LC DCG cheat sheet

Line types carry fixed meaning: continuous thick = visible outline; continuous thin = dimension, projection and leader lines; short-dashed = hidden edge; chain thin = centre line or plane of symmetry; chain thick at ends = cutting-plane line.

Dimensioning rules: place dimensions outside the outline where possible, never dimension a hidden edge, give each dimension once, and keep dimension lines at least 8 mm clear of the object.

Standard scales: full size 1:1; enlargements 2:1, 5:1, 10:1; reductions 1:2, 1:5, 1:10, 1:20, 1:50, 1:100, 1:200, 1:500, 1:1000. Scale = drawing length / real length.

Third-angle projection (ISO A/European practice): the plan is placed above the elevation, the end view to the side the observer looks from. First-angle projection (ISO E): plan below elevation, end view on the opposite side.

In first-angle projection the symbol shows a truncated cone with the small circle on the right of the front view and the two circles of the end view on the left; third-angle reverses this.

Sheet sizes ISO A series halve in area each step: A0 = 841 x 1189 mm, A1 = 594 x 841, A2 = 420 x 594, A3 = 297 x 420, A4 = 210 x 297 mm.

Title block must state title, drawing number, scale, projection symbol, material, date, and the names/initials of draughtsperson and checker.

Auxiliary dimension or reference dimension (shown in brackets) is given for information only and is not used for manufacture; tolerances are stated as limits or as plus/minus values after the nominal size.

Ground line XY separates the plan (horizontal plane) from the elevation (vertical plane); a point's height above XY in elevation equals its height above the horizontal plane, and its distance below XY in plan equals its distance in front of the vertical plane.

A line parallel to both planes appears true length in both plan and elevation. A line parallel to one plane only shows true length in that view; the other view is foreshortened and parallel to XY.

True length of a line from plan and elevation: TL = sqrt((plan length)^2 + (difference in heights)^2). True inclination to the horizontal plane is found from the right triangle whose base is the plan length.

To find true shape of a plane surface, project an auxiliary view at right angles to the edge view of the surface; the edge view is obtained by viewing in a direction parallel to the plane.

A plane appears as an edge when the line of sight lies in the plane; the edge view of an oblique plane is found by an auxiliary elevation taken perpendicular to a line in the plane that is already true length.

Trace of a plane: the horizontal trace is where the plane meets the horizontal plane; the vertical trace where it meets the vertical plane. Both traces meet on XY.

Angle between two planes equals the angle between their edge views, or between lines drawn perpendicular to their line of intersection in a view showing that line true length.

Point on a line dividing it in a given ratio appears in the same ratio in every orthographic view, because parallel projection preserves ratios along a line.

Intersection of a line with a plane: locate the point where the line's plan crosses the plan trace of a cutting plane containing the line, then project to elevation.

Feature-based parametric modelling: a part is a history tree of sketches and features (extrude, revolve, sweep, loft, fillet, shell, hole); editing an early sketch or dimension rebuilds all downstream features.

Fully constrained sketch: every degree of freedom removed, shown by a change of colour and no remaining drag; under-constrained geometry is free to move and breaks design intent.

Boolean operations: union (add material), difference (cut/subtract), intersection (keep common volume). In a solid modeller a cut is a subtract operation.

File exchange: native parametric files retain the feature tree; STEP (.stp) and IGES carry geometry only (B-rep/NURBS surfaces) and lose history; STL carries a triangulated mesh for 3D printing and has no units or features.

Orthographic views generated from a 3D model are associative: change the model and the drawing views, dimensions and sections update on rebuild.

Drawing standards in CAD: set line weights in mm (e.g. 0.5 visible, 0.25 hidden/dimension), use layers for line type and line weight, and place dimensions on a dedicated dimension layer.

Rendering versus modelling: a rendered image (material, lighting, shadow) communicates appearance; a section view or exploded view communicates internal or assembly construction.

A section view is produced by a cutting plane through the model; hatch the cut material at 45 degrees, and do not hatch standard parts such as shafts, bolts, nuts, pins or keys cut longitudinally.

Geometric constraints in sketchers: coincident, collinear, concentric, tangent, parallel, perpendicular, equal, symmetric, horizontal, vertical; dimensional constraints set size.

Design process sequence: identify the need, write a design brief, research, write specifications, generate concepts, evaluate and select, develop detail, model/prototype, test and evaluate, communicate.

Specification criteria split into constraints (must be met: budget, size, safety standard, deadline) and considerations/desired features (ranked preferences used to compare concepts).

Concept selection by weighted decision matrix: score each concept against criteria, multiply score by criterion weight, sum; the highest weighted total is selected, subject to all constraints being satisfied.

Anthropometric data for ergonomic design is quoted as a percentile (5th, 50th, 95th); use the 5th percentile for reach limits and the 95th for clearance, and state male/female population separately.

Standard drawing conventions for design communication: orthographic views for manufacture, isometric or pictorial for presentation, exploded view for assembly sequence, sectional view for internal detail.

Evaluation against the brief must cite measured evidence (test results, dimensions, cost figures) rather than opinion; each constraint is marked met or not met.

