Agricultural Engineering · Foundations · also Engineering Graphics and Design, CAD/CAM Machine Drawing
Reading and making drawings of machine parts and buildings, by hand and in CAD.
In the exams: NCEES PE graphics/CAD/GIS topic; design drawings in PRC ABE
Engineering drawing is the language in which an engineer tells a fabricator, a contractor or a test engineer exactly what to make: its shape, its size, how accurate each size must be, what it is made of and how its parts fit together. It is a language with a grammar. The grammar is set by standards: internationally by ISO, and nationally by bodies such as the Bureau of Indian Standards and ASME in the United States. National codes mostly follow ISO, with a few well-known differences that this manual points out.
For an agricultural engineer the subject is practical. Seed-drill hoppers, plough bottoms, dryer ducts, pump glands and dairy barns are all specified by drawings, and an engineer who spots a missing tolerance before a batch of hubs is machined saves real money.
The subject is taught in the first year of most B.Tech and B.Sc. agricultural engineering programmes as Engineering Drawing or Engineering Graphics, and again later as Machine Drawing and CAD. University papers ask students to draw: projections of points, lines, planes and solids, sections and developments, isometric views and machine-part assemblies. Licensure examinations test it differently. The NCEES PE Agricultural and Biological Engineering specification lists graphics, CAD and GIS among its common system applications, and the Philippine ABE licensure examination expects candidates to read and prepare design drawings of structures and machines. Questions here are text-only and describe views in words; sketch each object on rough paper as you read.
A drawing is a contract document, and standards remove ambiguity from it. The ISO technical product documentation family is the common base: ISO 128 sets line types and the presentation of views and sections, ISO 129 sets dimensioning, ISO 5455 sets scales, ISO 3098 sets lettering, ISO 5457 sets sheet sizes and layout, ISO 7200 sets the data fields of the title block, ISO 286 sets limits and fits, ISO 1101 sets geometrical tolerancing, ISO 1302 (replaced in 2021 by ISO 21920-1) sets surface texture indication, ISO 6410 sets the representation of screw threads, and ISO 2553 sets welding symbols. India's SP 46 (the Engineering Drawing Practice for Schools and Colleges published by the Bureau of Indian Standards) brings these conventions together for teaching and adopts first-angle projection. The United States uses the ASME Y14 series, whose most visible differences from ISO are third-angle projection, inch units in much legacy work, and some differences in geometric tolerancing defaults and weld-symbol layout.
A drawing sheet carries a border, a title block in the bottom right corner, and usually a grid reference along the margins so that a feature can be located by zone, like a map. The title block records the drawing number, title, scale, projection symbol, units, general tolerances, material, approvals and revision. A revision table records every change after first issue.
The ISO A-series sheet sizes have sides in the ratio 1 to the square root of 2, so halving a sheet across its long side gives the next size with the same proportions. A0 has an area of one square metre and measures 841 by 1189 mm; A1 is 594 by 841, A2 is 420 by 594, A3 is 297 by 420 and A4 is 210 by 297 mm.
ISO 128 assigns meaning to each line type. Continuous thick lines show visible outlines and edges. Continuous thin lines are used for dimension lines, extension (projection) lines, leader lines, hatching, short centre lines, outlines of revolved sections and imaginary lines of intersection. Dashed thin lines show hidden outlines and edges. Long-dash dotted thin lines (chain thin) show centre lines, axes of symmetry, pitch circles of gears and pitch circles of holes. A chain thin line made thick at its ends and at changes of direction shows a cutting plane. A long-dash dotted thick line marks a surface with a special requirement. A long-dash double-dotted thin line shows adjacent parts, alternative and extreme positions of moving parts, and the initial outline before forming. Continuous thin freehand or zigzag lines show the limits of partial views and break lines.
Line widths come from a series in which each width is the previous one multiplied by the square root of 2: 0.13, 0.18, 0.25, 0.35, 0.5, 0.7, 1, 1.4 and 2 mm. On one drawing the thick line is normally twice the thin line, for example 0.7 and 0.35 mm, or 0.5 and 0.25 mm. Where lines coincide, a visible outline takes priority over a hidden line, which takes priority over a cutting plane and then a centre line.
Lettering on a drawing must be legible after reduction and copying, so ISO 3098 standardises it. Nominal heights follow the same square-root-of-2 series: 1.8, 2.5, 3.5, 5, 7, 10, 14 and 20 mm. Type A lettering has a stroke width of one fourteenth of the height and type B one tenth. Letters may be vertical or sloped at 15 degrees to the vertical, that is 75 degrees to the horizontal. Single-stroke capitals are the norm; titles take the larger heights and dimensions and notes the smaller, such as 3.5 or 2.5 mm. In CAD, annotation scaling prints text at the intended height at any drawing scale.
