Engineering Drawing & Descriptive Geometry II Lecture 1

Mr. AHMED SAMIR M.Sc. P. E. Material Science

AHMED SAMIR [email protected] INRODUCTION

Descriptive Geometry: It is a science deals with the treatment way of representation of geometrical solids having three dimensions (length, width (breadth), and thickness) on the paper plane surface which has only two dimensions (length, width) in another word the descriptive geometry is the graphical solution of point, line, and plane in space. Descriptive Geometry is a method to study three dimensions (3D) geometry through two dimensions (2D) images. It provides insight into structure and metrical properties of spatial objects, processes and principles.

Applications of D.G.: This subject deals with graphic representation of solid objects having three dimensions (length, width (breadth), and thickness) upon a plan surface of paper which has only two dimensions (length, width), It deals with the graphical solution of problems which are difficult to solve analytically such as determination of: True length of lines and true shapes of objects for representations made on the paper; Pictorial drawing for example isometric, perspective, and oblique projections; Development of surfaces for sheet metal working; Paths traced out by curve surface along a straight path and along curved surfaces.

AHMED SAMIR 2 DEFINITIONS

Throughout our study, repeatedly we are using the following terms, understanding their meaning is imperative for proper study of descriptive geometry.

SOLID OBJECT It is any system which occupying a displacement in the space. It has three dimensions (length, width (breadth), and thickness). The amount of occupying space is its volume.

SURFACE It is the boundary which separates the object from surrounding. It has two dimensions (length, width).

LINE It is the path of a moving point. Also it can be defined as a thing that surrounds (bounds) the surface. It has only one dimension which its length. There are many types of lines:-

AHMED SAMIR 3 DEFINITIONS

1. Straight Line: It is the path of a point moving forward in one direction. It has a definite length which assigned by its two ends. Any two points on the line can be chosen and locate on the entire new line. a) Inclined Line: It is a line neither horizontal nor vertical. It can appear in its true length on either front or profile plane but its projection on the horizontal plane is shorter than its true length. b) Oblique (Skew) line: It is a line inclined to all three principal planes; it doesn’t appear in its true length on anyone of them. c) Vertical line: It is a line parallel to plumb line and it is perpendicular to a level plane. Its true length appears on any elevation view. d) Horizontal line: It is a line parallel to Still Water Lake; therefore all points which lie on the line are at the same elevation. It always appears in its true length on horizontal plane.

AHMED SAMIR 4 DEFINITIONS e) Frontal line: It is a line parallel to the image front plane. It appears in its true length on front plane. f) Profile line: It is a line parallel to the image profile plane. It appears in its true length on profile plane. g) Principle Line: It is a line parallel to both of the two principal line planes (horizontal & vertical) and it is perpendicular to the profile plane, therefore its true length appears on the both horizontal and front planes, while its projection on the profile plane is a point. It is parallel to the ground line. h) Reference Line (Ground Line): It is a line originated from intersecting of two principal planes of projection, it is denoted by G.L. and it has a great importance in solving problems.

2. Contour Line: It is a straight-curved line or curved line used in topographical drawing while locates a series of points at the same elevation; therefore the counter line can be considered level line. This line has a wide usage in Earth Sciences & Physical Geography.

AHMED SAMIR 5 DEFINITIONS

3. Line of Sight: It is an imaginary straight line joining the center of the eye of the observer with the object viewed. POINT A point is simply a location. It has no dimension (shape or size), is usually represented by a small dot, and named by a capital letter. SHAPE This word is released to a group of points, lines, and surfaces of an object. PLANE It is the simplest surface, if any two points taken on that surface and jointed by a line, this line is lie on that surface, and this surface is called plane. The plane can be classified to these types:- 1. Horizontal Plane: It is the plane that any point lies on it are at the same elevation, the top of plane view is determined by projection of the object on this plane. The sight lights for it are vertical, i.e. they are perpendicular to it.

AHMED SAMIR 6 DEFINITIONS

2. Frontal (Vertical Plane): It is an image plane at 90º to the horizontal and profile planes. The front view (elevation) is determined by projection of the object on this plane. The sight lights for it are horizontal, i.e. they are perpendicular to it.

