MATSEC IM Engineering Drawing and Graphical Communication cheat sheet

ISO 5457 defines sheet sizes A0–A4; each size is half the area of the previous one, with A0 = 841 × 1189 mm and the ratio fixed at 1:√2.

ISO 5455 sets scale categories: full size 1:1, enlargement (e.g. 2:1, 5:1), and reduction (e.g. 1:2, 1:10); the scale is stated in the title block, and a detail may carry its own scale.

Line types follow ISO 128: continuous thick for visible outlines (about 0.5–0.7 mm), continuous thin for dimension, extension, hatching and leader lines, dashed for hidden edges, chain thin for centre lines and cutting planes.

ISO 3098 lettering: upright capitals and numerals, height h not less than 2.5 mm; the ratio of height to line width is 10:1 for style B, and lowercase letters are used only where the standard permits.

First-angle projection (ISO, used in Europe and Malta) places the object between the observer and the plane, so the view seen from the front is drawn behind the object; third-angle projection (ASME) places the plane between observer and object.

First-angle symbol: a truncated cone shown as two concentric circles on the left with its side elevation on the right; third-angle symbol reverses this arrangement.

A drawing frame and title block per ISO 7200 record title, drawing number, scale, projection symbol, material, date, and the responsible person.

Line precedence when lines coincide: visible outlines take priority over hidden outlines, which take priority over centre lines, which take priority over dimension and extension lines.

Bisecting a line: strike equal arcs from both endpoints with radius greater than half the line; the line joining the arc intersections is the perpendicular bisector.

Bisecting an angle: strike an arc from the vertex cutting both arms, then equal arcs from those two points; the line from the vertex through their intersection is the bisector.

Regular polygon in a circle: for a hexagon, step the radius around the circumference six times; for any n-gon, divide the diameter into n equal parts and use the standard construction through the second division point.

An ellipse is the locus of points whose sum of distances to two foci is constant (2a); major axis = 2a, minor axis = 2b, and b² = a² − c², where c is the focal distance.

Ellipse by concentric circles: draw circles on the major and minor axes, divide them into the same number of equal sectors, and intersect corresponding vertical and horizontal lines.

Conic sections: a plane cutting a cone parallel to one generator gives a parabola, cutting at a steeper angle than the generator gives a hyperbola, and cutting obliquely through all generators gives an ellipse.

Tangent to a circle from an external point: bisect the line joining the point to the centre; the circle on that diameter meets the given circle at the tangent points.

A cycloid is traced by a point on a circle rolling along a straight line; an epicycloid rolls outside a base circle, a hypocycloid inside; the generating circle's circumference must be divided into the same number of parts as the base line or circle.

Standard arrangement of three views: front elevation, plan (top view) placed below it in first-angle, and end/side elevation placed to the right; heights transfer horizontally, depths transfer via a 45° mitre line.

Hidden detail is drawn as dashed lines only where it is not visible in that view; the dash length is roughly 3–4 times the gap, and dashes meet at corners.

Centre lines are chain-dotted thin lines extended slightly beyond the feature; they locate axes of symmetry, hole centres and pitch circles.

Choosing the front view: select the direction that shows the most characteristic shape and the fewest hidden features, and align the longest dimension horizontally.

A point's projection: the plan lies directly below the elevation, and the distance of the plan from the XY line equals the distance of the point in front of the vertical plane.

Inclined surfaces appear foreshortened in the views where they are not parallel to the plane of projection; an edge view appears only in the view perpendicular to the surface.

Six principal views exist (front, top, bottom, left, right, rear); a view is omitted only when it adds no information, e.g. for a body of revolution where one elevation plus the end view suffices.

Isometric axes are at 30° to the horizontal; all three axes are drawn to the same scale, and the true lengths are 0.816 times the isometric drawing length (isometric drawing uses full scale along the axes).

In isometric drawing, circles on the three principal faces become ellipses with a major axis 1.22 × diameter and a minor axis 0.71 × diameter; the four-centre approximate method is acceptable.

Non-isometric lines are lines not parallel to any isometric axis; their endpoints are located on isometric lines and then joined - they are never scaled directly.

Oblique projection: the front face is drawn true shape and size, and receding edges are drawn at a chosen angle (commonly 45°) with a scale of 1/2 for cavalier or 1/2–2/3 for cabinet projection.

Perspective: one-point uses a single vanishing point for receding edges, two-point uses two, and three-point adds a vertical vanishing point; objects on the picture plane keep true size.

Axonometric projection family: isometric (all three axes equally inclined), dimetric (two equal), trimetric (all different); all are orthographic projections from an inclined direction.

Exploded pictorial views show components separated along assembly axes, with thin chain lines or centre lines indicating the assembly path; item numbers link to a parts list.

Dimension lines are thin continuous lines terminated by arrowheads, placed outside the outline where possible, with the numeral above the line and readable from the bottom or right-hand edge.

Extension lines start about 1 mm clear of the object and extend about 2 mm beyond the dimension line; dimension lines must not coincide with outline, centre or extension lines.

Each dimension is given once only, on the view where the feature appears true shape; no dimension is repeated on another view.

ISO limits and fits notation: a hole is written uppercase (e.g. 30 H7) and a shaft lowercase (e.g. 30 g6); H denotes a hole whose lower deviation is zero, h a shaft whose upper deviation is zero.

Fundamental deviation letter gives the position of the tolerance zone, and the number gives the tolerance grade (IT01 to IT18); smaller grade numbers mean tighter tolerances.

Geometric tolerancing per ISO 1101 uses a rectangular frame: symbol (e.g. straightness, flatness, position, concentricity), tolerance value, and datum letters; the frame is linked to the feature by a leader.

Surface texture per ISO 1302 uses the tick symbol with Ra value in micrometres; the basic symbol means any process, the circle-in-tick means material removal not allowed, and the bar means removal required.

A taper is dimensioned by its ratio (e.g. 1:10) or by the included angle, not by both; a chamfer is dimensioned by its length and angle, e.g. 2 × 45°.

A full section removes the near half of the object; the cutting plane is shown as a chain thick line with arrows indicating the viewing direction and labelled A–A.

Hatching (section lining) uses thin continuous lines at 45° to the principal outlines, spaced evenly; adjacent parts in an assembly are hatched at different angles or spacings.

Standard parts such as shafts, bolts, nuts, rivets, keys and pins are not sectioned when cut longitudinally; webs and ribs are not hatched when the cutting plane passes along their length.

A half section shows one quarter removed and is used for symmetrical objects; a broken-out section uses a freehand break line to expose a local feature.

An auxiliary view is projected on a plane parallel to an inclined face so the face appears true shape; its depth from the reference plane is transferred from the view that shows the face as an edge.

Development of a right cylinder: the pattern is a rectangle of width πD and height equal to the cylinder height; a truncated cylinder's pattern is obtained by projecting generator heights onto the divided circumference.

Development of a right cone: the pattern is a sector of radius equal to the slant height L, with sector angle θ = 360° × (D / 2L), where D is the base diameter.

True length of an inclined line is found by rotating it parallel to a reference plane, or by constructing a right triangle with the plan length as base and the difference in heights as altitude.

Thread conventions: the crest of an external thread is a thick continuous line and the root a thin continuous line about 0.25 mm inside; in the end view the root circle is drawn as a thin line broken at about three-quarters.

Metric thread designation M20 × 2.5 means nominal diameter 20 mm and pitch 2.5 mm; a coarse thread omits the pitch, and a left-hand thread is marked LH.

A key transmits torque between shaft and hub; a keyway depth is dimensioned from the shaft side, and the key width is nominally one-quarter of the shaft diameter.

A rolling bearing is designated by a basic number whose last two digits give the bore in units of 5 mm (e.g. 6205 has a 25 mm bore); a prefix or suffix denotes shield, seal or clearance class.

Assembly drawings show all parts in position with item numbers, a parts list (item, description, quantity, material) and overall dimensions; detail drawings give each part's full dimensions and tolerances.