A scale is the ratio of a length on the drawing to the corresponding true length of the object, written as the drawing length first. Full size is 1:1; a reduction scale such as 1:5 means 1 mm on paper represents 5 mm on the object; an enlargement scale such as 2:1 means the drawing is twice the object size. The representative fraction (RF) is the same ratio written as a fraction with both lengths in the same unit: a scale of 1 cm to 5 m has RF = 1/500. ISO 5455 recommends enlargement scales of 2:1, 5:1, 10:1, 20:1 and 50:1 and reduction scales of 1:2, 1:5, 1:10, 1:20, 1:50, 1:100, 1:200, 1:500, 1:1000 and so on.
Classical drawing courses teach the construction of scales. A plain scale shows two units, such as metres and decimetres. Its length is the RF multiplied by the maximum length to be measured; for RF 1/50 and a maximum of 8 m the scale is 160 mm long. A diagonal scale reads three units (for example metres, decimetres and centimetres) by drawing ten equally spaced horizontal lines and diagonals across one main division, using the similar-triangles principle. A vernier scale also reads a third unit: its least count equals one main scale division minus one vernier scale division, which is one main division divided by the number of vernier divisions in the usual forward vernier. Every drawing states its scale, and a dimension always gives the true size of the object, never the paper length; never scale a part off a print.
Before CAD, every drawing was built from a small set of constructions with compass and straightedge, and they still underlie CAD commands and shop layout work. The core set is bisecting lines and angles, dividing a line into equal parts by the similar-triangles method, and drawing tangent arcs. A regular hexagon is drawn by stepping the radius six times round its circumscribing circle, because the side of a regular hexagon equals the radius of that circle. Across flats and across corners of a hexagon, which matter for nuts and bolt heads, are related by the cosine of 30 degrees: across corners equals across flats divided by 0.866, about 1.155 times the across-flats size.
Tangency is the construction most used in machine drawing. To blend two lines with an arc of radius R, draw lines parallel to each at distance R; their intersection is the arc centre. To blend two circles externally, the centre lies at R plus each circle's radius from the two centres.
Cutting a right circular cone with a plane gives the conic sections. A plane perpendicular to the axis cuts a circle. A plane inclined to the axis that cuts all the generators gives an ellipse. A plane parallel to one generator gives a parabola. A plane that cuts both nappes of the double cone, for example one parallel to the axis, gives a hyperbola.
Each conic is also the locus of a point whose distance from a fixed point (the focus) bears a constant ratio, the eccentricity e, to its distance from a fixed line (the directrix). For an ellipse e is less than 1, for a parabola e equals 1, and for a hyperbola e is greater than 1. An ellipse has two foci; the sum of the distances from any point on it to the two foci is constant and equals the major axis. With semi-major axis a and semi-minor axis b, each focus lies at a distance c from the centre, where c squared equals a squared minus b squared. Ellipses are drawn by the concentric-circles, rectangle, arcs-of-circles, trammel or eccentricity methods. Parabolas appear in solar concentrator reflectors, and the curve PV = constant of an isothermal process is a rectangular hyperbola.
A cycloid is the path of a point on the circumference of a circle rolling without slipping along a straight line; in one revolution the circle travels a distance equal to its circumference, pi times its diameter, which is therefore the base length of one cycloid arch. An epicycloid is traced when the circle rolls on the outside of another circle, and a hypocycloid when it rolls on the inside.
An involute is the path of the end of a taut string unwound from a circle (the base circle) or from a polygon. The involute of a circle is the standard tooth profile of almost all power-transmission gears, including tractor gearboxes, because two involute teeth keep a constant velocity ratio even if the centre distance changes slightly.
An Archimedean spiral is the path of a point that moves away from a centre at a uniform rate while the radius line rotates at a uniform rate, so the radius grows equally for equal angles. It is used for the profile of uniform-rise cams and appears in the scroll of a self-centring lathe chuck. A helix is the path of a point that moves along a cylinder or cone at a uniform rate while rotating about the axis at a uniform rate; the axial distance travelled in one revolution is the lead. Screw threads, coil springs and auger flights follow a helix.
Orthographic projection shows an object by projecting it onto planes with parallel projectors that are perpendicular to each plane. Two principal planes are used: the vertical plane (VP), also called the frontal plane, and the horizontal plane (HP). The projection on the VP is the front view, also called the front elevation; the projection on the HP is the top view, also called the plan. A third plane perpendicular to both, the profile plane (PP), receives the side view or end view. The line in which the VP and HP intersect is the reference line, labelled XY. Each view shows two of the three dimensions.
The two principal planes divide space into four quadrants (dihedral angles). The first quadrant is above HP and in front of VP, the second above and behind, the third below and behind, the fourth below and in front. After projecting, the HP is rotated about XY to lie in the plane of the VP, conventionally by turning the front half of the HP downwards. In the second and fourth quadrants the two views then overlap, which makes the drawing unreadable, so only the first and third quadrants are used for drawings of objects.
