JC Graphics cheat sheet

Orthographic projection rule: adjacent views align on shared projection lines; front and top views share width, front and side views share height, top and side views share depth.

Third-angle projection places the top view above the front view and the right-side view to the right; first-angle projection reverses both placements.

Line types by function: continuous thick for visible outlines, dashed for hidden edges, chain thin for centre lines and pitch circles, continuous thin for dimension and projection lines.

Dimensioning: place dimensions outside the outline where possible, never dimension to a hidden line, and give each feature one dimension only to avoid duplication.

Section views use uniformly spaced hatching at 45 degrees; adjacent parts are hatched in opposite directions; section lines are omitted on shafts, ribs, and fasteners cut lengthwise.

Isometric axes are 120 degrees apart with true lengths along all three axes; isometric drawings are about 1.22 times the true isometric projection, so use full scale for clarity.

Auxiliary views are projected perpendicular to a slanted surface to show its true shape; an oblique surface appears foreshortened in all three principal views.

Scale formula: drawing length divided by real length gives the representative fraction, e.g. 1:50 means 1 mm on paper equals 50 mm in reality.

Polygon interior angle sum = (n - 2) x 180 degrees; each interior angle of a regular n-gon = (n - 2) x 180 / n.

Circle theorems: angle in a semicircle is 90 degrees; angle at the centre is twice the angle at the circumference on the same arc; angles in the same segment are equal.

Tangency construction: the tangent at a point is perpendicular to the radius there; for two circles, the point of contact lies on the line joining centres.

Conic sections: a plane parallel to the generator gives a parabola; cutting one nappe at an angle steeper than the generator gives an ellipse; cutting both nappes gives a hyperbola.

Ellipse construction: sum of focal distances is constant (2a); the trammel or concentric-circle method gives points, and the minor axis relates by b squared = a squared minus c squared.

Solid volumes: prism and cylinder V = base area x height; pyramid and cone V = one third base area x height; sphere V = four thirds pi r cubed.

Surface areas: cylinder curved area = 2 pi r h; cone curved area = pi r l where l is slant height; sphere = 4 pi r squared.

Regular tetrahedron, cube, and octahedron are the Platonic solids with triangular, square, and triangular faces meeting three, three, and four at each vertex respectively.

Drawing sheet sizes follow ISO A series: A0 is 841 x 1189 mm and each subsequent size halves the longer side, so A1 is 594 x 841 mm.

Title block content: drawing number, title, scale, projection symbol, material, tolerances, date, and approval signatures; the projection symbol distinguishes first- from third-angle.

Lettering standards: ISO 3098 specifies vertical or sloped capitals; text height must be at least 2.5 mm for readability on reproduction.

Line width hierarchy: thick lines are twice thin lines; recommended thick widths are 0.5 or 0.7 mm, with thin lines 0.25 or 0.35 mm.

Colour and contrast: use high value contrast between figure and ground; avoid red-green pairings for colour-blind users, roughly 8 percent of men.

Layout principles: alignment, proximity, repetition, and contrast group related information; the golden ratio 1:1.618 or the rule of thirds guides proportion.

Geometric construction for communication: a logo or symbol built on a grid or circle base is reproducible by construction, so specify radii, centres, and tangent conditions.

Technical report structure: define the problem, state assumptions, present the construction or calculation, then evaluate the result against the brief.