A welded joint is shown by a reference line with an arrow, the symbol above the line for the arrow side and below for the other side; a fillet weld symbol is a right triangle with the leg size in front.

A gear is specified by module m = pitch circle diameter / number of teeth; addendum = m, dedendum = 1.25 m, and the outside diameter = m(z + 2) for standard spur gears.

A bar chart compares discrete categories, a histogram shows the frequency distribution of continuous data, and a line graph shows a trend against a continuous variable such as time.

On a graph, the independent variable goes on the horizontal axis; each axis carries a quantity and unit (e.g. Time / s) and a scale of equal increments with a stated step.

Pie charts show parts of a whole and must sum to 100%; the sector angle for a category is 360° × (category value / total).

A technical report drawing set includes a title block, parts list, revision table and notes; revisions are recorded with a letter or number, date and description.

Flow charts use standard symbols: oval for start/stop, rectangle for process, diamond for decision, parallelogram for input/output, and arrows for flow direction.

Gantt charts show activities as horizontal bars against a time axis, with dependencies and milestones marked; critical-path items are those with zero float.

Orthographic drawings presented for manufacture must carry units (usually millimetres, stated in a general note), projection symbol, scale, material and general tolerances.

A circuit or system diagram uses standard symbols, and lines represent connections rather than physical wires; layout drawings show physical positions instead.

ISO 5457 defines sheet sizes A0–A4; each size is half the area of the previous one, with A0 = 841 × 1189 mm and the ratio fixed at 1:√2.

ISO 5455 sets scale categories: full size 1:1, enlargement (e.g. 2:1, 5:1), and reduction (e.g. 1:2, 1:10); the scale is stated in the title block, and a detail may carry its own scale.

Line types follow ISO 128: continuous thick for visible outlines (about 0.5–0.7 mm), continuous thin for dimension, extension, hatching and leader lines, dashed for hidden edges, chain thin for centre lines and cutting planes.

ISO 3098 lettering: upright capitals and numerals, height h not less than 2.5 mm; the ratio of height to line width is 10:1 for style B, and lowercase letters are used only where the standard permits.

First-angle projection (ISO, used in Europe and Malta) places the object between the observer and the plane, so the view seen from the front is drawn behind the object; third-angle projection (ASME) places the plane between observer and object.

First-angle symbol: a truncated cone shown as two concentric circles on the left with its side elevation on the right; third-angle symbol reverses this arrangement.

A drawing frame and title block per ISO 7200 record title, drawing number, scale, projection symbol, material, date, and the responsible person.

Line precedence when lines coincide: visible outlines take priority over hidden outlines, which take priority over centre lines, which take priority over dimension and extension lines.

Bisecting a line: strike equal arcs from both endpoints with radius greater than half the line; the line joining the arc intersections is the perpendicular bisector.

Bisecting an angle: strike an arc from the vertex cutting both arms, then equal arcs from those two points; the line from the vertex through their intersection is the bisector.

Regular polygon in a circle: for a hexagon, step the radius around the circumference six times; for any n-gon, divide the diameter into n equal parts and use the standard construction through the second division point.

An ellipse is the locus of points whose sum of distances to two foci is constant (2a); major axis = 2a, minor axis = 2b, and b² = a² − c², where c is the focal distance.

Ellipse by concentric circles: draw circles on the major and minor axes, divide them into the same number of equal sectors, and intersect corresponding vertical and horizontal lines.

Conic sections: a plane cutting a cone parallel to one generator gives a parabola, cutting at a steeper angle than the generator gives a hyperbola, and cutting obliquely through all generators gives an ellipse.

Tangent to a circle from an external point: bisect the line joining the point to the centre; the circle on that diameter meets the given circle at the tangent points.

A cycloid is traced by a point on a circle rolling along a straight line; an epicycloid rolls outside a base circle, a hypocycloid inside; the generating circle's circumference must be divided into the same number of parts as the base line or circle.

Standard arrangement of three views: front elevation, plan (top view) placed below it in first-angle, and end/side elevation placed to the right; heights transfer horizontally, depths transfer via a 45° mitre line.

Hidden detail is drawn as dashed lines only where it is not visible in that view; the dash length is roughly 3–4 times the gap, and dashes meet at corners.

Centre lines are chain-dotted thin lines extended slightly beyond the feature; they locate axes of symmetry, hole centres and pitch circles.

Choosing the front view: select the direction that shows the most characteristic shape and the fewest hidden features, and align the longest dimension horizontally.

A point's projection: the plan lies directly below the elevation, and the distance of the plan from the XY line equals the distance of the point in front of the vertical plane.

Inclined surfaces appear foreshortened in the views where they are not parallel to the plane of projection; an edge view appears only in the view perpendicular to the surface.

Six principal views exist (front, top, bottom, left, right, rear); a view is omitted only when it adds no information, e.g. for a body of revolution where one elevation plus the end view suffices.

Isometric axes are at 30° to the horizontal; all three axes are drawn to the same scale, and the true lengths are 0.816 times the isometric drawing length (isometric drawing uses full scale along the axes).

In isometric drawing, circles on the three principal faces become ellipses with a major axis 1.22 × diameter and a minor axis 0.71 × diameter; the four-centre approximate method is acceptable.

Non-isometric lines are lines not parallel to any isometric axis; their endpoints are located on isometric lines and then joined - they are never scaled directly.

Oblique projection: the front face is drawn true shape and size, and receding edges are drawn at a chosen angle (commonly 45°) with a scale of 1/2 for cavalier or 1/2–2/3 for cabinet projection.

Perspective: one-point uses a single vanishing point for receding edges, two-point uses two, and three-point adds a vertical vanishing point; objects on the picture plane keep true size.

Axonometric projection family: isometric (all three axes equally inclined), dimetric (two equal), trimetric (all different); all are orthographic projections from an inclined direction.

Exploded pictorial views show components separated along assembly axes, with thin chain lines or centre lines indicating the assembly path; item numbers link to a parts list.

Dimension lines are thin continuous lines terminated by arrowheads, placed outside the outline where possible, with the numeral above the line and readable from the bottom or right-hand edge.

Extension lines start about 1 mm clear of the object and extend about 2 mm beyond the dimension line; dimension lines must not coincide with outline, centre or extension lines.

Each dimension is given once only, on the view where the feature appears true shape; no dimension is repeated on another view.

ISO limits and fits notation: a hole is written uppercase (e.g. 30 H7) and a shaft lowercase (e.g. 30 g6); H denotes a hole whose lower deviation is zero, h a shaft whose upper deviation is zero.

Fundamental deviation letter gives the position of the tolerance zone, and the number gives the tolerance grade (IT01 to IT18); smaller grade numbers mean tighter tolerances.

Geometric tolerancing per ISO 1101 uses a rectangular frame: symbol (e.g. straightness, flatness, position, concentricity), tolerance value, and datum letters; the frame is linked to the feature by a leader.

Surface texture per ISO 1302 uses the tick symbol with Ra value in micrometres; the basic symbol means any process, the circle-in-tick means material removal not allowed, and the bar means removal required.

A taper is dimensioned by its ratio (e.g. 1:10) or by the included angle, not by both; a chamfer is dimensioned by its length and angle, e.g. 2 × 45°.

A full section removes the near half of the object; the cutting plane is shown as a chain thick line with arrows indicating the viewing direction and labelled A–A.

Hatching (section lining) uses thin continuous lines at 45° to the principal outlines, spaced evenly; adjacent parts in an assembly are hatched at different angles or spacings.

Standard parts such as shafts, bolts, nuts, rivets, keys and pins are not sectioned when cut longitudinally; webs and ribs are not hatched when the cutting plane passes along their length.

A half section shows one quarter removed and is used for symmetrical objects; a broken-out section uses a freehand break line to expose a local feature.

