Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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.

Performance objectives

• Construct an isometric axis and grid.
• Draw isometric views from orthographic projections.
• Dimension isometric drawings correctly.
• Interpret information from isometric drawings.
• Draw isometric circles and arcs.

Lesson summary

Isometric drawing is a type of pictorial representation that allows us to depict three-dimensional objects on a two-dimensional surface. Unlike perspective drawings, isometric drawings do not employ vanishing points, resulting in measurements being relatively easier to make. This makes them incredibly useful in various fields like engineering, architecture, and design, especially in South Africa where accurate and understandable technical communication is critical for construction projects, manufacturing, and even DIY projects. Being able to create and interpret isometric drawings is a fundamental skill for any aspiring engineer, designer, or technician.

Lesson notes

What is Isometric Projection? Isometric projection is a type of axonometric projection where all three axes (length, width, and height) are equally foreshortened. This means that all three axes make an equal angle of 120 degrees with each other. In practice, this is achieved by setting up the horizontal axis and then drawing two lines from a central point on that axis, each at 30 degrees to the horizontal. These lines form the isometric axes.

Key Components: Isometric Axes: The three axes along which measurements are taken. Two axes are drawn at 30 degrees to the horizontal, and one is vertical.

Isometric Lines: Lines parallel to the isometric axes. These lines represent edges of the object.

Non-Isometric Lines: Lines that are not parallel to the isometric axes. These lines require special treatment and cannot be directly measured or drawn using isometric scales. We often locate the endpoints of such lines using coordinates derived from the orthographic projections.

Isometric Scale: Because the axes are foreshortened, measurements along the isometric axes are also foreshortened.

However, for simplicity in EGD at Grade 10 level, we generally draw using a true scale isometric projection, meaning we use the same measurements as in the orthographic projections. This simplifies the drawing process while still providing a good visual representation. Drawing Isometric Views from Orthographic Projections: Analyze the Orthographic Projections: Carefully examine the front, top, and side views to understand the overall shape and dimensions of the object. Note all visible edges, surfaces, and any hidden details (using hidden detail lines, if provided).

Establish the Isometric Axes: Draw the horizontal axis and then construct the two 30-degree lines emanating from a point on that axis, and the vertical axis. This establishes your three isometric axes. Decide on the viewing position – which face will be the front, the side, and the top. This will dictate how you align your orthographic views with the isometric axes.

Block Construction: Start by constructing a "box" or a rectangular prism that encompasses the entire object. This box will serve as a guide for drawing the actual object. Use the overall length, width, and height dimensions from the orthographic projections to determine the dimensions of the box.

Locate Key Points and Lines: Within the box, locate key points and lines that define the shape of the object. Use measurements from the orthographic views to transfer these points onto the isometric drawing. Remember that measurements are taken along the isometric axes.

Connect the Points: Connect the located points with isometric lines to create the visible edges of the object. Refer back to the orthographic projections to ensure accuracy.

Draw Hidden Details (Optional): If required, draw hidden details using dashed lines. This can help to clarify the object's construction.

Erase Construction Lines: Once the object is complete, erase the construction lines and the enclosing box to reveal the final isometric view.

Add Dimensions: Dimension the drawing using isometric dimensioning techniques (see below). Drawing Isometric Circles and Arcs (Four-Centre Method): Circles in isometric projection appear as ellipses. The four-centre method provides a relatively simple way to approximate an ellipse.

Draw a Rhombus: Draw a rhombus within which the circle would be inscribed in its true shape. The sides of the rhombus are equal to the diameter of the circle and are at 30 degrees to the horizontal. This rhombus lies on one of the isometric planes (front, top, or side).

Locate Midpoints: Find the midpoints of each side of the rhombus.

Draw Lines from Obtuse Angles: From each obtuse angle of the rhombus (the angles greater than 90 degrees), draw lines to the midpoints of the opposite sides. These lines will intersect at two points within the rhombus. These intersection points, along with the two obtuse angles, will be the four centres for drawing the ellipse.

Draw Arcs: Using each of the four centres, draw arcs connecting the nearest midpoints of the rhombus. These arcs will form the approximate ellipse.

Erase Construction Lines: Erase the rhombus and construction lines to leave the final isometric circle (ellipse).

Isometric Dimensioning: Extension Lines: Extension lines extend from the feature being dimensioned. They should start slightly away from the object.

Dimension Lines: Dimension lines show the extent of the dimension. They must be parallel to the isometric plane of the object.

Dimension Numbers: Dimension numbers indicate the size of the feature. The numbers should be placed above and parallel to the dimension line, typically in the centre. Arrowheads should be placed at the ends of the dimension lines, touching the extension lines.

Avoid Crossing Lines: Avoid crossing dimension lines and extension lines whenever possible.

Worked example

Example 1: Draw the isometric view of a rectangular block with dimensions 50mm x 30mm x 20mm.

Step 1: Establish the isometric axes.

Step 2: Draw a rectangular prism (box) 50mm long, 30mm wide, and 20mm high along the isometric axes.

Step 3: The rectangular prism is the object in this case. Darken the lines of the prism to complete the isometric view.

Example 2: Draw the isometric view of a cylinder with a diameter of 40mm and a height of 60mm, standing vertically.

Step 1: Establish the isometric axes.

Step 2: Draw a rectangular prism (box) to represent the height of the cylinder, 60mm. The base of this prism will define where we draw the isometric circle (ellipse).

Step 3: On the top face of the box, construct a rhombus with sides of 40mm (the diameter of the cylinder), and angles of 60 and 120 degrees.

Step 4: Use the four-centre method to draw the ellipse within the rhombus. This represents the top circular face of the cylinder.

Step 5: Draw vertical lines (parallel to the vertical isometric axis) down from the points where the ellipse touches the rhombus at its sides (the midpoints of the sides of the rhombus), a distance of 60mm.

Step 6: Construct another rhombus at the base of the box, identical to the one at the top.

Step 7: Use the four-centre method again to draw the ellipse within the bottom rhombus. This represents the bottom circular face of the cylinder.

Step 8: Darken the visible lines of the cylinder and erase construction lines.

Guided Practice (With Solutions)

Question 1: Draw an isometric view of a cube with sides of 40mm.

Solution:

Step 1: Establish the isometric axes.

Step 2: Draw a line 40mm long along one of the 30-degree isometric axes.

Step 3: From each end of this line, draw another line 40mm long, one going vertically upwards (parallel to the vertical isometric axis) and the other along the other 30-degree isometric axis.

Step 4: Complete the isometric view by drawing lines parallel to the existing lines to form a complete cube. The last three lines drawn should connect the ends of the lines drawn in Step 3 to each other and to the starting point.

Step 5: Erase any unnecessary construction lines.