In first-angle projection the object sits between the observer and the plane of projection. When the planes are opened out, the top view falls below the front view, the view from the left is placed to the right of the front view, and the view from the right is placed to the left. In third-angle projection the plane of projection sits between the observer and the object, as if the viewer were looking through a glass box. The top view then lies above the front view, the view from the right is placed to the right, and the view from the left to the left. The views themselves are identical in the two systems; only their positions on the sheet differ.
Usage varies by country. Most of Europe, India and many other countries use first angle; India's SP 46 specifies it. The United States, Canada and some other countries use third angle. ISO 5456-2 allows both, which is why the projection symbol, a truncated cone shown in two views, must be printed in the title block. Reading a third-angle drawing as first angle swaps the side views and the top and bottom views, so check the symbol on any imported drawing first.
Six principal views are possible: front, top, bottom, left, right and rear. Draw only as many as are needed to define the shape completely and unambiguously, usually two or three. Choose as the front view the one that shows the most characteristic shape with the fewest hidden lines, in the object's functional position.
Views are aligned. Width is shared by the front and top views, height by the front and side views, and depth by the top and side views, transferred by a 45-degree mitre line.
To read a multiview drawing, take one feature at a time, find it in every view, and build up a mental picture. A circle in the front view that appears as a rectangle of hidden lines in the top view is a hole running from front to back. Read the views together, never one alone. A surface parallel to a plane of projection appears in true shape there; a surface perpendicular to a plane appears as a line (its edge view); a surface inclined to a plane appears foreshortened but with the same number of sides, which is the principle of configuration used to check views. Hidden lines are drawn when they clarify the shape and omitted when they only add clutter.
A point is located by its distance above or below the HP and in front of or behind the VP. In first-angle drawing, a point 20 mm above HP and 30 mm in front of VP has its front view 20 mm above XY and its top view 30 mm below XY, on the same vertical projector. A point in the second quadrant has both views above XY; in the third quadrant the front view is below and the top view above; in the fourth both are below.
A straight line is shown by the views of its end points. If a line is parallel to a plane, its projection on that plane is its true length. If it is inclined to a plane, its projection on that plane is shorter than the true length. A line inclined at theta to the HP and phi to the VP has a top view of length TL cos theta and a front view of length TL cos phi. The difference in heights of the ends (seen in the front view) equals TL sin theta, and the difference in distances from the VP (seen in the top view) equals TL sin phi. So, with the length of the top view and the difference in heights known, the true length is the square root of the sum of their squares, and theta follows from its sine. With the three coordinate differences, along XY, in height and in depth, the true length is the three-dimensional distance formula. For a line inclined to both planes, theta plus phi is less than 90 degrees; it equals 90 degrees only when the line lies in a profile plane.
True length is found graphically by rotating one view parallel to XY, or by an auxiliary plane parallel to the line. The points where a line, extended, meets the HP and VP are its horizontal trace (HT) and vertical trace (VT); finding traces is a classic examination exercise, and a line parallel to a plane has no trace on it.
A plane figure such as a triangle, square, hexagon or circle (a lamina) is shown in true shape on a plane to which it is parallel, as a line on a plane to which it is perpendicular, and foreshortened on a plane to which it is inclined. Problems are solved in stages: draw the lamina parallel to one plane, then tilt it, then rotate it, carrying points across by projectors. The angle a plane makes with the HP is seen in true size only in a view in which the plane appears as an edge.
An auxiliary view is a view projected onto a plane that is not one of the principal planes, usually one placed parallel to an inclined surface so that its true shape is seen. An auxiliary inclined plane (AIP) is perpendicular to the VP and inclined to the HP; its view is projected from the front view, and heights are transferred from the top view's distances from XY. An auxiliary vertical plane (AVP) is perpendicular to the HP and inclined to the VP; its view is projected from the top view with distances transferred from the front view. Auxiliary views show the true shape of a sloping hopper face or inclined bracket.
Solids are polyhedra (prisms, pyramids, regular solids) or solids of revolution (cylinder, cone, sphere). Frusta are truncated pyramids or cones. A solid is located by the position of its axis. With the axis perpendicular to the HP, the top view shows the true shape of the base and is drawn first. With the axis inclined to one plane, the solid is first drawn with the axis perpendicular to that plane, then the appropriate view is tilted to the given angle and the other view projected. With the axis inclined to both planes, a third stage rotates the top view.
A sectional view shows an object as if cut by an imaginary cutting plane, with the near portion removed, so that interior features appear as visible outlines instead of confusing hidden lines. The cutting plane is shown on an adjacent view with arrows for the viewing direction and letters such as A–A. Cut surfaces are hatched with continuous thin lines, normally at 45 degrees to the main outline or axis of symmetry, evenly spaced to suit the size of the area. Separate parts in an assembly are hatched in different directions or with different spacing, while every cut area of the same part is hatched identically in all views.