An auxiliary view is projected on a plane parallel to an inclined face so the face appears true shape; its depth from the reference plane is transferred from the view that shows the face as an edge.

Development of a right cylinder: the pattern is a rectangle of width πD and height equal to the cylinder height; a truncated cylinder's pattern is obtained by projecting generator heights onto the divided circumference.

Development of a right cone: the pattern is a sector of radius equal to the slant height L, with sector angle θ = 360° × (D / 2L), where D is the base diameter.

True length of an inclined line is found by rotating it parallel to a reference plane, or by constructing a right triangle with the plan length as base and the difference in heights as altitude.

Thread conventions: the crest of an external thread is a thick continuous line and the root a thin continuous line about 0.25 mm inside; in the end view the root circle is drawn as a thin line broken at about three-quarters.

Metric thread designation M20 × 2.5 means nominal diameter 20 mm and pitch 2.5 mm; a coarse thread omits the pitch, and a left-hand thread is marked LH.

A key transmits torque between shaft and hub; a keyway depth is dimensioned from the shaft side, and the key width is nominally one-quarter of the shaft diameter.

A rolling bearing is designated by a basic number whose last two digits give the bore in units of 5 mm (e.g. 6205 has a 25 mm bore); a prefix or suffix denotes shield, seal or clearance class.

Assembly drawings show all parts in position with item numbers, a parts list (item, description, quantity, material) and overall dimensions; detail drawings give each part's full dimensions and tolerances.

A welded joint is shown by a reference line with an arrow, the symbol above the line for the arrow side and below for the other side; a fillet weld symbol is a right triangle with the leg size in front.

A gear is specified by module m = pitch circle diameter / number of teeth; addendum = m, dedendum = 1.25 m, and the outside diameter = m(z + 2) for standard spur gears.

A bar chart compares discrete categories, a histogram shows the frequency distribution of continuous data, and a line graph shows a trend against a continuous variable such as time.

On a graph, the independent variable goes on the horizontal axis; each axis carries a quantity and unit (e.g. Time / s) and a scale of equal increments with a stated step.

Pie charts show parts of a whole and must sum to 100%; the sector angle for a category is 360° × (category value / total).

A technical report drawing set includes a title block, parts list, revision table and notes; revisions are recorded with a letter or number, date and description.

Flow charts use standard symbols: oval for start/stop, rectangle for process, diamond for decision, parallelogram for input/output, and arrows for flow direction.

Gantt charts show activities as horizontal bars against a time axis, with dependencies and milestones marked; critical-path items are those with zero float.

Orthographic drawings presented for manufacture must carry units (usually millimetres, stated in a general note), projection symbol, scale, material and general tolerances.

A circuit or system diagram uses standard symbols, and lines represent connections rather than physical wires; layout drawings show physical positions instead.

Bisecting a line: strike equal arcs from both endpoints with radius greater than half the line; the line joining the arc intersections is the perpendicular bisector.

Bisecting an angle: strike an arc from the vertex cutting both arms, then equal arcs from those two points; the line from the vertex through their intersection is the bisector.

Regular polygon in a circle: for a hexagon, step the radius around the circumference six times; for any n-gon, divide the diameter into n equal parts and use the standard construction through the second division point.

An ellipse is the locus of points whose sum of distances to two foci is constant (2a); major axis = 2a, minor axis = 2b, and b² = a² − c², where c is the focal distance.

Ellipse by concentric circles: draw circles on the major and minor axes, divide them into the same number of equal sectors, and intersect corresponding vertical and horizontal lines.

Conic sections: a plane cutting a cone parallel to one generator gives a parabola, cutting at a steeper angle than the generator gives a hyperbola, and cutting obliquely through all generators gives an ellipse.

Tangent to a circle from an external point: bisect the line joining the point to the centre; the circle on that diameter meets the given circle at the tangent points.

A cycloid is traced by a point on a circle rolling along a straight line; an epicycloid rolls outside a base circle, a hypocycloid inside; the generating circle's circumference must be divided into the same number of parts as the base line or circle.

Standard arrangement of three views: front elevation, plan (top view) placed below it in first-angle, and end/side elevation placed to the right; heights transfer horizontally, depths transfer via a 45° mitre line.

Hidden detail is drawn as dashed lines only where it is not visible in that view; the dash length is roughly 3–4 times the gap, and dashes meet at corners.

Centre lines are chain-dotted thin lines extended slightly beyond the feature; they locate axes of symmetry, hole centres and pitch circles.

Choosing the front view: select the direction that shows the most characteristic shape and the fewest hidden features, and align the longest dimension horizontally.

A point's projection: the plan lies directly below the elevation, and the distance of the plan from the XY line equals the distance of the point in front of the vertical plane.

Inclined surfaces appear foreshortened in the views where they are not parallel to the plane of projection; an edge view appears only in the view perpendicular to the surface.

Six principal views exist (front, top, bottom, left, right, rear); a view is omitted only when it adds no information, e.g. for a body of revolution where one elevation plus the end view suffices.

Isometric axes are at 30° to the horizontal; all three axes are drawn to the same scale, and the true lengths are 0.816 times the isometric drawing length (isometric drawing uses full scale along the axes).

In isometric drawing, circles on the three principal faces become ellipses with a major axis 1.22 × diameter and a minor axis 0.71 × diameter; the four-centre approximate method is acceptable.

Non-isometric lines are lines not parallel to any isometric axis; their endpoints are located on isometric lines and then joined - they are never scaled directly.

Oblique projection: the front face is drawn true shape and size, and receding edges are drawn at a chosen angle (commonly 45°) with a scale of 1/2 for cavalier or 1/2–2/3 for cabinet projection.

Perspective: one-point uses a single vanishing point for receding edges, two-point uses two, and three-point adds a vertical vanishing point; objects on the picture plane keep true size.

Axonometric projection family: isometric (all three axes equally inclined), dimetric (two equal), trimetric (all different); all are orthographic projections from an inclined direction.

Exploded pictorial views show components separated along assembly axes, with thin chain lines or centre lines indicating the assembly path; item numbers link to a parts list.

Dimension lines are thin continuous lines terminated by arrowheads, placed outside the outline where possible, with the numeral above the line and readable from the bottom or right-hand edge.

Extension lines start about 1 mm clear of the object and extend about 2 mm beyond the dimension line; dimension lines must not coincide with outline, centre or extension lines.

Each dimension is given once only, on the view where the feature appears true shape; no dimension is repeated on another view.

ISO limits and fits notation: a hole is written uppercase (e.g. 30 H7) and a shaft lowercase (e.g. 30 g6); H denotes a hole whose lower deviation is zero, h a shaft whose upper deviation is zero.

Fundamental deviation letter gives the position of the tolerance zone, and the number gives the tolerance grade (IT01 to IT18); smaller grade numbers mean tighter tolerances.

Geometric tolerancing per ISO 1101 uses a rectangular frame: symbol (e.g. straightness, flatness, position, concentricity), tolerance value, and datum letters; the frame is linked to the feature by a leader.

Surface texture per ISO 1302 uses the tick symbol with Ra value in micrometres; the basic symbol means any process, the circle-in-tick means material removal not allowed, and the bar means removal required.

A taper is dimensioned by its ratio (e.g. 1:10) or by the included angle, not by both; a chamfer is dimensioned by its length and angle, e.g. 2 × 45°.

A full section removes the near half of the object; the cutting plane is shown as a chain thick line with arrows indicating the viewing direction and labelled A–A.

Hatching (section lining) uses thin continuous lines at 45° to the principal outlines, spaced evenly; adjacent parts in an assembly are hatched at different angles or spacings.

Standard parts such as shafts, bolts, nuts, rivets, keys and pins are not sectioned when cut longitudinally; webs and ribs are not hatched when the cutting plane passes along their length.

A half section shows one quarter removed and is used for symmetrical objects; a broken-out section uses a freehand break line to expose a local feature.

