Lesson Notes By Weeks and Term v5 - Grade 11
Intersection and development of surfaces – Week 6 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Intersection and development of surfaces – Week 6 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Engineering Graphics and Design
Class: Grade 11
Term: 1st Term
Week: 6
Theme: General lesson support
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Intersection and development of surfaces are fundamental concepts in engineering design and manufacturing. Understanding how different surfaces interact and how to create flat patterns (developments) for those surfaces is crucial for creating a wide range of products, from water tanks to ventilation systems. In South Africa, these skills are directly applicable in industries like mining (designing ventilation shafts), construction (creating roofing systems), and manufacturing (producing containers and pipe systems).
2. 1. Intersection of Surfaces The intersection of surfaces refers to the common line or curve formed where two or more surfaces meet. To determine this line, we generally use graphical methods. The basic principle is to find points that lie on both surfaces and then connect these points to form the line of intersection. Finding Points on the Line of Intersection: Cutting Planes: The most common method involves using cutting planes. These planes are strategically positioned to intersect both surfaces. The intersections of the cutting plane with each surface result in lines. The points where these lines intersect are points that lie on both original surfaces, and thus, on the line of intersection.
Auxiliary Views: In some cases, auxiliary views can simplify the process. An auxiliary view is a projection of the object onto a plane that is not parallel to any of the principal planes (Front, Top, Side). By selecting an auxiliary plane that is perpendicular to one of the surfaces, the line of intersection can often be seen as a line or curve in the auxiliary view.
Types of Intersections: Prism-Prism: This typically results in a series of straight line segments.
Prism-Cylinder: This can result in a curved or segmented line, depending on the orientation of the surfaces.
Cylinder-Cylinder: Often results in complex curves, requiring multiple cutting planes to accurately define. 2.
2. Development of Surfaces Development of a surface refers to creating a two-dimensional pattern that can be folded or formed to create the three-dimensional object. Developments are essential for manufacturing objects from sheet metal, cardboard, or other flat materials.
Types of Development: Parallel Line Development: Used for surfaces that can be unfolded onto a plane without distortion. Prisms and cylinders are typically developed using this method.
Radial Line Development: Used for surfaces with a common apex, such as cones and pyramids.
Triangulation: Used for warped surfaces that cannot be developed directly. The surface is divided into a series of triangles, and each triangle is developed individually. 2.
3. Development of a Prism (Parallel Line Development)
True Lengths: Ensure all edges of the prism are shown in their true length in the front or top view.
Stretch-Out Line: Draw a horizontal line (the stretch-out line). The length of this line is equal to the perimeter of the prism's cross-section (e.g., if the prism is a square prism with sides of 20mm each, the stretch-out line is 4 * 20mm = 80mm long).
Divisions: Divide the stretch-out line into equal segments corresponding to the sides of the prism's cross-section.
Height: At each division point, draw vertical lines perpendicular to the stretch-out line. The length of these vertical lines is equal to the height of the prism.
Connect: Connect the ends of the vertical lines to form the rectangular faces of the prism.
End Caps: Add the shapes of the prism's ends (e.g., squares, triangles) to either end of the rectangle.
Seam Line: Indicate a seam line (where the pattern will be joined to form the prism). This is typically located along one of the vertical edges. 2.
4. Development of a Cylinder (Parallel Line Development)
True Length: Ensure the height of the cylinder is shown in true length.
Stretch-Out Line: Draw a horizontal line (the stretch-out line). The length of this line is equal to the circumference of the cylinder (Circumference = π * diameter).
Divisions: Divide the stretch-out line into equal segments. The more segments, the more accurate the development will be. A common practice is to divide the circle into 12 or 24 equal parts.
Height: At each division point, draw vertical lines perpendicular to the stretch-out line. The length of these vertical lines is equal to the height of the cylinder.
Connect: Connect the ends of the vertical lines to form a rectangle.
End Caps: Add the circular ends of the cylinder to the top and bottom of the rectangle. Alternatively, for a truncated cylinder, project the truncated shape from the front view onto the development.
Seam Line: Indicate a seam line.
Example 1: Intersection of a Square Prism and a Triangular Prism Imagine a square prism penetrating a triangular prism perpendicularly.
Front View: Draw the front view, showing the outlines of both prisms and where they appear to intersect.
Top View: Draw the top view, aligning it with the front view. The top view will show the true shape of the prisms' cross-sections.
Cutting Planes: Use vertical cutting planes (in the top view) that pass through key points on the edges of the prisms.
Intersection Points: In the front view, project these cutting planes up to intersect the corresponding edges of the prisms. The points where the projected cutting planes intersect are points on the line of intersection.
Join the Points: Connect the intersection points in the front view to create the line of intersection. Use hidden detail lines where the intersection is obscured by the prisms' surfaces.