The main types are: the full section, in which the cutting plane passes right through the object; the half section, used for symmetrical parts, which shows one half in section and the other half in outside view, separated by a centre line, with hidden lines usually omitted; the offset section, in which the cutting plane steps to pass through features not in line; the aligned section, in which an angled part of the cut is rotated into the plane of projection, as for the spokes or holes of a pulley; the revolved section, drawn in place on the view, for the cross-section of an arm, rib or lever; the removed section, the same idea placed off the view; and the local or broken-out section, bounded by a freehand line, to show a small interior detail.
By convention, certain parts are not sectioned when the cutting plane passes along their length, because hatching them adds nothing and hides their identity: shafts, bolts, nuts, screws, studs, pins, keys, rivets, washers, balls and rollers of bearings, and also ribs, webs and the arms or spokes of wheels and pulleys.
In descriptive geometry exercises a section plane cuts a prism, pyramid, cylinder or cone, and the task is to draw the sectional view and the true shape of the section. If the section plane is perpendicular to the VP and inclined to the HP, it appears as a line in the front view; the points where it crosses each edge or generator are projected to the top view, and the true shape is drawn on an auxiliary plane parallel to the section plane. For a cone, the generator or circle method locates points on curved sections. The true shape of a section of a cylinder by an inclined plane is an ellipse whose minor axis equals the cylinder diameter and whose major axis is the diameter divided by the cosine of the angle between the plane and the base. The sections of a cone by planes at different angles are the conics described in the previous chapter.
A development is the surface of a solid unfolded onto a plane, the shape cut from flat sheet before it is rolled, bent and joined. Hoppers, dryer ducts, cyclones, chutes and tanks are all made from developments. Every line in a development is true length.
There are three methods. The parallel-line method develops prisms and cylinders: the lateral surface of a right cylinder of diameter D and height h is a rectangle pi D by h, and a prism develops into a row of rectangles. If the cylinder is cut obliquely, the heights of equally spaced elements are carried across to give a curved top edge. The radial-line method develops pyramids and cones: a right cone of base radius r and slant height L develops into a sector of a circle of radius L whose angle, in degrees, is 360 multiplied by r divided by L. A frustum develops as the difference of two sectors. The triangulation method develops surfaces that are neither prismatic nor conical, such as transition pieces that join a square duct to a round one; the surface is divided into triangles whose true lengths are found from the views and laid out in sequence. Spheres and other doubly curved surfaces cannot be developed exactly and are approximated by zones or gores.
Real patterns also need seam, hem and bend allowances, and are laid out on the neutral axis of the sheet; the seam is usually placed on the shortest line.
A pictorial view shows three faces of an object in one view and is easier for non-specialists to read. Isometric projection is an orthographic projection in which the object is turned so that its three principal edges make equal angles with the plane of projection. The three isometric axes then appear 120 degrees apart, usually with one vertical and the other two at 30 degrees to the horizontal, and every length along those axes is foreshortened by the same factor, the square root of 2/3, about 0.816. A drawing made with lengths reduced by this factor, using an isometric scale, is an isometric projection. A drawing made with true lengths along the axes is an isometric drawing (sometimes called an isometric view); it has exactly the same shape but is about 22 per cent larger in every direction, and because it is quicker to draw it is the usual choice. Examination questions often turn on this distinction.
Only lines parallel to the isometric axes (isometric lines) can be measured. Lines not parallel to the axes (non-isometric lines), such as sloping edges, are drawn by locating their end points with coordinates along the axes, usually by first drawing an enclosing box. Angles are not shown in true size. Hidden lines are normally omitted.
A circle on an isometric face appears as an ellipse. By hand it is drawn either by plotting points from a grid of offsets or by the four-centre approximate method, which draws the ellipse as four circular arcs inside the isometric square (rhombus) that encloses it. In CAD, an isometric ellipse command or a true 3D model is used. A sphere in isometric projection appears as a circle of its true radius.
Oblique projection keeps one face, the front face, in true shape and draws receding lines at an angle, commonly 30 or 45 degrees. In cavalier oblique the receding lines are drawn full length, which makes deep objects look distorted; in cabinet oblique they are drawn half length, which looks more natural. Oblique suits flanges and pulleys, whose front circles stay circles. Perspective, with vanishing points, is for presentation, not manufacture.
A dimension states a required size or location. ISO 129 sets the rules. Every feature is dimensioned once, in the view where its shape is clearest, and never twice. Dimensions should be placed outside the view where possible, should not be taken to hidden lines, and should not cross each other or other lines unnecessarily. Dimension lines end in arrowheads or, in building practice, in oblique strokes or dots. Linear dimensions on mechanical drawings are in millimetres and the unit is stated once in the title block.
Two text orientations are allowed. In the aligned system, figures are placed parallel to the dimension line and read from the bottom or right-hand side of the sheet. In the unidirectional system all figures read from the bottom of the sheet. Symbols prefix the value: ⌀ for diameter, R for radius, S⌀ and SR for spherical diameter and radius, a square symbol for a square section, and abbreviations or symbols for countersink, counterbore and depth. A dimension enclosed in parentheses is auxiliary, given for information only and not toleranced. A dimension enclosed in a rectangular box is theoretically exact, used with geometrical tolerances.