An auxiliary view is projected on a plane parallel to an inclined face so the face appears true shape; its depth from the reference plane is transferred from the view that shows the face as an edge.

Development of a right cylinder: the pattern is a rectangle of width πD and height equal to the cylinder height; a truncated cylinder's pattern is obtained by projecting generator heights onto the divided circumference.

Development of a right cone: the pattern is a sector of radius equal to the slant height L, with sector angle θ = 360° × (D / 2L), where D is the base diameter.

True length of an inclined line is found by rotating it parallel to a reference plane, or by constructing a right triangle with the plan length as base and the difference in heights as altitude.

Thread conventions: the crest of an external thread is a thick continuous line and the root a thin continuous line about 0.25 mm inside; in the end view the root circle is drawn as a thin line broken at about three-quarters.

Metric thread designation M20 × 2.5 means nominal diameter 20 mm and pitch 2.5 mm; a coarse thread omits the pitch, and a left-hand thread is marked LH.

A key transmits torque between shaft and hub; a keyway depth is dimensioned from the shaft side, and the key width is nominally one-quarter of the shaft diameter.

A rolling bearing is designated by a basic number whose last two digits give the bore in units of 5 mm (e.g. 6205 has a 25 mm bore); a prefix or suffix denotes shield, seal or clearance class.

Assembly drawings show all parts in position with item numbers, a parts list (item, description, quantity, material) and overall dimensions; detail drawings give each part's full dimensions and tolerances.

A welded joint is shown by a reference line with an arrow, the symbol above the line for the arrow side and below for the other side; a fillet weld symbol is a right triangle with the leg size in front.

A gear is specified by module m = pitch circle diameter / number of teeth; addendum = m, dedendum = 1.25 m, and the outside diameter = m(z + 2) for standard spur gears.

A bar chart compares discrete categories, a histogram shows the frequency distribution of continuous data, and a line graph shows a trend against a continuous variable such as time.

On a graph, the independent variable goes on the horizontal axis; each axis carries a quantity and unit (e.g. Time / s) and a scale of equal increments with a stated step.

Pie charts show parts of a whole and must sum to 100%; the sector angle for a category is 360° × (category value / total).

A technical report drawing set includes a title block, parts list, revision table and notes; revisions are recorded with a letter or number, date and description.

Flow charts use standard symbols: oval for start/stop, rectangle for process, diamond for decision, parallelogram for input/output, and arrows for flow direction.

Gantt charts show activities as horizontal bars against a time axis, with dependencies and milestones marked; critical-path items are those with zero float.

Orthographic drawings presented for manufacture must carry units (usually millimetres, stated in a general note), projection symbol, scale, material and general tolerances.

A circuit or system diagram uses standard symbols, and lines represent connections rather than physical wires; layout drawings show physical positions instead.

ISO 5457 defines sheet sizes A0–A4; each size is half the area of the previous one, with A0 = 841 × 1189 mm and the ratio fixed at 1:√2.

ISO 5455 sets scale categories: full size 1:1, enlargement (e.g. 2:1, 5:1), and reduction (e.g. 1:2, 1:10); the scale is stated in the title block, and a detail may carry its own scale.

Line types follow ISO 128: continuous thick for visible outlines (about 0.5–0.7 mm), continuous thin for dimension, extension, hatching and leader lines, dashed for hidden edges, chain thin for centre lines and cutting planes.

ISO 3098 lettering: upright capitals and numerals, height h not less than 2.5 mm; the ratio of height to line width is 10:1 for style B, and lowercase letters are used only where the standard permits.

First-angle projection (ISO, used in Europe and Malta) places the object between the observer and the plane, so the view seen from the front is drawn behind the object; third-angle projection (ASME) places the plane between observer and object.

First-angle symbol: a truncated cone shown as two concentric circles on the left with its side elevation on the right; third-angle symbol reverses this arrangement.

A drawing frame and title block per ISO 7200 record title, drawing number, scale, projection symbol, material, date, and the responsible person.

Line precedence when lines coincide: visible outlines take priority over hidden outlines, which take priority over centre lines, which take priority over dimension and extension lines.

Bisecting a line: strike equal arcs from both endpoints with radius greater than half the line; the line joining the arc intersections is the perpendicular bisector.

Bisecting an angle: strike an arc from the vertex cutting both arms, then equal arcs from those two points; the line from the vertex through their intersection is the bisector.

Regular polygon in a circle: for a hexagon, step the radius around the circumference six times; for any n-gon, divide the diameter into n equal parts and use the standard construction through the second division point.

An ellipse is the locus of points whose sum of distances to two foci is constant (2a); major axis = 2a, minor axis = 2b, and b² = a² − c², where c is the focal distance.

Ellipse by concentric circles: draw circles on the major and minor axes, divide them into the same number of equal sectors, and intersect corresponding vertical and horizontal lines.

Conic sections: a plane cutting a cone parallel to one generator gives a parabola, cutting at a steeper angle than the generator gives a hyperbola, and cutting obliquely through all generators gives an ellipse.

Tangent to a circle from an external point: bisect the line joining the point to the centre; the circle on that diameter meets the given circle at the tangent points.

A cycloid is traced by a point on a circle rolling along a straight line; an epicycloid rolls outside a base circle, a hypocycloid inside; the generating circle's circumference must be divided into the same number of parts as the base line or circle.

Standard arrangement of three views: front elevation, plan (top view) placed below it in first-angle, and end/side elevation placed to the right; heights transfer horizontally, depths transfer via a 45° mitre line.

Hidden detail is drawn as dashed lines only where it is not visible in that view; the dash length is roughly 3–4 times the gap, and dashes meet at corners.

Centre lines are chain-dotted thin lines extended slightly beyond the feature; they locate axes of symmetry, hole centres and pitch circles.

Choosing the front view: select the direction that shows the most characteristic shape and the fewest hidden features, and align the longest dimension horizontally.

A point's projection: the plan lies directly below the elevation, and the distance of the plan from the XY line equals the distance of the point in front of the vertical plane.

Inclined surfaces appear foreshortened in the views where they are not parallel to the plane of projection; an edge view appears only in the view perpendicular to the surface.

Six principal views exist (front, top, bottom, left, right, rear); a view is omitted only when it adds no information, e.g. for a body of revolution where one elevation plus the end view suffices.

Isometric axes are at 30° to the horizontal; all three axes are drawn to the same scale, and the true lengths are 0.816 times the isometric drawing length (isometric drawing uses full scale along the axes).

In isometric drawing, circles on the three principal faces become ellipses with a major axis 1.22 × diameter and a minor axis 0.71 × diameter; the four-centre approximate method is acceptable.

Non-isometric lines are lines not parallel to any isometric axis; their endpoints are located on isometric lines and then joined - they are never scaled directly.

Oblique projection: the front face is drawn true shape and size, and receding edges are drawn at a chosen angle (commonly 45°) with a scale of 1/2 for cavalier or 1/2–2/3 for cabinet projection.

Perspective: one-point uses a single vanishing point for receding edges, two-point uses two, and three-point adds a vertical vanishing point; objects on the picture plane keep true size.

Axonometric projection family: isometric (all three axes equally inclined), dimetric (two equal), trimetric (all different); all are orthographic projections from an inclined direction.

Exploded pictorial views show components separated along assembly axes, with thin chain lines or centre lines indicating the assembly path; item numbers link to a parts list.

Dimension lines are thin continuous lines terminated by arrowheads, placed outside the outline where possible, with the numeral above the line and readable from the bottom or right-hand edge.

Extension lines start about 1 mm clear of the object and extend about 2 mm beyond the dimension line; dimension lines must not coincide with outline, centre or extension lines.

Each dimension is given once only, on the view where the feature appears true shape; no dimension is repeated on another view.

ISO limits and fits notation: a hole is written uppercase (e.g. 30 H7) and a shaft lowercase (e.g. 30 g6); H denotes a hole whose lower deviation is zero, h a shaft whose upper deviation is zero.

