Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Solve interpenetration problems for prisms, cylinders, and cones.
• Develop the surfaces of geometric solids.
• Determine the lines of intersection between solids.
• Analyse and interpret EGD drawings.
• Manage time effectively in an exam.

Lesson summary

This week is crucial for consolidating your understanding of the key concepts covered in Grade 11 Engineering Graphics and Design. As we approach examinations, it's vital to not only recall information but also to apply it confidently and accurately. EGD skills are essential for many careers in South Africa, from architecture and engineering to manufacturing and design. A solid understanding of these concepts will open doors to future opportunities and contribute to the growth and development of our country's infrastructure and economy.

Lesson notes

This week's focus is on Descriptive Geometry, specifically the interpenetration of solids and surface development. These are critical skills for visualizing and representing 3D objects in 2D, which is fundamental to engineering design.

A. Interpenetration of Solids: Interpenetration refers to the lines of intersection formed when two or more geometric solids pass through each other. The goal is to accurately project these lines of intersection onto different orthographic views (front, top, and side views).

Principles of Orthographic Projection: Remember that orthographic projection uses parallel projectors perpendicular to the planes of projection (Horizontal Plane - HP, Vertical Plane - VP, and Auxiliary Vertical Plane - AVP or Profile Plane - PP). The lines of intersection, therefore, must be projected accurately from one view to another using these projectors.

Identifying Key Points: The most crucial part is identifying key points on the surfaces of the solids where the intersection occurs.

These points are usually located: Where edges of one solid intersect the surfaces of another. At points of tangency between the solids. At the extreme limits of penetration.

Drawing the Lines of Intersection: Once you have identified the key points, you can connect them with smooth curves or straight lines to form the lines of intersection.

Remember to consider visibility: lines that are hidden behind a solid are drawn as hidden detail (dashed lines).

Example 1: Cylinder Interpenetrating a Prism: Imagine a vertical cylinder penetrating a horizontal rectangular prism. Draw the orthographic views (Top, Front, and Right View) of the cylinder and the prism.

Identify Key Points: In the top view, where the cylinder overlaps the prism, locate points where the cylinder's circumference intersects the edges of the prism. Project these points down to the front view. The height of these points on the front view will depend on where they lie on the cylinder's circumference in the side view (obtained by projecting from the top view to the side view, then horizontally to the front view).

Connect the points: Connect the points in the front view with smooth curves. Some parts of the curve will be visible, and some will be hidden. Use hidden detail lines where appropriate.

Remember symmetry: The lines of intersection are often symmetrical about the centre lines of the solids. Use this to your advantage.

Example 2: Cone Interpenetrating a Cylinder: Consider a cone penetrating a cylinder at an angle. Draw the orthographic projections of both solids.

Auxiliary View: Because the cone intersects the cylinder at an angle, it is often necessary to create an auxiliary view showing the true shape of the cone's base and the cylinder's axis as a point. This view simplifies the process of finding the points of intersection.

Divide and Conquer: Divide the base of the cone in the auxiliary view into several equal parts. Project these points back to the cylinder in the auxiliary view.

Project back to the principal views: Project these points from the auxiliary view to the top and front views. Connect the points with smooth curves. Remember to consider visibility.

B. Surface Development: Surface development, also known as unfolding or unrolling, is the process of creating a 2D pattern (net) that, when folded, will form the 3D shape of a solid. This is essential for manufacturing processes like sheet metal work.

Types of Development Methods: Parallel Line Development: Used for prisms and cylinders. The surface is unfolded onto a flat plane, and parallel lines are used to represent the edges or elements of the solid.

Radial Line Development: Used for cones and pyramids. All the edges converge at a single point (the apex), so the development uses radial lines emanating from the apex.

Triangulation: Used for complex shapes that cannot be developed using the other methods. The surface is divided into a series of triangles, and each triangle is developed individually.

Example 3: Development of a Rectangular Prism: Draw the orthographic views (Front and Top View).

Calculate the perimeter: The perimeter of the base of the prism is the width of the development.

Draw a straight line: Draw a straight line representing the perimeter.

Mark the distances: Mark off the lengths of each side of the prism on the line, in the correct order.

Draw the heights: At each mark, draw a perpendicular line equal to the height of the prism.

Connect the top ends of these lines: This creates the development of the sides of the prism. Add the top and bottom faces by attaching them to appropriate sides. Remember to add tabs for gluing or welding.

Example 4: Development of a Right Circular Cone: Draw the orthographic view (Front View). Calculate the radius of the development arc: The radius of the arc is equal to the slant height of the cone.