Dimensions are arranged in chain (one after another), parallel or baseline (all from a common datum), running (a compact form of baseline with a single line), or coordinate form (in a table, as for a hole pattern on a CNC-cut plate), or a combination. Chain dimensioning accumulates tolerances: if each of four steps carries plus or minus 0.1 mm, the overall length can vary by plus or minus 0.4 mm. Baseline dimensioning from a functional datum avoids this accumulation, so functional dimensions, those that affect fit or performance, are given directly from the surfaces that matter.
No part can be made to an exact size, so a dimension carries a tolerance: the permitted difference between the maximum and minimum limits of size. A dimension of 50 plus 0.05 minus 0.02 has an upper limit of 50.05 mm, a lower limit of 49.98 mm and a tolerance of 0.07 mm. A general tolerance note in the title block, for example to ISO 2768 in a stated class, covers dimensions that carry no individual tolerance.
ISO 286 (adopted in India as IS 919) builds a system of limits and fits. The nominal or basic size is the reference size. The fundamental deviation, identified by a letter, places the tolerance zone relative to the nominal size; capital letters (A to ZC) are for holes and lower-case letters (a to zc) for shafts. The width of the zone is set by the standard tolerance grade, from IT01 and IT0 through IT1 to IT18; the number of standard tolerance units grows with grade, for example 10 units for IT6 and 16 for IT7, the unit for sizes up to 500 mm being i = 0.45 times the cube root of D plus 0.001 D micrometres, where D is the geometric mean of the size step in millimetres. A hole marked 25 H7 has its lower deviation zero (H always does) and a tolerance of IT7 for that size range.
A fit is the relation between a hole and a shaft before assembly. In a clearance fit the hole is always larger than the shaft; in an interference fit the shaft is always larger; in a transition fit either may occur. Maximum clearance equals the largest hole minus the smallest shaft; minimum clearance (or maximum interference, if negative) equals the smallest hole minus the largest shaft. The hole-basis system (hole H, shaft letter varied) is common because holes are made with fixed-size tools; the shaft-basis system keeps the shaft at h. Textbook hole-basis examples are H7/g6 (sliding), H7/k6 (transition) and H7/p6 (light press).
A drawing must also state how smooth a surface must be, because a bearing seat, a seal face and a casting skin need very different finishes and costs. Roughness is most commonly specified by Ra, the arithmetic mean deviation of the profile from its mean line, in micrometres. The surface texture symbol of ISO 1302 is a tick made of two unequal legs at 60 degrees to each other. The basic symbol alone means any process may be used. A horizontal bar closing the symbol means material removal by machining is required. A small circle inside the symbol means material removal is not permitted, so the surface is left as cast, forged or rolled. The roughness value is written near the symbol, with the production method and the lay (direction of tool marks) if needed. Older drawings used roughness grade numbers N1 to N12, each grade doubling Ra, with N1 at 0.025 micrometres, N6 at 0.8, N7 at 1.6, N8 at 3.2 and N12 at 50 micrometres; the grade numbers are no longer in the current ISO standard but remain on many legacy drawings.
Plus-and-minus tolerances on size control how big a feature is, but not how straight, flat, round, square or well placed it is. A shaft can be within its diameter limits everywhere and still be bent like a banana; a hole can be the right size but in the wrong place for its bolt. Geometric dimensioning and tolerancing (GD&T) adds controls of form, orientation, location and run-out, each tied to datums that reproduce how the part is held and functions. ISO 1101 and ASME Y14.5 share symbols and most concepts but differ in some defaults.
The most important difference is the default relationship between size and form. ASME Y14.5 applies Rule #1, the envelope principle: a feature of size at its maximum material size must have perfect form, so the size limits themselves limit form error. ISO 8015 applies the independency principle by default: size and form are controlled separately unless the envelope requirement is called for, using the circled E symbol after the size tolerance or a general note.
ISO 1101 groups the geometrical characteristics as follows. Form tolerances, which need no datum: straightness, flatness, roundness (circularity) and cylindricity. Orientation tolerances, which need a datum: parallelism, perpendicularity and angularity. Location tolerances: position, concentricity or coaxiality, and symmetry. Run-out tolerances: circular run-out and total run-out. Profile of a line and profile of a surface can be used for form, orientation or location depending on whether datums are referenced. ASME traditionally listed fourteen characteristics in five groups; its 2018 edition withdrew concentricity and symmetry, leaving twelve, an example of the two systems diverging.
A geometric tolerance is written in a feature control frame, a rectangle divided into compartments read from left to right: the characteristic symbol; the tolerance value, preceded by a diameter symbol when the tolerance zone is cylindrical, as it usually is for the position of a hole; any modifier such as M in a circle for maximum material condition (MMC) or L in a circle for least material condition (LMC); and then the datum letters in order of precedence, primary, secondary and tertiary. The frame is connected by a leader to the feature, or placed with the size dimension of a feature of size.