Fundamental deviation letter gives the position of the tolerance zone, and the number gives the tolerance grade (IT01 to IT18); smaller grade numbers mean tighter tolerances.

Geometric tolerancing per ISO 1101 uses a rectangular frame: symbol (e.g. straightness, flatness, position, concentricity), tolerance value, and datum letters; the frame is linked to the feature by a leader.

Surface texture per ISO 1302 uses the tick symbol with Ra value in micrometres; the basic symbol means any process, the circle-in-tick means material removal not allowed, and the bar means removal required.

A taper is dimensioned by its ratio (e.g. 1:10) or by the included angle, not by both; a chamfer is dimensioned by its length and angle, e.g. 2 × 45°.

A full section removes the near half of the object; the cutting plane is shown as a chain thick line with arrows indicating the viewing direction and labelled A–A.

Hatching (section lining) uses thin continuous lines at 45° to the principal outlines, spaced evenly; adjacent parts in an assembly are hatched at different angles or spacings.

Standard parts such as shafts, bolts, nuts, rivets, keys and pins are not sectioned when cut longitudinally; webs and ribs are not hatched when the cutting plane passes along their length.

A half section shows one quarter removed and is used for symmetrical objects; a broken-out section uses a freehand break line to expose a local feature.

An auxiliary view is projected on a plane parallel to an inclined face so the face appears true shape; its depth from the reference plane is transferred from the view that shows the face as an edge.

Development of a right cylinder: the pattern is a rectangle of width πD and height equal to the cylinder height; a truncated cylinder's pattern is obtained by projecting generator heights onto the divided circumference.

Development of a right cone: the pattern is a sector of radius equal to the slant height L, with sector angle θ = 360° × (D / 2L), where D is the base diameter.

True length of an inclined line is found by rotating it parallel to a reference plane, or by constructing a right triangle with the plan length as base and the difference in heights as altitude.

Thread conventions: the crest of an external thread is a thick continuous line and the root a thin continuous line about 0.25 mm inside; in the end view the root circle is drawn as a thin line broken at about three-quarters.

Metric thread designation M20 × 2.5 means nominal diameter 20 mm and pitch 2.5 mm; a coarse thread omits the pitch, and a left-hand thread is marked LH.

A key transmits torque between shaft and hub; a keyway depth is dimensioned from the shaft side, and the key width is nominally one-quarter of the shaft diameter.

A rolling bearing is designated by a basic number whose last two digits give the bore in units of 5 mm (e.g. 6205 has a 25 mm bore); a prefix or suffix denotes shield, seal or clearance class.

Assembly drawings show all parts in position with item numbers, a parts list (item, description, quantity, material) and overall dimensions; detail drawings give each part's full dimensions and tolerances.

A welded joint is shown by a reference line with an arrow, the symbol above the line for the arrow side and below for the other side; a fillet weld symbol is a right triangle with the leg size in front.

A gear is specified by module m = pitch circle diameter / number of teeth; addendum = m, dedendum = 1.25 m, and the outside diameter = m(z + 2) for standard spur gears.

A bar chart compares discrete categories, a histogram shows the frequency distribution of continuous data, and a line graph shows a trend against a continuous variable such as time.

On a graph, the independent variable goes on the horizontal axis; each axis carries a quantity and unit (e.g. Time / s) and a scale of equal increments with a stated step.

Pie charts show parts of a whole and must sum to 100%; the sector angle for a category is 360° × (category value / total).

A technical report drawing set includes a title block, parts list, revision table and notes; revisions are recorded with a letter or number, date and description.

Flow charts use standard symbols: oval for start/stop, rectangle for process, diamond for decision, parallelogram for input/output, and arrows for flow direction.

Gantt charts show activities as horizontal bars against a time axis, with dependencies and milestones marked; critical-path items are those with zero float.

Orthographic drawings presented for manufacture must carry units (usually millimetres, stated in a general note), projection symbol, scale, material and general tolerances.

A circuit or system diagram uses standard symbols, and lines represent connections rather than physical wires; layout drawings show physical positions instead.

ISO 5457 defines sheet sizes A0–A4; each size is half the area of the previous one, with A0 = 841 × 1189 mm and the ratio fixed at 1:√2.

ISO 5455 sets scale categories: full size 1:1, enlargement (e.g. 2:1, 5:1), and reduction (e.g. 1:2, 1:10); the scale is stated in the title block, and a detail may carry its own scale.

Line types follow ISO 128: continuous thick for visible outlines (about 0.5–0.7 mm), continuous thin for dimension, extension, hatching and leader lines, dashed for hidden edges, chain thin for centre lines and cutting planes.

ISO 3098 lettering: upright capitals and numerals, height h not less than 2.5 mm; the ratio of height to line width is 10:1 for style B, and lowercase letters are used only where the standard permits.

First-angle projection (ISO, used in Europe and Malta) places the object between the observer and the plane, so the view seen from the front is drawn behind the object; third-angle projection (ASME) places the plane between observer and object.

First-angle symbol: a truncated cone shown as two concentric circles on the left with its side elevation on the right; third-angle symbol reverses this arrangement.

A drawing frame and title block per ISO 7200 record title, drawing number, scale, projection symbol, material, date, and the responsible person.

Line precedence when lines coincide: visible outlines take priority over hidden outlines, which take priority over centre lines, which take priority over dimension and extension lines.

Bisecting a line: strike equal arcs from both endpoints with radius greater than half the line; the line joining the arc intersections is the perpendicular bisector.

Bisecting an angle: strike an arc from the vertex cutting both arms, then equal arcs from those two points; the line from the vertex through their intersection is the bisector.

Regular polygon in a circle: for a hexagon, step the radius around the circumference six times; for any n-gon, divide the diameter into n equal parts and use the standard construction through the second division point.

An ellipse is the locus of points whose sum of distances to two foci is constant (2a); major axis = 2a, minor axis = 2b, and b² = a² − c², where c is the focal distance.

Ellipse by concentric circles: draw circles on the major and minor axes, divide them into the same number of equal sectors, and intersect corresponding vertical and horizontal lines.

Conic sections: a plane cutting a cone parallel to one generator gives a parabola, cutting at a steeper angle than the generator gives a hyperbola, and cutting obliquely through all generators gives an ellipse.

Tangent to a circle from an external point: bisect the line joining the point to the centre; the circle on that diameter meets the given circle at the tangent points.

A cycloid is traced by a point on a circle rolling along a straight line; an epicycloid rolls outside a base circle, a hypocycloid inside; the generating circle's circumference must be divided into the same number of parts as the base line or circle.

Standard arrangement of three views: front elevation, plan (top view) placed below it in first-angle, and end/side elevation placed to the right; heights transfer horizontally, depths transfer via a 45° mitre line.

Hidden detail is drawn as dashed lines only where it is not visible in that view; the dash length is roughly 3–4 times the gap, and dashes meet at corners.

Centre lines are chain-dotted thin lines extended slightly beyond the feature; they locate axes of symmetry, hole centres and pitch circles.

Choosing the front view: select the direction that shows the most characteristic shape and the fewest hidden features, and align the longest dimension horizontally.

A point's projection: the plan lies directly below the elevation, and the distance of the plan from the XY line equals the distance of the point in front of the vertical plane.

Inclined surfaces appear foreshortened in the views where they are not parallel to the plane of projection; an edge view appears only in the view perpendicular to the surface.

Six principal views exist (front, top, bottom, left, right, rear); a view is omitted only when it adds no information, e.g. for a body of revolution where one elevation plus the end view suffices.

Isometric axes are at 30° to the horizontal; all three axes are drawn to the same scale, and the true lengths are 0.816 times the isometric drawing length (isometric drawing uses full scale along the axes).

In isometric drawing, circles on the three principal faces become ellipses with a major axis 1.22 × diameter and a minor axis 0.71 × diameter; the four-centre approximate method is acceptable.

