Introduction To Engineering Graphics

http://homepages.cae.wisc.edu/~me231/online_notes/section_views/section_views.htmIntroduction to Engineering

Graphics Why do we bother with learning mechanical drawing? Isn't everything done with high powered 3D solid modeling software? While CAD systems have revolutionized the mechanical design process, a large amount of information is still conveyed using traditional 2D mechanical drawings. These 2D drawings are not generated by hand but rather extracted from 3D solid models. However all the rules, standards and techniques of traditional mechanical drafting still apply and that is where this course impacts your engineering career. Students should be aware that this course is for all intents and purposes a course in communication, specifically the graphic language. The objective of the course is to teach students to communicate using graphic techniques. This involves learing to "read" or interpret the information contained in a 2D mechanical drawing. To accomplish this the student must learn the principals and standards of mechanical drawing and dimensioning.

Standards The graphic language is quite similar to the spoken/written language familiar to all. Specific rules, or standards, have been developed to retain consistency in industry. Imagine the confusion if each individual decided how to spell words as they were written, with no standards. Or if pronunciation of the spoken language was not consistent. That is why the standards you will learn are so important, even if many seem to be trivial. Books are written in chapters, that are broken up into paragraphs. Words are spoken in different tones to communicate meaning. Engineering drawings must also be presented and arranged in a certain format so the information they contain can be interpreted. It is true that many companies create their own internal standards, but most companies rely on resources from outside sources, especially in the current business environment. Pressure to reduce the work force and cut costs has left many companies with no choice but to hire outside contractors to complete work which was previously performed by company employees. Therefore the importance of a standard graphic language is steadily increasing.

Course Objectives Students completing the course should realize the following objectives: • • • • •

Comprehend general projection theory, with an emphasis on the use of orthographic projection to represent three-dimensional objects in two-dimensional views Understand the application of industry standards and techniques applied in engineering graphics Apply auxiliary or sectional views to most practically represent engineered parts Dimension and annotate two-dimensional engineering drawings Employ freehand 3D pictorial sketching to aid in the visualization process and to efficiently communicate ideas graphically

Introduction Proper Form and Technique for Vertical Lettering

Proper Form and Technique for Inclined Lettering

COMMON DRAFTING LINE TYPES Object lines Bold continuous lines. Construction lines _____________ Very light thin continuous lines. Hidden lines _ _ _ _ _ _ _ _ _ Dashed lines used to represent hidden features. Center lines _____ _ _____ Used to locate the center of arcs, circles, etc. (thin). Phantom lines truly exist, for

_____ _ _ ______

Used to illustrate features which do not

example section cuts, the extents of travel for machine parts, etc

What is Descriptive Geometry?

Descriptive Geometry is the graphical solution of point, line and plane problems in space. These solutions are accomplished by means of the same principles of orthographics projection which are used in making a 3 view drawing of an object.

Some Definitions Used in Descriptive Geometry and Orthographic Projection (1) Orthographic Projection - the use of parallel lines of sight at 90 degrees (orthogonal) to an image plane (2) Image Plane - the plane which is perpendicular to the line of sight (LOS). This plane is located between the observer and the object being viewed. (3) Line of Sight - the vector path from the viewer to a particular point on an object. For our purposes, these LOS are parallel. (4) Principal Views (planes) - any of the six orthogonal image planes defined by the six mutually othogonal LOS (5) Fold Line - line defined by the intersection of two adjacent image planes. The fold line is represented on the drawing by a phantom line.

Projection of lines

True length of a line Given: Line ab. Required: Find the true length of line ab.

Given: Line ab. Required: Find the true length of line ab.

Area of a plane surface Given: Plane abc. Required: Find and measure the area of abc.

Area of a plane surface - Graphical solution Given: Plane abc. Required: Find and measure the area of abc.

Solving problems with auxiliary views Now that you can use auxiliary views to create desired views of geometric entities, you can solve many descriptive geometry problems. There are basically only four separate manipulations you can generate with auxilliary views: 1. Show true length of any line. 2. Show point view of any line. 3. Show line or edge view of any plane. 4. Show true size view of any plane.

When presented with a problem, these are the only tools you have to solve it graphically. Before beginning any of them to solve the problem, you must determine first what view is required. Creating that view is a matter of using one or more of the four previouly listed steps. We will solve the first set of problems graphically, and deal with intersections through the use of auxiliary views. We have already discussed intersections of two lines. Remember that if two lines intersect, they have a single point in common, and that point must project from view to view. Now let us consider the intersection of a line and a plane in space.