The primary datum establishes three points of contact (a plane), the secondary two (a line) and the tertiary one (a point), which together remove the six degrees of freedom of the part. This 3-2-1 principle should mirror how the part is located in assembly.
Maximum material condition is the state in which a feature contains the most material: the smallest hole or the largest shaft. Least material condition is the opposite: the largest hole or the smallest shaft. When a position tolerance on a hole is specified at MMC, the stated tolerance applies when the hole is at its smallest size, and as the hole departs towards its largest size, the departure is added as bonus tolerance. For a hole of diameter 10.0 to 10.2 mm with a position tolerance of diameter 0.1 at MMC, a hole made at 10.2 mm may be off position by up to diameter 0.3. The bonus is functional: a larger hole leaves more room for the bolt.
The virtual condition is the worst-case boundary generated by size and geometric tolerance together. For an internal feature at MMC it is the MMC size minus the geometric tolerance, so the hole above has a virtual condition of 9.9 mm, which is the largest pin that will always pass through it. For an external feature at MMC it is the MMC size plus the tolerance. Virtual conditions drive functional gauge design.
A cylindrical position tolerance zone also gives more usable area than the square zone produced by plus-or-minus coordinate tolerances. A square zone of plus or minus 0.05 mm in each direction has a diagonal of about 0.141 mm; a cylindrical zone of that diameter enclosing the square has an area about 57 per cent larger, accepting good parts that coordinate tolerancing would reject. On farm machines GD&T matters for hub bolt patterns, gearbox face perpendicularity and PTO shaft run-out.
A screw thread is a helical ridge on a cylinder (external thread) or in a hole (internal thread). The pitch is the axial distance between adjacent threads; the lead is the axial advance in one turn and equals the pitch multiplied by the number of starts. A thread is right-hand unless marked LH. The ISO metric thread has a 60-degree included angle and is designated by M followed by the nominal (major) diameter, with the pitch added only for fine threads: M12 is the coarse thread of 1.75 mm pitch, M12×1.25 a fine thread. Other forms include Whitworth (55 degrees), square and trapezoidal (ISO 30 degrees, Acme 29 degrees) power threads, buttress threads and pipe threads.
Threads are not drawn as true helices. ISO 6410 represents them conventionally. On an external thread seen from the side, the crests (major diameter) are drawn as continuous thick lines and the roots (minor diameter) as continuous thin lines; in the end view the root is a thin circle broken for about a quarter of its circumference. The end of the useful thread is a thick line across. On an internal thread in section, the minor diameter (crests) is thick and the major diameter (roots) thin, and hatching runs up to the crest line. In assembly, the external thread hides the internal one where they engage. For a tapped blind hole, the drill depth is drawn deeper than the thread, ending in a 120-degree drill point cone.
Bolts, studs, cap screws and set screws are the commonest fasteners on farm machines. A through bolt passes through clearance holes and takes a nut; a stud is threaded at both ends, one screwed permanently into a tapped casting; a cap screw screws into a tapped hole without a nut; a set screw has a pointed, cup or flat end and locks a collar or pulley on a shaft. Hexagonal heads and nuts are drawn either from catalogue data or, in classroom drawings, from approximate proportions related to the nominal diameter d, such as a nut thickness near 0.8d and an across-flats width near 1.5d plus 3 mm; these proportions are drawing conventions and actual standard dimensions should be taken from the relevant standard.
Vibration loosens nuts, so locking devices matter: lock nuts, spring washers, castle nuts with split pins, tab washers and prevailing-torque nuts. Keys transmit torque between a shaft and a hub: the sunk taper key (typically tapered 1 in 100 on its top face), the parallel or feather key, which allows axial sliding, the gib-head key, which can be drawn out from one end, the Woodruff key (a semicircular disc), and the saddle key, which relies on friction. Splines carry larger torque, as on a PTO shaft. Rivets join plates permanently in lap or butt joints with single or double cover plates; heads include snap (cup), pan, countersunk and conical forms. In sectional views of assemblies, bolts, nuts, keys and rivets cut along their length are not hatched.
Frames, hitches and toolbars are welded, so weld symbols are essential reading. In ISO 2553, a weld symbol consists of an arrow line pointing to the joint, a reference line, and the elementary symbol that indicates the type of weld: a triangle for a fillet weld, and various symbols for square, V, bevel, U and J butt welds, plug welds, spot welds and seam welds. In ISO 2553 system A, the reference line is doubled: a continuous line and a dashed identification line. If the symbol is placed on the continuous line side, the weld is on the arrow side of the joint; if on the dashed line side, it is on the other side. The American AWS A2.4 convention uses a single reference line, with the symbol below the line meaning arrow side and above it meaning other side.