Non-isometric lines are lines not parallel to any isometric axis; their endpoints are located on isometric lines and then joined - they are never scaled directly.

Oblique projection: the front face is drawn true shape and size, and receding edges are drawn at a chosen angle (commonly 45°) with a scale of 1/2 for cavalier or 1/2–2/3 for cabinet projection.

Perspective: one-point uses a single vanishing point for receding edges, two-point uses two, and three-point adds a vertical vanishing point; objects on the picture plane keep true size.

Axonometric projection family: isometric (all three axes equally inclined), dimetric (two equal), trimetric (all different); all are orthographic projections from an inclined direction.

Exploded pictorial views show components separated along assembly axes, with thin chain lines or centre lines indicating the assembly path; item numbers link to a parts list.

Dimension lines are thin continuous lines terminated by arrowheads, placed outside the outline where possible, with the numeral above the line and readable from the bottom or right-hand edge.

Extension lines start about 1 mm clear of the object and extend about 2 mm beyond the dimension line; dimension lines must not coincide with outline, centre or extension lines.

Each dimension is given once only, on the view where the feature appears true shape; no dimension is repeated on another view.

ISO limits and fits notation: a hole is written uppercase (e.g. 30 H7) and a shaft lowercase (e.g. 30 g6); H denotes a hole whose lower deviation is zero, h a shaft whose upper deviation is zero.

Fundamental deviation letter gives the position of the tolerance zone, and the number gives the tolerance grade (IT01 to IT18); smaller grade numbers mean tighter tolerances.

Geometric tolerancing per ISO 1101 uses a rectangular frame: symbol (e.g. straightness, flatness, position, concentricity), tolerance value, and datum letters; the frame is linked to the feature by a leader.

Surface texture per ISO 1302 uses the tick symbol with Ra value in micrometres; the basic symbol means any process, the circle-in-tick means material removal not allowed, and the bar means removal required.

A taper is dimensioned by its ratio (e.g. 1:10) or by the included angle, not by both; a chamfer is dimensioned by its length and angle, e.g. 2 × 45°.

A full section removes the near half of the object; the cutting plane is shown as a chain thick line with arrows indicating the viewing direction and labelled A–A.

Hatching (section lining) uses thin continuous lines at 45° to the principal outlines, spaced evenly; adjacent parts in an assembly are hatched at different angles or spacings.

Standard parts such as shafts, bolts, nuts, rivets, keys and pins are not sectioned when cut longitudinally; webs and ribs are not hatched when the cutting plane passes along their length.

A half section shows one quarter removed and is used for symmetrical objects; a broken-out section uses a freehand break line to expose a local feature.

An auxiliary view is projected on a plane parallel to an inclined face so the face appears true shape; its depth from the reference plane is transferred from the view that shows the face as an edge.

Development of a right cylinder: the pattern is a rectangle of width πD and height equal to the cylinder height; a truncated cylinder's pattern is obtained by projecting generator heights onto the divided circumference.

Development of a right cone: the pattern is a sector of radius equal to the slant height L, with sector angle θ = 360° × (D / 2L), where D is the base diameter.

True length of an inclined line is found by rotating it parallel to a reference plane, or by constructing a right triangle with the plan length as base and the difference in heights as altitude.

Thread conventions: the crest of an external thread is a thick continuous line and the root a thin continuous line about 0.25 mm inside; in the end view the root circle is drawn as a thin line broken at about three-quarters.

Metric thread designation M20 × 2.5 means nominal diameter 20 mm and pitch 2.5 mm; a coarse thread omits the pitch, and a left-hand thread is marked LH.

A key transmits torque between shaft and hub; a keyway depth is dimensioned from the shaft side, and the key width is nominally one-quarter of the shaft diameter.

A rolling bearing is designated by a basic number whose last two digits give the bore in units of 5 mm (e.g. 6205 has a 25 mm bore); a prefix or suffix denotes shield, seal or clearance class.

Assembly drawings show all parts in position with item numbers, a parts list (item, description, quantity, material) and overall dimensions; detail drawings give each part's full dimensions and tolerances.

A welded joint is shown by a reference line with an arrow, the symbol above the line for the arrow side and below for the other side; a fillet weld symbol is a right triangle with the leg size in front.

A gear is specified by module m = pitch circle diameter / number of teeth; addendum = m, dedendum = 1.25 m, and the outside diameter = m(z + 2) for standard spur gears.

A bar chart compares discrete categories, a histogram shows the frequency distribution of continuous data, and a line graph shows a trend against a continuous variable such as time.

On a graph, the independent variable goes on the horizontal axis; each axis carries a quantity and unit (e.g. Time / s) and a scale of equal increments with a stated step.

Pie charts show parts of a whole and must sum to 100%; the sector angle for a category is 360° × (category value / total).

A technical report drawing set includes a title block, parts list, revision table and notes; revisions are recorded with a letter or number, date and description.

Flow charts use standard symbols: oval for start/stop, rectangle for process, diamond for decision, parallelogram for input/output, and arrows for flow direction.

Gantt charts show activities as horizontal bars against a time axis, with dependencies and milestones marked; critical-path items are those with zero float.

Orthographic drawings presented for manufacture must carry units (usually millimetres, stated in a general note), projection symbol, scale, material and general tolerances.

A circuit or system diagram uses standard symbols, and lines represent connections rather than physical wires; layout drawings show physical positions instead.

ISO 5457 defines sheet sizes A0–A4; each size is half the area of the previous one, with A0 = 841 × 1189 mm and the ratio fixed at 1:√2.

ISO 5455 sets scale categories: full size 1:1, enlargement (e.g. 2:1, 5:1), and reduction (e.g. 1:2, 1:10); the scale is stated in the title block, and a detail may carry its own scale.

Line types follow ISO 128: continuous thick for visible outlines (about 0.5–0.7 mm), continuous thin for dimension, extension, hatching and leader lines, dashed for hidden edges, chain thin for centre lines and cutting planes.

ISO 3098 lettering: upright capitals and numerals, height h not less than 2.5 mm; the ratio of height to line width is 10:1 for style B, and lowercase letters are used only where the standard permits.

First-angle projection (ISO, used in Europe and Malta) places the object between the observer and the plane, so the view seen from the front is drawn behind the object; third-angle projection (ASME) places the plane between observer and object.

First-angle symbol: a truncated cone shown as two concentric circles on the left with its side elevation on the right; third-angle symbol reverses this arrangement.

A drawing frame and title block per ISO 7200 record title, drawing number, scale, projection symbol, material, date, and the responsible person.

Line precedence when lines coincide: visible outlines take priority over hidden outlines, which take priority over centre lines, which take priority over dimension and extension lines.

Bisecting a line: strike equal arcs from both endpoints with radius greater than half the line; the line joining the arc intersections is the perpendicular bisector.

Bisecting an angle: strike an arc from the vertex cutting both arms, then equal arcs from those two points; the line from the vertex through their intersection is the bisector.

Regular polygon in a circle: for a hexagon, step the radius around the circumference six times; for any n-gon, divide the diameter into n equal parts and use the standard construction through the second division point.

An ellipse is the locus of points whose sum of distances to two foci is constant (2a); major axis = 2a, minor axis = 2b, and b² = a² − c², where c is the focal distance.

Ellipse by concentric circles: draw circles on the major and minor axes, divide them into the same number of equal sectors, and intersect corresponding vertical and horizontal lines.

Conic sections: a plane cutting a cone parallel to one generator gives a parabola, cutting at a steeper angle than the generator gives a hyperbola, and cutting obliquely through all generators gives an ellipse.

Tangent to a circle from an external point: bisect the line joining the point to the centre; the circle on that diameter meets the given circle at the tangent points.

A cycloid is traced by a point on a circle rolling along a straight line; an epicycloid rolls outside a base circle, a hypocycloid inside; the generating circle's circumference must be divided into the same number of parts as the base line or circle.