Visibility As entities intersect in 3D space, it is often desirable to show the intersections with correct visibility.

Intersection of line and plane Realize that the intersection between a line and a plane in space is still a single point. This single point is defined as the piercing point, the point at which the line pierces the plane. To solve the problem graphically, first determine what view must be drawn to find the solution. Using aids to visualize the problem is helpful. A pencil can represent the line and a clear plastic drafting triangle can represent the plane. Hold the pencil so it passes through or intersects the opening in the triangle. To find the single point on the line which lies on the plane, how must these objects be viewed? It should be clear that in a view in which the plane appears as a line, the single point the line has in common with the plane can be indentified easily. The construction of views to obtain that view has been previously reviewed. Once the piercing point is located, it can be projected back into the given views. A "two-view" method can also be used to find the piercing point of a line and a given plane. The construction to solve the problem is quite simple, but, it is more difficult to grasp conceptually than the auxilliary view method.

Intersection of two planes Two planes in space intersect to form a single line. If the planes are assumed to extend indefinitely in all directions, the line of intersection will have infinite length. If the planes are defined as having a certain size and shape, the line of intersection will be finite, and will appear as a visible line where it lies within the boundaries of both planes. To find the line of intersection using auxilliary views, you must construct a view where either one of the given planes appears in edge view. In that view, the line defined by the two points that lie on the boundary of the plane that appears forshortened and the plane that appears as a line,

define the line of intersection. This is basically a piercing point problem you do twice. Find where any line on one plane pierces the other plane. Now repeat that step and find where a different line on either plane pierces the other plane. The two points you have will define the line of intersection between the two planes.

True angle between two lines The true angle between any two lines can be measured in a view where both lines are true length. To construct that particular view, choose one of the two lines and construct a view where it appears as a point. If neither of the given lines is true length, this will take two views. Remember to project both lines into each view. Once the point view of one of the lines is constructed, the other line will appear foreshortened (unless they are parallel). An additional auxiliary view parallel to the foreshortened line in that view will show both lines TL. Measure the angle between the lines in that view. If the two lines lie on the same plane (i.e. if they intersect), an alternate approach usually can reduce the number of views required to solve to problem. The intersecting lines define a plane. Draw that plane true size, and every line on the plane will be TL, and the angle can be measured in that view.

True angle between line and plane The true angle between a line and a plane can be measured in a view where the line is TL and the plane appears as a line (or edge). There are two different approaches to construct this desired view. To solve using the plane method, first construct the TS view of the plane. If the plane does not appear as a line in the given problem, the edge view must be constructed before you can obtain the TS view. Project the line into each view as well. Once the TS view of the plane is constructed, any adjacent view will show that plane as a line. Construct an auxiliary view parallel to the foreshortened line in the view where the plane appears TS. Projection onto this view will show the TL line, and the plane will appear as a line. Measure the angle in that view. To solve using the line method, first construct the point view of the line. The plane will appear foreshortened in this view. Once the point view of the line is constructed, any adjacent view of the line will show it TL. Determine the auxiliary view direction, which will also show the plane as a line by constructing a TL line on the plane in the view where the given line appears TL. An auxiliary view perpendicular to this line will show the plane as a line, and the line will be TL. Measure the angle in that view.

True angle between two planes The true angle between two planes can be measured in a view where both planes appear as lines. How does the line of intersection between two planes appear when both planes appear as lines?

To measure the true angle between two planes, a view must be constructed where both planes appear as lines. In that view, the line of intersection will appear as a point. Once the line of intersection is determined, it is simply a matter of constructing the required views to show that line as a point.

Shortest distance from point to line The shortest distance from a point to a line is always a line through the given point that is perpendicular to the line. This is very similar to a true angle problem, where the true angle must be 90 degrees. To find the shortest distance from a point to a line, construct a view where the line is TL. A line drawn from the given point perpendicular to the line will be a view of the shortest distance from the point to the line. If the shortest distance must be measured, that line must be projected into a view where it appears TL. An alternative method also can be used. A line and a point define a plane. Construct a view where that plane appears TS. Every line on that plane is TL, and angles between lines are true. A line can be drawn from the given point perpendicular to the given line and measured in that view.

Shortest distance point to plane The shortest distance from a point to a plane is always a line through the given point that is perpendicular to the plane. To find the shortest distance from a point to a plane, construct the edge view of the plane. A line from the point drawn perpendicular to the plane will be the shortest line from the point to the plane. The line will always be TL and can be measured in that same view.