Supplementary symbols include a circle at the junction of the arrow and reference line for a weld all round, and a flag for a site or field weld. The size of a fillet weld is given either as the throat thickness a or as the leg length z; for an equal-leg fillet with a flat face, the throat is the leg multiplied by the cosine of 45 degrees, about 0.707 times the leg. Confusing leg and throat makes a weld about 30 per cent weaker or 40 per cent larger than intended.
A machine is documented by two kinds of drawing. A detail drawing (part drawing) defines one part completely: every view, dimension, tolerance, surface finish, material and heat treatment needed to make and inspect it. An assembly drawing shows how the parts fit together. It normally carries only the dimensions needed for assembly and installation, such as overall size, mounting hole centres and critical clearances, and it identifies each part with an item number in a balloon (a circle at the end of a leader) that refers to the parts list or bill of materials. The parts list gives item number, part name, drawing or standard number, material, quantity and remarks.
A general assembly shows the whole machine, a sub-assembly one unit such as a disc gang, and an exploded pictorial view, common in parts catalogues, separates parts along their assembly axes. University examinations give dimensioned part sketches of an element such as a plummer block, flange coupling, universal joint, stuffing box or screw jack and ask for the assembled views, one in half section, with a parts list.
The mouldboard plough bottom is the classic agricultural assembly. Its frog is the central casting or fabrication to which the other parts bolt: the share, which cuts the furrow slice horizontally; the mouldboard, which lifts, turns and inverts the slice; and the landside, which presses against the furrow wall and resists side thrust. A shin may form the leading edge of the mouldboard. Share and mouldboard are fastened with countersunk plough bolts so that the heads lie flush and do not obstruct soil flow, a detail that the assembly drawing must show.
A disc harrow gang is assembled on a square gang bolt that passes through the discs and through spools (spacers) between them, with bearings carrying the gang on the frame and a nut at the end clamping the stack. A cultivator tine is held on a toolbar by a clamp and U-bolts; a spring-loaded tine adds a spring and pivot. A plummer block (pedestal bearing) consists of a body, a cap, split bushes or a rolling bearing, and cap bolts with nuts; it is used for line shafts in threshers and mills. A Hooke's (universal) joint, used in PTO drive shafts, consists of two yokes, a cross (spider) and bearings; the assembly drawing shows the two yokes at right angles. A protected flange coupling has two flanges keyed to the shafts, joined by bolts on a pitch circle, with a projecting rim covering the bolt heads for safety.
When drawing an assembly, start from the largest or locating part, add parts in their order of assembly, apply the sectioning conventions (shafts, bolts, keys and pins unhatched, adjacent parts hatched in different directions), show hidden detail only where needed, and check every fit: holes and shafts that must mate need matching sizes and suitable fits on their detail drawings.
Computer-aided design (CAD) replaced the drawing board for most work, but it uses the same principles: projection, standards and dimensioning. In 2D CAD the drafter works in a model space at full size (1:1 in real units) and composes printed sheets in a layout or paper space, where viewports show the model at chosen scales and where the border and title block live. Points are entered by absolute Cartesian coordinates (x, y from the origin), relative Cartesian coordinates (dx, dy from the last point) or relative polar coordinates (a distance and an angle from the last point, with angles normally measured anticlockwise from the positive x-axis). Object snaps lock to endpoints, midpoints, centres, intersections, tangents and perpendiculars, so that geometry is exact rather than visually close.
Layers organise a drawing by type of content, for example outlines, hidden lines, centre lines, dimensions, hatching and text, each with its own line type, line weight and colour, so that the line conventions of ISO 128 are applied consistently. Blocks (symbols or library parts) store repeated items such as bolts, doors or north points once and insert them many times. Dimension styles and text styles encode the standard once for the whole firm. Arrays, mirrors, offsets, fillets and trims perform the classical constructions. Common neutral exchange formats are DXF for 2D geometry, and for 3D models STEP (ISO 10303) and IGES.
Three-dimensional models come in three kinds. A wireframe model stores only edges, so it cannot distinguish inside from outside and cannot hide lines automatically. A surface model stores the faces, which is enough for shaded pictures and for complex sheet or body shapes. A solid model stores a closed volume, so mass, volume, centre of gravity and moments of inertia can be computed, interference between parts can be detected and sections can be cut. Solids are represented internally by constructive solid geometry (CSG), a tree of Boolean union, difference and intersection operations on primitive solids, or by boundary representation (B-rep), which stores the faces, edges and vertices and their connections. Most current mechanical modellers use B-rep with a feature history.
Parametric feature-based modelling is the usual method for machine parts. A 2D sketch is drawn on a plane and controlled by geometric constraints (horizontal, vertical, parallel, perpendicular, tangent, coincident, concentric, equal, symmetric) and dimensional constraints. A sketch with no remaining degrees of freedom is fully constrained, which makes later edits predictable. Features are then created from sketches: extrude, revolve, sweep along a path, loft between profiles, and applied features such as holes, fillets, chamfers, shells, ribs, drafts and patterns. Design intent is captured by choosing which dimensions drive which, so that changing a shaft diameter updates its keyway, bearing seat and the matching hub. Sheet-metal modules unfold parts into developments automatically.
