Short Answer:

An isometric scale is used to measure true lengths in isometric drawings because in isometric view, lengths appear shorter due to the 30° angles. To construct an isometric scale, we convert true lengths into isometric lengths using a special method involving angled lines and projection.

The construction involves drawing a horizontal line (for true length), a 45° line, and a 30° line from the same starting point. True lengths are marked on the 45° line, then projected down to the 30° line. The points on the 30° line give the reduced isometric lengths, which are then used for accurate isometric drawings.

Detailed Explanation:

Constructing an isometric scale

When we draw in isometric view, objects are shown at 30° angles to represent 3D shapes. But when we measure lengths along these 30° lines, they appear shorter than their actual lengths. This is due to the visual compression caused by the angled view. So, if we use normal scales directly, the isometric drawing will look wrong. That’s why we need an isometric scale, which helps us convert real (true) lengths into isometric lengths correctly.

Let us now understand the simple and step-by-step method to construct an isometric scale.

1. Draw the base line (horizontal line)
   Start by drawing a straight horizontal line. This line will represent the true length. On this line, you will mark the original lengths as per the given object or scale (like 10 mm, 20 mm, 30 mm, etc.).
2. Draw a 45° line from the same point
   From the same starting point (where the horizontal line begins), draw another line at 45° angle upwards. This line will be used to mark the true lengths from the horizontal line.
3. Mark true lengths on 45° line
   Take a compass or scale and mark equal divisions on the 45° line—like 10 mm, 20 mm, and so on. These represent true lengths from the object that we want to convert into isometric lengths.
4. Draw a 30° line from the same starting point
   Now, from the same base point, draw another line at 30° angle. This line will be used to get the isometric lengths.
5. Drop perpendiculars from 45° line to 30° line
   From each marked point on the 45° line, draw vertical (perpendicular) lines downwards until they meet the 30° line. Where these vertical lines touch the 30° line, mark those points. These are your isometric length points.
6. Join isometric scale points
   Now, along the 30° line, join the points smoothly and write down the converted values. These values represent how a true length (e.g., 10 mm) will appear in isometric view (slightly less than 10 mm).
7. Use this scale for isometric drawings
   Once the isometric scale is complete, you can use it like a normal scale while drawing isometric views. When you need to measure 50 mm in isometric drawing, you will use the 50 mm mark from this isometric scale, not from the regular scale.

Why do we use an isometric scale?

• Because in isometric view, the axis is tilted and compresses the length visually.
• A 1 cm length becomes about 0.82 cm (about 82%) in isometric view.
• Without the isometric scale, your drawing may look stretched or incorrect.
• It ensures all parts are in correct proportion and look realistic in 3D.

Key tips while constructing isometric scale:

• Use a protractor to get exact 30° and 45° angles.
• Use a sharp pencil for accurate marking.
• You only need to make this once and can reuse it for many drawings.
• Always double-check the scale before using it in actual drawing.

Conclusion:

Constructing an isometric scale is an important step when creating accurate isometric drawings. It helps convert true lengths into correct isometric lengths by using a simple geometric construction. This scale ensures that the 3D drawing looks realistic and proportional even when viewed at 30° angles. By following a few easy steps with a protractor and ruler, anyone can create and use an isometric scale for technical sketches and engineering designs.