3. Profile Plane: It is an image plane at right angles to both horizontal and vertical planes, the right and left side elevation views are determined by projection of the object on this plane. The sight lights for it are horizontal and parallel to the front plane, i.e. they are perpendicular to it.

4. Image Plane: There are planes which they are perpendicular to the sight lines; they are located between the eye of the observer and the object which being viewed. NORMAL VIEW It is the view which shows the true length of line or true shape (Size) of the plane. The normal view of the plane shows true size of any angle which being in that plane and also the true length of any lines on that plane too.

AHMED SAMIR 7 DEFINITIONS

Right Profile Plane

Left Profile Plane

AHMED SAMIR 8 SLOPE OF THE LINE

It is the tangent of the angle between the line and horizontal plane. The slope of line to be determined, two coordinated have to be present; first the line should be shown in an elevation view and second the line must be appears in its true length on elevation view. BEARING The true bearing to a point is the angle measured in degrees in a clockwise direction from the north line. We will refer to the true bearing simply as the bearing.

For example, the bearing of point P is 065º which is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the center of the compass at O with the point P (i.e. OP). The bearing of point Q is 300º which is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the center of the compass at O with the point Q (i.e. OQ).

Note: All bearings are measured in a horizontal plane.

AHMED SAMIR 9 PROJECTION

When representing a three-dimensional object on the two-dimensional surface of our retina, of a camera film or array of sensors, of a paper sheet, or of a TV or computer screen, the number of dimensions is reduced from three to two. The general process of reducing the number of dimensions of a given object is called projection. The planar image of an object in three-dimensional space is found by passing a line through each point of the object and finding the intersections of these lines with the projection plane. These lines, the projectors, emanate from a single point called the center of projection. When the center of projection is at infinity, so that the projectors are all parallel, the projection is known as a parallel projection. When the center of projection is at a finite distance from the projection plane, the projection is known as a perspective projection.

AHMED SAMIR 10 PROJECTION

The projection methods can be classified as following:

Planer Geometric Projection

Parallel Perspective

One Two Three Orthographic Oblique point point Point

Multi-view Axonometric Cavalier Cabinet orthographic

Isometric Di-metric Trimetric

AHMED SAMIR 11 PROJECTION

1. Perspective (Central) Projections: A perspective projection represents an object as it would be seen by an observer positioned at a certain vantage point. An object appears smaller as its distance from the observer increases, and parallel lines of an object converge in the drawing. • Observer is at finite distance. • Rays or Projectors are converging at observer’s eye. • It does not provide exact size and shape of object.

2. Parallel projection: In this type of projection the center of projection is at infinity, so the projectors are all parallel. The classification of parallel projections is determined by the angle between the projectors and the projection plane. When the projectors are perpendicular to the projection plane, the projection is orthographic; otherwise, it is oblique. Orthographic projections are represented either as multi-view orthographic projections or axonometric projections.

AHMED SAMIR 12 PROJECTION

2.1. Oblique Projection: • Observer is at infinite distance. • Rays or Projectors are parallel to each other. • Rays or Projectors are not perpendicular to the Plane of projection (i.e. projectors are inclined to the plane of projection i.e. oblique).

2.2. Orthogonal Projection: is a means of representing a three-dimensional object in two dimensions. It is a form of parallel projection, where the view direction is orthogonal to the projection plane.

• Assume that observer is at infinite distance and rays or Projection lines are parallel to each other and Perpendicular to the Plane of Projection. • Since the projectors are perpendicular to the plane of projection, the view is called Orthographic View and the projection method is called Orthographic projection.

AHMED SAMIR 13 COORDINATE PLANES

The planes upon which the representations are made are called coordinate planes, or planes of projection, and are usually conceived to be perpendicular to each other and indefinite in extent. The plane designated by H.P. is called the horizontal plane, and the representation made thereon is known as the horizontal projection, plan, or top view. The plane designated by V.P. is called the vertical plane, and the representation made thereon is known as the vertical projection, elevation, or front view. The plane designated by P.P. is called the profile plane, and the representation made thereon is known as the profile projection, side elevation, end or side view. The line of intersection between the V.P. and H.P. planes is known as the ground line (GL).

AHMED SAMIR 14