of the Rule of Configuration of planes

Rule 6: Parallel features Parallel features will always appear parallel in all views

For example, at surface C, lines 3-4 and 5-6 are parallel in all views (front, top and right). Also, edge 3-6 and 4-5 are parallel in both the top view and the right view.

Rule 7: Edge view Surfaces that are parallel to the lines of sight will appear on edge and be represented as lines.

For example, surface A, C, D and F are parallel to the line of sight and will appear as on edges which represented as lines at projected front view.

Example of normal face projection A normal face projects on all three principle image planes. (follow the rule of edges view)

Creating a tree-view sketch

Example of representing filleted and rounded corners

Example of Runouts

Representing the intersection of two cylinders

Small cylinder

Large cylinder (same size)

Representing the intersection btw a cylinder and a prism

Small prism

Large prism

Representing the intersection btw a cylinder and a hole

Representing the intersection btw a cylinder and a slot

Center lines

Good & Poor Orientation

The major surface are parallel or perpendicular to the sides of the box (projections planes)

The surface are not parallel to the sides of the glass box produces views with many hidden lines.

End