Material and process selection: consider strength-to-weight, cost per unit, formability, joining method, finish and recyclability; process choice (injection moulding, laser cutting, 3D printing) constrains draft angles, minimum wall thickness and tolerances.

Sustainability checks: material mass, recycled content, energy in manufacture, disassembly for repair and end-of-life route.

Isometric drawing: axes at 30 degrees to the horizontal, all three axes drawn to the same scale; circles in isometric appear as ellipses with major axis about 1.22 x diameter and minor axis about 0.71 x diameter.

Isometric versus oblique: isometric uses three equal 30-degree axes; cavalier oblique draws the front face true shape with receding edges at 45 degrees full scale; cabinet oblique halves the receding scale.

One-point and two-point perspective: one-point has a single vanishing point for receding edges; two-point uses two vanishing points on the horizon, and vertical edges stay vertical.

Perspective construction: the horizon line carries the vanishing points; the station point distance and picture plane position control the cone of vision; keep the object within about a 30-degree cone to limit distortion.

Presentation drawing layout: dominant pictorial or elevation, secondary views, title and annotation, consistent line hierarchy (thickest for foreground outline, thin for construction and hidden detail).

Exploded isometric assemblies: parts are drawn along a common axis or leader lines in assembly order; each part is numbered with a balloon and listed in a parts table.

Colour and shading in presentation: a single consistent light source, hatching or tonal shading to show form, and contrast reserved for the focal component.

Right triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent; Pythagoras a^2 + b^2 = c^2.

Sine rule: a/sin A = b/sin B = c/sin C = 2R (R = circumradius). Use when given a side and its opposite angle plus one more part.

Cosine rule: a^2 = b^2 + c^2 - 2bc cos A; use when given two sides and the included angle, or all three sides.

Area of triangle = (1/2)ab sin C; area of any polygon can be found by splitting into triangles or by the coordinate (shoelace) formula.

Circle: circumference = pi d, area = pi r^2; arc length = (theta/360) x 2 pi r for theta in degrees; sector area = (theta/360) x pi r^2.

Radians: 180 degrees = pi radians; arc length s = r theta and sector area = (1/2) r^2 theta with theta in radians.

Angle in a semicircle is 90 degrees; angle at the centre is twice the angle at the circumference; opposite angles of a cyclic quadrilateral sum to 180 degrees.

Tangent to a circle is perpendicular to the radius at the point of contact; the angle between a tangent and a chord equals the angle in the alternate segment.

Volume and surface: cylinder V = pi r^2 h; cone V = (1/3) pi r^2 h; sphere V = (4/3) pi r^3, surface = 4 pi r^2; prism V = area of cross-section x length.

Line types have fixed meanings: continuous thick for visible outlines, continuous thin for dimension and projection lines, short dashes for hidden edges, chain thin for centre lines, and chain thick at the ends for cutting planes.

Dimensioning rules: dimension outside the outline where possible, never dimension a hidden edge, give each dimension once only, and keep dimension lines at least 8 mm clear of the object.

Standard scale ratios: 1:1 full size; enlargements 2:1, 5:1, 10:1; reductions 1:2, 1:5, 1:10, 1:20, 1:50, 1:100, 1:200, 1:500, 1:1000. Scale = drawing length divided by real length.

Third-angle projection places the plan above the elevation and the end view on the side the observer looks from; first-angle places the plan below the elevation and the end view on the opposite side.

The projection symbol shows a truncated cone: in first-angle the small circle is on the right of the front view and the end view is drawn on the left; third-angle reverses this arrangement.

ISO A series sheet sizes halve in area at each step: A0 841 x 1189 mm, A1 594 x 841, A2 420 x 594, A3 297 x 420, A4 210 x 297 mm.

The title block records title, drawing number, scale, projection symbol, material, date, and the names or initials of the draughtsperson and checker.

A reference dimension is shown in brackets for information only and is not used for manufacture; tolerances are given as limit sizes or as a plus/minus value after the nominal size.

The ground line XY separates plan from elevation: a point's height above XY in elevation equals its height above the horizontal plane, and its distance below XY in plan equals its distance in front of the vertical plane.

A line parallel to both reference planes shows true length in both plan and elevation; a line parallel to one plane only shows true length in that view, and its other view is foreshortened and parallel to XY.

True length of a line from plan and elevation: TL = square root of (plan length squared plus difference in heights squared). The inclination to the horizontal plane comes from the right triangle whose base is the plan length.

To obtain the true shape of a plane surface, take an auxiliary view at right angles to the edge view of that surface; the edge view is found by viewing in a direction parallel to the plane.

A plane appears as an edge when the line of sight lies in the plane; for an oblique plane the edge view is found by an auxiliary elevation taken perpendicular to a line in the plane that is already true length.

The horizontal trace is where a plane meets the horizontal plane and the vertical trace is where it meets the vertical plane; both traces intersect on XY.

The angle between two planes equals the angle between their edge views, or between lines drawn perpendicular to their line of intersection in a view that shows that line true length.

A point dividing a line in a given ratio appears in the same ratio in every orthographic view, because parallel projection preserves ratios along a line.

