ISOMETRIC PROJECTION IS AN AXONOMETRIC (PICTORIAL) PROJECTION IN WHICH THE OBJECT IS TILTED SO THAT ALL THREE PRINCIPAL AXES MAKE EQUAL ANGLES WITH THE PLANE OF PROJECTION. "ISO-METRIC" = EQUAL MEASURE. That is the definition and the name simultaneously: the three axes are foreshortened EQUALLY. THE RESULTING ANGLES, which must be memorised: · THE THREE AXES APPEAR 120° APART on the paper. · The vertical axis stays VERTICAL. · The two horizontal axes are drawn at 30° TO THE HORIZONTAL. Hence isometric paper's 30°/60° grid, and hence a 30°–60° set square is the only tool needed. z (vertical) │ │ │ ╱ ╲ 30° ╱ ╲ 30° ╱ ╲ x y THE FORESHORTENING FACTOR, and the distinction that examiners reliably test: THE TRUE GEOMETRIC FORESHORTENING is cos(35.264°) = √(2/3) = 0.8165 So a 100 mm edge PROJECTS to 81.65 mm. Drawing with this factor gives an ISOMETRIC PROJECTION, and it requires either an isometric scale or a multiplication on every dimension. IN PRACTICE, EDGES ARE DRAWN AT FULL LENGTH. A 100 mm edge is drawn 100 mm. This gives an ISOMETRIC DRAWING (or isometric VIEW), which is 1 / 0.8165 = 1.2247 times larger than the true projection — ABOUT 22.5% OVERSIZE — BUT IDENTICAL IN SHAPE. ISOMETRIC PROJECTION → uses 0.8165 ×; geometrically exact ISOMETRIC DRAWING → uses 1.0 ×; 22.5% larger; THE NORMAL CHOICE, because the shape is unaffected and no arithmetic is needed on any dimension THE RULES FOR CONSTRUCTION: 1. MEASUREMENTS ARE MADE ONLY ALONG THE THREE ISOMETRIC AXES (or lines parallel to them). Such lines are ISOMETRIC LINES and are drawn to scale. 2. NON-ISOMETRIC LINES — any edge not parallel to an axis, such as a slope — ARE NOT TRUE LENGTH AND CANNOT BE MEASURED DIRECTLY. They are constructed by locating their two END POINTS by isometric coordinates and joining them. THIS IS THE SINGLE MOST COMMON ERROR: measuring an inclined edge directly along its own direction. 3. ANGLES ARE NEVER TRUE. A 90° corner draws as 60° or 120°, so an angle can never be set with a protractor — it must be located by coordinates. 4. CIRCLES BECOME ELLIPSES. A circle on any isometric face draws as an ellipse, constructed by the FOUR-CENTRE METHOD: draw the isometric square (a rhombus) enclosing the circle, then draw four arcs from the four centres given by the rhombus's corners and the midpoints of its sides. The major axis of the ellipse is perpendicular to the axis of the cylinder. 5. HIDDEN LINES ARE NORMALLY OMITTED in pictorial views — the purpose is comprehension, not complete specification. THE ISOMETRIC BOX METHOD, which is how these are actually drawn: Enclose the object in an isometric rectangular box of its overall dimensions, then cut material away by locating features on the box faces. THIS TURNS A HARD FREEHAND PROBLEM INTO A SEQUENCE OF MEASUREMENTS ALONG AXES. THE THREE AXONOMETRIC PROJECTIONS, of which isometric is one: ISOMETRIC — all three axes equally foreshortened (0.8165 each). ONE scale, so it is the easiest to draw; used almost universally. DIMETRIC — TWO axes equally foreshortened, the third different. Two scales needed. TRIMETRIC — ALL THREE different. Three scales; the most realistic and the least drawn by hand. THE TRADE-OFF IS SIMPLICITY AGAINST REALISM, and isometric wins on simplicity so decisively that the other two are rare outside CAD.

THE ADVANTAGES: · SHOWS THREE FACES IN ONE VIEW, so the object is grasped immediately. · REQUIRES NO TRAINING TO READ — this is why it goes in assembly instructions and sales literature. · ALL THREE AXES USE THE SAME SCALE, so it is quick to draw with one set square. · NO PERSPECTIVE CONVERGENCE, so parallel edges stay parallel and the drawing can still be measured along the axes. · EXCELLENT FOR ASSEMBLY AND EXPLODED VIEWS, where spatial relationships matter more than dimensions. THE DISADVANTAGES, and they are the reason it does not replace orthographic projection: · NO FACE IS IN TRUE SHAPE. Every face is a distorted parallelogram. · ANGLES ARE ALL WRONG, so angular features cannot be dimensioned naturally. · CIRCLES BECOME ELLIPSES and are laborious to construct. · IT LOOKS SLIGHTLY UNNATURAL, because the human eye expects perspective convergence — distant edges appear the same size as near ones, which the brain reads as a mild distortion. · DIMENSIONING IS AWKWARD, since dimension lines and text must lie in the plane of the face they describe. THE DIVISION OF LABOUR IN A REAL DRAWING SET, which is the concluding point of this topic: ORTHOGRAPHIC VIEWS ARE FOR MANUFACTURING — they carry the true sizes, the tolerances and the complete specification. THE ISOMETRIC VIEW IS FOR COMPREHENSION — it appears on the same sheet, usually in a corner, so the machinist can see at a glance what the part is before reading the views. NEITHER REPLACES THE OTHER. A drawing that has only an isometric view cannot be made from; a drawing with only orthographic views can be made from but is slower to understand. ISOMETRIC VERSUS PERSPECTIVE, the last comparison: ISOMETRIC PERSPECTIVE ─────────────────────────────────────────────────────────── projectors PARALLEL CONVERGE at the eye parallel edges stay parallel CONVERGE to vanishing points equal lengths draw equal draw SHORTER when everywhere further away measurable? YES, along the NO axes realism moderate HIGH use engineering, architecture, assembly presentation, art ─────────────────────────────────────────────────────────── PERSPECTIVE IS HOW THE EYE SEES; ISOMETRIC IS HOW THE OBJECT IS. An architect showing a client a building uses perspective; an engineer showing a fitter an assembly uses isometric.