Standard arrangement of three views: front elevation, plan (top view) placed below it in first-angle, and end/side elevation placed to the right; heights transfer horizontally, depths transfer via a 45° mitre line.

Hidden detail is drawn as dashed lines only where it is not visible in that view; the dash length is roughly 3–4 times the gap, and dashes meet at corners.

Centre lines are chain-dotted thin lines extended slightly beyond the feature; they locate axes of symmetry, hole centres and pitch circles.

Choosing the front view: select the direction that shows the most characteristic shape and the fewest hidden features, and align the longest dimension horizontally.

A point's projection: the plan lies directly below the elevation, and the distance of the plan from the XY line equals the distance of the point in front of the vertical plane.

Inclined surfaces appear foreshortened in the views where they are not parallel to the plane of projection; an edge view appears only in the view perpendicular to the surface.

Six principal views exist (front, top, bottom, left, right, rear); a view is omitted only when it adds no information, e.g. for a body of revolution where one elevation plus the end view suffices.

Isometric axes are at 30° to the horizontal; all three axes are drawn to the same scale, and the true lengths are 0.816 times the isometric drawing length (isometric drawing uses full scale along the axes).

In isometric drawing, circles on the three principal faces become ellipses with a major axis 1.22 × diameter and a minor axis 0.71 × diameter; the four-centre approximate method is acceptable.

Non-isometric lines are lines not parallel to any isometric axis; their endpoints are located on isometric lines and then joined - they are never scaled directly.

Oblique projection: the front face is drawn true shape and size, and receding edges are drawn at a chosen angle (commonly 45°) with a scale of 1/2 for cavalier or 1/2–2/3 for cabinet projection.

Perspective: one-point uses a single vanishing point for receding edges, two-point uses two, and three-point adds a vertical vanishing point; objects on the picture plane keep true size.

Axonometric projection family: isometric (all three axes equally inclined), dimetric (two equal), trimetric (all different); all are orthographic projections from an inclined direction.

Exploded pictorial views show components separated along assembly axes, with thin chain lines or centre lines indicating the assembly path; item numbers link to a parts list.

Dimension lines are thin continuous lines terminated by arrowheads, placed outside the outline where possible, with the numeral above the line and readable from the bottom or right-hand edge.

Extension lines start about 1 mm clear of the object and extend about 2 mm beyond the dimension line; dimension lines must not coincide with outline, centre or extension lines.

Each dimension is given once only, on the view where the feature appears true shape; no dimension is repeated on another view.

ISO limits and fits notation: a hole is written uppercase (e.g. 30 H7) and a shaft lowercase (e.g. 30 g6); H denotes a hole whose lower deviation is zero, h a shaft whose upper deviation is zero.

Fundamental deviation letter gives the position of the tolerance zone, and the number gives the tolerance grade (IT01 to IT18); smaller grade numbers mean tighter tolerances.

Geometric tolerancing per ISO 1101 uses a rectangular frame: symbol (e.g. straightness, flatness, position, concentricity), tolerance value, and datum letters; the frame is linked to the feature by a leader.

Surface texture per ISO 1302 uses the tick symbol with Ra value in micrometres; the basic symbol means any process, the circle-in-tick means material removal not allowed, and the bar means removal required.

A taper is dimensioned by its ratio (e.g. 1:10) or by the included angle, not by both; a chamfer is dimensioned by its length and angle, e.g. 2 × 45°.

A full section removes the near half of the object; the cutting plane is shown as a chain thick line with arrows indicating the viewing direction and labelled A–A.

Hatching (section lining) uses thin continuous lines at 45° to the principal outlines, spaced evenly; adjacent parts in an assembly are hatched at different angles or spacings.

Standard parts such as shafts, bolts, nuts, rivets, keys and pins are not sectioned when cut longitudinally; webs and ribs are not hatched when the cutting plane passes along their length.

A half section shows one quarter removed and is used for symmetrical objects; a broken-out section uses a freehand break line to expose a local feature.

An auxiliary view is projected on a plane parallel to an inclined face so the face appears true shape; its depth from the reference plane is transferred from the view that shows the face as an edge.

Development of a right cylinder: the pattern is a rectangle of width πD and height equal to the cylinder height; a truncated cylinder's pattern is obtained by projecting generator heights onto the divided circumference.

Development of a right cone: the pattern is a sector of radius equal to the slant height L, with sector angle θ = 360° × (D / 2L), where D is the base diameter.

True length of an inclined line is found by rotating it parallel to a reference plane, or by constructing a right triangle with the plan length as base and the difference in heights as altitude.

Thread conventions: the crest of an external thread is a thick continuous line and the root a thin continuous line about 0.25 mm inside; in the end view the root circle is drawn as a thin line broken at about three-quarters.

Metric thread designation M20 × 2.5 means nominal diameter 20 mm and pitch 2.5 mm; a coarse thread omits the pitch, and a left-hand thread is marked LH.

A key transmits torque between shaft and hub; a keyway depth is dimensioned from the shaft side, and the key width is nominally one-quarter of the shaft diameter.

A rolling bearing is designated by a basic number whose last two digits give the bore in units of 5 mm (e.g. 6205 has a 25 mm bore); a prefix or suffix denotes shield, seal or clearance class.

Assembly drawings show all parts in position with item numbers, a parts list (item, description, quantity, material) and overall dimensions; detail drawings give each part's full dimensions and tolerances.

A welded joint is shown by a reference line with an arrow, the symbol above the line for the arrow side and below for the other side; a fillet weld symbol is a right triangle with the leg size in front.

A gear is specified by module m = pitch circle diameter / number of teeth; addendum = m, dedendum = 1.25 m, and the outside diameter = m(z + 2) for standard spur gears.

A bar chart compares discrete categories, a histogram shows the frequency distribution of continuous data, and a line graph shows a trend against a continuous variable such as time.

On a graph, the independent variable goes on the horizontal axis; each axis carries a quantity and unit (e.g. Time / s) and a scale of equal increments with a stated step.

Pie charts show parts of a whole and must sum to 100%; the sector angle for a category is 360° × (category value / total).

A technical report drawing set includes a title block, parts list, revision table and notes; revisions are recorded with a letter or number, date and description.

Flow charts use standard symbols: oval for start/stop, rectangle for process, diamond for decision, parallelogram for input/output, and arrows for flow direction.

Gantt charts show activities as horizontal bars against a time axis, with dependencies and milestones marked; critical-path items are those with zero float.

Orthographic drawings presented for manufacture must carry units (usually millimetres, stated in a general note), projection symbol, scale, material and general tolerances.

A circuit or system diagram uses standard symbols, and lines represent connections rather than physical wires; layout drawings show physical positions instead.

ISO 5457 defines sheet sizes A0–A4; each size is half the area of the previous one, with A0 = 841 × 1189 mm and the ratio fixed at 1:√2.

ISO 5455 sets scale categories: full size 1:1, enlargement (e.g. 2:1, 5:1), and reduction (e.g. 1:2, 1:10); the scale is stated in the title block, and a detail may carry its own scale.

Line types follow ISO 128: continuous thick for visible outlines (about 0.5–0.7 mm), continuous thin for dimension, extension, hatching and leader lines, dashed for hidden edges, chain thin for centre lines and cutting planes.

ISO 3098 lettering: upright capitals and numerals, height h not less than 2.5 mm; the ratio of height to line width is 10:1 for style B, and lowercase letters are used only where the standard permits.

First-angle projection (ISO, used in Europe and Malta) places the object between the observer and the plane, so the view seen from the front is drawn behind the object; third-angle projection (ASME) places the plane between observer and object.

First-angle symbol: a truncated cone shown as two concentric circles on the left with its side elevation on the right; third-angle symbol reverses this arrangement.

A drawing frame and title block per ISO 7200 record title, drawing number, scale, projection symbol, material, date, and the responsible person.

Line precedence when lines coincide: visible outlines take priority over hidden outlines, which take priority over centre lines, which take priority over dimension and extension lines.