To find where a line meets a plane, use a cutting plane containing the line, find where its plan trace crosses the plan of the line, then project that point to the elevation.

Feature-based parametric modelling builds a part as a history tree of sketches and features such as extrude, revolve, sweep, loft, fillet, shell and hole; editing an early sketch or dimension rebuilds every downstream feature.

A fully constrained sketch has every degree of freedom removed, shown by a colour change and no remaining draggable geometry; under-constrained geometry can move and breaks design intent.

Boolean operations: union adds material, difference (cut) subtracts material, intersection keeps only the common volume; a cut in a solid modeller is a subtract operation.

File exchange: native parametric files keep the feature tree; STEP (.stp) and IGES carry geometry only as B-rep/NURBS surfaces and lose the history; STL carries a triangulated mesh for 3D printing with no units or features.

Orthographic views generated from a 3D model are associative, so changing the model updates drawing views, dimensions and sections on rebuild.

CAD drawing standards: set line weights in millimetres (for example 0.5 visible, 0.25 hidden and dimension), use layers to control line type and line weight, and keep dimensions on a dedicated dimension layer.

A rendered image with material, lighting and shadow communicates appearance, whereas a section or exploded view communicates internal construction or assembly sequence.

A section view comes from a cutting plane through the model; hatch the cut material at 45 degrees and do not hatch standard parts such as shafts, bolts, nuts, pins and keys cut longitudinally.

Common sketcher constraints: coincident, collinear, concentric, tangent, parallel, perpendicular, equal, symmetric, horizontal and vertical; dimensional constraints set size.

Design process sequence: identify the need, write the design brief, research, write the specification, generate concepts, evaluate and select, develop detail, model or prototype, test and evaluate, then communicate the outcome.

Specification criteria split into constraints that must be met (budget, size, safety standard, deadline) and considerations or ranked desired features used to compare concepts.

Weighted decision matrix: score each concept against each criterion, multiply each score by the criterion weight and sum; the highest weighted total is selected provided all constraints are satisfied.

Anthropometric data is quoted by percentile (5th, 50th, 95th); use the 5th percentile for reach limits and the 95th for clearance, and state male and female populations separately.

Communication conventions: orthographic views for manufacture, isometric or pictorial views for presentation, exploded views for assembly sequence, and sectional views for internal detail.

Evaluation against the brief cites measured evidence such as test results, dimensions and cost figures rather than opinion, and marks each constraint as met or not met.

Material and process selection weighs strength-to-weight, unit cost, formability, joining method, finish and recyclability; the chosen process constrains draft angles, minimum wall thickness and achievable tolerance.

Sustainability checks cover material mass, recycled content, energy in manufacture, disassembly for repair, and the end-of-life route.

Isometric drawing uses three axes at 30 degrees to the horizontal at the same scale; a circle in isometric appears as an ellipse with major axis about 1.22 x diameter and minor axis about 0.71 x diameter.

Isometric uses three equal 30-degree axes; cavalier oblique draws the front face true shape with receding edges at 45 degrees at full scale, and cabinet oblique halves the receding scale.

One-point perspective has a single vanishing point for receding edges; two-point perspective uses two vanishing points on the horizon while vertical edges stay vertical.

Perspective construction: the horizon line carries the vanishing points; the station point distance and picture plane position control the cone of vision, and keeping the object within about a 30-degree cone limits distortion.

Presentation layout: a dominant pictorial or elevation, secondary views, title and annotation, and a consistent line hierarchy with the thickest line for the foreground outline and thin lines for construction and hidden detail.

Exploded isometric assemblies draw parts along a common axis or leader lines in assembly order; each part carries a balloon number and appears in the parts table.

Colour and shading in presentation use a single consistent light source, hatching or tonal shading to describe form, and reserve the strongest contrast for the focal component.

Right triangle ratios: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent; Pythagoras gives a^2 + b^2 = c^2.

Sine rule: a/sin A = b/sin B = c/sin C = 2R where R is the circumradius; use it when given a side and its opposite angle plus one further part.

Cosine rule: a^2 = b^2 + c^2 - 2bc cos A; use it when given two sides and the included angle, or all three sides.

Triangle area = (1/2)ab sin C; the area of any polygon follows from splitting it into triangles or from the coordinate shoelace formula.

Circle: circumference = pi d and area = pi r^2; arc length = (theta/360) x 2 pi r and sector area = (theta/360) x pi r^2 for theta in degrees.

Radians: 180 degrees = pi radians; arc length s = r theta and sector area = (1/2) r^2 theta with theta in radians.

Circle theorems: the angle in a semicircle is 90 degrees, the angle at the centre is twice the angle at the circumference, and opposite angles of a cyclic quadrilateral sum to 180 degrees.

A tangent is perpendicular to the radius at the point of contact, and the angle between a tangent and a chord equals the angle in the alternate segment.

Volumes: cylinder V = pi r^2 h; cone V = (1/3) pi r^2 h; sphere V = (4/3) pi r^3 with surface 4 pi r^2; prism V = area of cross-section x length.