Shortest distance between two lines The shortest distance between two lines is always a line which is perpendicular to both lines. To find the shortest distance between two lines, construct a view where either of the given lines appears as a point. Construct a line, from that point view, perpendicular to the other given line shown in that view. In order for the line you construct to be perpendicular to both given lines, it must be TL in this view. Remember that to determine whether or not two lines are perpendicular, only one of them has to be TL. If the angle between them is 90 degrees in a view where either of the lines is TL, they are perpendicular.

Views of line

Given: The point view of a line Required: How does it appear in any adjacent view.

Views of line

Given: The point view of a line Required: How does it appear in any adjacent view

Views of Plane

Given: TS view of plane surface. Required: How does it appear in any adjacent view.

Views of Plane

Given: TS view of plane surface. Required: How does it appear in any adjacent view.

Section of solids Sectional Views - Overview Conventional views, either principal or auxiliary views, may not always give the clearest representation of an object. Many objects in the engineering world have complex internal features which will appear as hidden lines in conventional views. It is often desirable for the sake of clarity to represent the interior features as visible. To present objects in this method, the component can be imagined as being separated by a cutting plane in a location selected to most clearly show interior features. The cutting plane may be placed in several different positions, depending upon the symmetry and complexity of the object. After the cutting plane location is selected, the object is drawn as if the portion of the object to one side of the cutting plane is removed. The remaining object outline and all visible features are drawn. To indicate the cross-sectional shape of the object along the cutting plane, sections lines are added. Section lines, or crosshatching, are included to clearly indicate where the defined cutting plane passes through solid material of the object. The pattern of the section lines can be used to define the material of which the object is to be made. This is done in assembly drawing which show multiple components in an asembled state. In detail drawing, continuous line hatching is more common. Hatching is constructed at a 45 degree angle (with respect to the view) if possible. Other angles my be used if the hatching is parallel to too many object lines, hence making reading of the drawing more difficult. The cutting plane is shown as a dashed or phantom line, thicker than the normal object lines in a view where is appears as an edge. In cases where the location of the cutting plane is easily understood, and no other logical sections would be presented, the cutting plane line may be omitted. This is usually done on circular objects, where the cutting plane line is placed along one of the axial centerlines. If there is any chance that omission of the cutting plane could introduce confusion to the drawing reader, it must be shown. When the cutting plane line is shown, arrowheads must be added to indicate the direction from which the object is to be viewed. The arrowheads also indicate which part of the object is to be removed for the section view. If the cutting plane line coincides with a centerline, the cutting plane line takes precedence. If the arrowheads point to the left, everything to the right of the cutting plane is imagined to be removed. The view would then be drawn to the right of the view where the cutting plane is shown. If the arrowheads point up, everything to the below the cutting plane is imagined to be removed. The view would then be drawn directly below the view where the cutting plane is shown.

Conventional view

Sectional Views Conventions - Cutting Plane

Sectional Views Conventions - Cutting Plane

Representation Formats for Threaded Holes in Section Simplified--

Schematic (conventional)-

Detailed (graphic)-

Sectional Views Sectional Views Example

Sectional Views Sectional Views Example

Sectional Views Sectional Views Example S2 Conventional View

Sectional Views Sectional Views Example S2 Full View

Sectional Views Sectional Views Example S2 Half View

Example S3 - Full vs. Removed Sections Given:Top and Front Conventional Views. Required: Draw Section Views As Indicated.

Example S3 - Full vs. Removed Sections

Solutions Drawn As Full Sections Solutions projected off the front view

Example S3 - Full vs. Removed Sections

Solutions Drawn As Removed Sections

Removed sections must be drawn to the right of the cutting plane lines since the arrowheads are pointing to the left. They cannot be drawn as a direct projection off the front view

Example 4 - Removed Section

Given:Top and Front Conventional Views. Required: Draw Section View As Indicated.

Example - Removed Section

Given:Top and Front Conventional Views. Required: Draw Section View As Indicated.

Example - Revolved Section Given: Front and Right Side Conventional Views. Required: Draw Revolved Section.

Example - Revolved Section Given: Front and Right Side Conventional Views. Required: Draw Revolved Section.

Orthographic projections Orthographic Projection is a way of drawing an object from different directions. Usually a front, side and plan view is drawn so that a person looking at the drawing can see all the important sides. Orthographic drawings are useful especially when a design has been developed to a stage whereby it is almost ready to manufacture. IMPORTANT: There are two ways of drawing in orthographic - First Angle and Third Angle. They differ only in the position of the plan, front and side views. Below is an example of first angle projection.