Bisecting a line: strike equal arcs from both endpoints with radius greater than half the line; the line joining the arc intersections is the perpendicular bisector.

Bisecting an angle: strike an arc from the vertex cutting both arms, then equal arcs from those two points; the line from the vertex through their intersection is the bisector.

Regular polygon in a circle: for a hexagon, step the radius around the circumference six times; for any n-gon, divide the diameter into n equal parts and use the standard construction through the second division point.

An ellipse is the locus of points whose sum of distances to two foci is constant (2a); major axis = 2a, minor axis = 2b, and b² = a² − c², where c is the focal distance.

Ellipse by concentric circles: draw circles on the major and minor axes, divide them into the same number of equal sectors, and intersect corresponding vertical and horizontal lines.

Conic sections: a plane cutting a cone parallel to one generator gives a parabola, cutting at a steeper angle than the generator gives a hyperbola, and cutting obliquely through all generators gives an ellipse.

Tangent to a circle from an external point: bisect the line joining the point to the centre; the circle on that diameter meets the given circle at the tangent points.

A cycloid is traced by a point on a circle rolling along a straight line; an epicycloid rolls outside a base circle, a hypocycloid inside; the generating circle's circumference must be divided into the same number of parts as the base line or circle.

Standard arrangement of three views: front elevation, plan (top view) placed below it in first-angle, and end/side elevation placed to the right; heights transfer horizontally, depths transfer via a 45° mitre line.

Hidden detail is drawn as dashed lines only where it is not visible in that view; the dash length is roughly 3–4 times the gap, and dashes meet at corners.

Centre lines are chain-dotted thin lines extended slightly beyond the feature; they locate axes of symmetry, hole centres and pitch circles.

Choosing the front view: select the direction that shows the most characteristic shape and the fewest hidden features, and align the longest dimension horizontally.

A point's projection: the plan lies directly below the elevation, and the distance of the plan from the XY line equals the distance of the point in front of the vertical plane.

Inclined surfaces appear foreshortened in the views where they are not parallel to the plane of projection; an edge view appears only in the view perpendicular to the surface.

Six principal views exist (front, top, bottom, left, right, rear); a view is omitted only when it adds no information, e.g. for a body of revolution where one elevation plus the end view suffices.

Isometric axes are at 30° to the horizontal; all three axes are drawn to the same scale, and the true lengths are 0.816 times the isometric drawing length (isometric drawing uses full scale along the axes).

In isometric drawing, circles on the three principal faces become ellipses with a major axis 1.22 × diameter and a minor axis 0.71 × diameter; the four-centre approximate method is acceptable.

Non-isometric lines are lines not parallel to any isometric axis; their endpoints are located on isometric lines and then joined - they are never scaled directly.

Oblique projection: the front face is drawn true shape and size, and receding edges are drawn at a chosen angle (commonly 45°) with a scale of 1/2 for cavalier or 1/2–2/3 for cabinet projection.

Perspective: one-point uses a single vanishing point for receding edges, two-point uses two, and three-point adds a vertical vanishing point; objects on the picture plane keep true size.

Axonometric projection family: isometric (all three axes equally inclined), dimetric (two equal), trimetric (all different); all are orthographic projections from an inclined direction.

Exploded pictorial views show components separated along assembly axes, with thin chain lines or centre lines indicating the assembly path; item numbers link to a parts list.

Dimension lines are thin continuous lines terminated by arrowheads, placed outside the outline where possible, with the numeral above the line and readable from the bottom or right-hand edge.

Extension lines start about 1 mm clear of the object and extend about 2 mm beyond the dimension line; dimension lines must not coincide with outline, centre or extension lines.

Each dimension is given once only, on the view where the feature appears true shape; no dimension is repeated on another view.

ISO limits and fits notation: a hole is written uppercase (e.g. 30 H7) and a shaft lowercase (e.g. 30 g6); H denotes a hole whose lower deviation is zero, h a shaft whose upper deviation is zero.

Fundamental deviation letter gives the position of the tolerance zone, and the number gives the tolerance grade (IT01 to IT18); smaller grade numbers mean tighter tolerances.

Geometric tolerancing per ISO 1101 uses a rectangular frame: symbol (e.g. straightness, flatness, position, concentricity), tolerance value, and datum letters; the frame is linked to the feature by a leader.

Surface texture per ISO 1302 uses the tick symbol with Ra value in micrometres; the basic symbol means any process, the circle-in-tick means material removal not allowed, and the bar means removal required.

A taper is dimensioned by its ratio (e.g. 1:10) or by the included angle, not by both; a chamfer is dimensioned by its length and angle, e.g. 2 × 45°.

A full section removes the near half of the object; the cutting plane is shown as a chain thick line with arrows indicating the viewing direction and labelled A–A.

Hatching (section lining) uses thin continuous lines at 45° to the principal outlines, spaced evenly; adjacent parts in an assembly are hatched at different angles or spacings.

Standard parts such as shafts, bolts, nuts, rivets, keys and pins are not sectioned when cut longitudinally; webs and ribs are not hatched when the cutting plane passes along their length.

A half section shows one quarter removed and is used for symmetrical objects; a broken-out section uses a freehand break line to expose a local feature.

An auxiliary view is projected on a plane parallel to an inclined face so the face appears true shape; its depth from the reference plane is transferred from the view that shows the face as an edge.

Development of a right cylinder: the pattern is a rectangle of width πD and height equal to the cylinder height; a truncated cylinder's pattern is obtained by projecting generator heights onto the divided circumference.

Development of a right cone: the pattern is a sector of radius equal to the slant height L, with sector angle θ = 360° × (D / 2L), where D is the base diameter.

True length of an inclined line is found by rotating it parallel to a reference plane, or by constructing a right triangle with the plan length as base and the difference in heights as altitude.

Thread conventions: the crest of an external thread is a thick continuous line and the root a thin continuous line about 0.25 mm inside; in the end view the root circle is drawn as a thin line broken at about three-quarters.

Metric thread designation M20 × 2.5 means nominal diameter 20 mm and pitch 2.5 mm; a coarse thread omits the pitch, and a left-hand thread is marked LH.

A key transmits torque between shaft and hub; a keyway depth is dimensioned from the shaft side, and the key width is nominally one-quarter of the shaft diameter.

A rolling bearing is designated by a basic number whose last two digits give the bore in units of 5 mm (e.g. 6205 has a 25 mm bore); a prefix or suffix denotes shield, seal or clearance class.

Assembly drawings show all parts in position with item numbers, a parts list (item, description, quantity, material) and overall dimensions; detail drawings give each part's full dimensions and tolerances.

A welded joint is shown by a reference line with an arrow, the symbol above the line for the arrow side and below for the other side; a fillet weld symbol is a right triangle with the leg size in front.

A gear is specified by module m = pitch circle diameter / number of teeth; addendum = m, dedendum = 1.25 m, and the outside diameter = m(z + 2) for standard spur gears.

A bar chart compares discrete categories, a histogram shows the frequency distribution of continuous data, and a line graph shows a trend against a continuous variable such as time.

On a graph, the independent variable goes on the horizontal axis; each axis carries a quantity and unit (e.g. Time / s) and a scale of equal increments with a stated step.

Pie charts show parts of a whole and must sum to 100%; the sector angle for a category is 360° × (category value / total).

A technical report drawing set includes a title block, parts list, revision table and notes; revisions are recorded with a letter or number, date and description.

Flow charts use standard symbols: oval for start/stop, rectangle for process, diamond for decision, parallelogram for input/output, and arrows for flow direction.

Gantt charts show activities as horizontal bars against a time axis, with dependencies and milestones marked; critical-path items are those with zero float.

Orthographic drawings presented for manufacture must carry units (usually millimetres, stated in a general note), projection symbol, scale, material and general tolerances.

A circuit or system diagram uses standard symbols, and lines represent connections rather than physical wires; layout drawings show physical positions instead.