Technical Drawing · Lesson 6

Isometric, oblique, one- and two-point perspective, freehand and exploded views

WAECNECO

What the syllabus asks

WAEC: WAEC/NECO Technical Drawing, Solid Geometry item 13 (pictorial drawing: isometric, oblique, perspective in one- and two-point; freehand sketching) and Paper 3 Section A sketching. (Not a JAMB UTME subject: Technical Drawing is absent from JAMB’s official IBASS e-syllabus list.)

NECO: WAEC/NECO Technical Drawing, Solid Geometry item 13 (pictorial drawing: isometric, oblique, perspective in one- and two-point; freehand sketching) and Paper 3 Section A sketching. (Not a JAMB UTME subject: Technical Drawing is absent from JAMB’s official IBASS e-syllabus list.)

What you will learn

Distinguish isometric, oblique and perspective drawings and choose suitably.
Construct an isometric scale and draw isometric views from orthographic views.
Draw isometric circles and curves.
Draw cavalier and cabinet oblique views.
Construct one- and two-point perspectives.
Produce clear freehand sketches and exploded views.

Key points

Isometric axes: vertical and two at 30°.
Isometric scale 0.816; isometric drawing uses true lengths.
Measure only along isometric lines.
Four-centre ellipses for circles.
Oblique: true front; cabinet halves depth.
Put circles and long dimensions on the oblique front face.
Perspective: SP, PP, HL, GL, VP.
One-point: one VP; two-point: two VPs on the horizon.
VP found by parallels from SP.
Sketch freehand with light boxes, then firm outlines and labels.

Start here: Pictorial drawing: purpose and types

Orthographic views (td5) are exact but need training to read. A pictorial drawing shows three faces of an object in one view, so anyone can understand it: a customer looking at a wardrobe design in a furniture showroom in Ibadan, a learner assembling flat-pack furniture, or an examiner checking that you have understood a set of views.

Types required by the syllabus

Type	Key feature	Typical use
Isometric	Three axes 120° apart; two at 30° to horizontal	Machine parts, exam “draw the isometric view”
Oblique	Front face true shape; receding lines at 30° or 45°	Objects with circles on one face
Perspective	Receding lines meet at vanishing points	Buildings, interiors, presentations
Freehand sketch	Any of the above without instruments	Paper 3 Section A, quick ideas

Axonometric family

Isometric belongs to the axonometric projections, in which the object is turned and tilted so that three faces are seen, and projectors are parallel. If all three axes are equally foreshortened it is isometric (equal measure); if two are equal, dimetric; if none, trimetric. Only isometric is examined in depth.

Choosing the type

Rectangular parts with features on several faces: isometric.
Parts with many circles on one face (a flange, a pulley, a gear blank): oblique, with that face to the front.
Buildings and anything where realism matters: perspective.

Continue this lesson in the free app →

Practice questions

1. In isometric drawing, the receding axes are drawn at

30° to the horizontal
45° to the horizontal
60° to the horizontal
15° to the horizontal

Show answer

A: 30° to the horizontal
Isometric axes are 120° apart.

2. A true length of 50 mm on the isometric scale measures about

50 mm
35.4 mm
61.2 mm
40.8 mm

Show answer

D: 40.8 mm
50 × 0.816 ≈ 40.8 mm.

3. The isometric scale factor is about

0.707
1.225
0.816
0.5

Show answer

C: 0.816
√(2/3) ≈ 0.816.

4. A circle in isometric appears as

a rhombus
an ellipse
a circle
a parabola

Show answer

B: an ellipse
Circles on isometric faces become ellipses.

5. In oblique drawing, circles are drawn as true circles when they lie

on the front face
on the top face
on a receding face
in any face

Show answer

A: on the front face
The front plane is true shape.

Key words

Pictorial drawing: Drawing showing three faces in one view.
Axonometric: Parallel projection of a turned and tilted object.
Isometric: Axonometric with equal foreshortening on three axes.
Isometric scale: Scale reducing true lengths to 0.816.
Non-isometric line: Line not parallel to an isometric axis.
Four-centre method: Approximate isometric ellipse with four arcs.
Oblique: Front face true shape with receding lines.
Cavalier: Oblique with full-length receding lines.
Cabinet: Oblique with half-length receding lines.
Perspective: Drawing with converging lines like the eye sees.
Station point: Position of the eye.
Picture plane: Plane on which the perspective is traced.

Learn Isometric, oblique, one- and two-point perspective, freehand and exploded views step by step, free.
The Cara's Tips app teaches every topic from the very basics, with quick checks, worked examples and exam practice. It works offline.
Open this lesson in the free app Download for Android