Parts are combined in an assembly by mates such as coincident faces and concentric axes. A free rigid body has six degrees of freedom; each mate removes some, and a mechanism keeps the freedoms it needs, so that a linkage can be animated and checked for interference. The 2D production drawing is then generated from the model, with projected views, sections, detail views and auxiliary views that update when the model changes; the drafter adds dimensions, tolerances, surface texture and notes, and the parts list is generated from the assembly structure.
Models also feed finite element analysis, CNC programming and 3D printing, for which they are exported as STL, a triangle mesh. For buildings, building information modelling (BIM) stores walls, doors, slabs and services as objects with properties, producing plans, elevations, sections and quantities from one model. Whatever the software, the engineer remains responsible for checking the output against the standards.
Farm buildings, including dairy sheds, poultry houses, implement sheds, grain stores, pump houses, greenhouses and processing rooms, are specified by a set of architectural and structural drawings. The site plan shows the building on its plot with boundaries, north point, access roads, drainage, levels and distances to other structures; it is drawn at a small scale such as 1:200, 1:500 or smaller. The floor plan is a horizontal section taken a little above window-sill height, looking down, so that walls, doors, windows, columns and fixed equipment are shown with their sizes and positions; it is usually drawn at 1:50 or 1:100. Elevations are external views of each face of the building, named by the direction they face (north elevation) or by the side (front, rear, side elevation), showing heights, openings, roof slope and finishes. Sections are vertical cuts through the building at chosen lines marked on the plan, showing foundation, plinth, floor, wall, lintel, roof structure and heights. Foundation, roof, framing and services drawings complete the set.
Plans, elevations and sections are orthographic projections, so elevations project from the plan and heights must agree. On a building drawing, dimension lines commonly end in oblique strokes or dots, and dimensions are given in millimetres or in metres depending on national practice, which the drawing states. Walls cut by the plan section are drawn with thick lines or are filled or hatched, while things seen beyond the cut, such as a floor step, are drawn thin.
Doors on plans are shown by an opening in the wall with the door leaf drawn as a line and the swing as an arc, so that clearance can be checked; sliding doors, common on implement sheds and barns, are shown by the leaf displaced along the wall. Windows are shown by thin lines across the wall thickness. Columns, grid lines and grid labels, numbered one way and lettered the other, locate the structural frame; post-frame and portal-frame sheds are set out on such grids. Symbols differ between countries, so each set should carry a legend.
Reading a farm-building plan is a matter of checking function. In a dairy shed, the plan shows the standing or stall layout, feed alley, manger, dung channel and its slope towards the drain, water troughs and the milking area; the section shows the roof height and ventilation openings. In a grain store the plan shows stacks and aisles, and the section shows plinth height, damp-proof course and ventilators. Dimensions read on a plan must be converted by the scale: at 1:100, 1 mm on paper is 100 mm on the ground, and an area measured on paper is multiplied by the square of the scale factor. Recommended sizes, space per animal, roof slopes and loads vary by country, species, climate and building code, and must be taken from the applicable national code or extension standard.
In the first year you learn to think in three dimensions on flat paper. You will draw scales, curves, projections of lines and solids, sections, developments and isometric views by hand, then in CAD. Practise sketching every object you meet in three orthographic views, and check your views by the alignment rules: width shared by front and top, height by front and side, depth by top and side. Later, in machine drawing, you will assemble a plummer block or plough bottom from its parts and write the parts list. Learn the standard line types, the first-angle and third-angle layouts, the fit and tolerance arithmetic and the weld-symbol conventions until you can apply them without looking them up; examinations and job interviews test them.
Five years into an implement firm, a testing station or a consultancy, you read and approve drawings more than you draw them. You check a supplier's drawing for the projection symbol, missing tolerances and unclear weld calls before an order is placed; you prepare detail drawings and developments for hoppers, ducts and frames from a 3D model; you set fits for bearing seats and hubs; you mark up as-built changes after field trials; and you draw farm-building plans for approval. You keep the firm's CAD template and drawing standards up to date, and you know which national code governs each drawing.
With twenty-five years of experience you own the drawing system. You decide the company's standards (ISO or ASME, first or third angle for each market), the tolerancing policy, the CAD and product-data management practice, and the revision control process. You review designs for manufacturability and for tolerance stack-ups that cause field failures, settle disputes with suppliers by reference to the drawing as a contract, and train young engineers to read drawings critically. You decide when a 3D model with model-based definition can replace a paper drawing and when a site crew or a village fabricator still needs a simple dimensioned sketch.
At the research level, drawing and CAD become tools for design science and for the digital thread from model to field. You might study tolerance allocation that minimises cost while guaranteeing function, generative or topology-optimised design of lightweight implement frames, automatic generation of developments for complex sheet parts, digital twins of tractors and processing plants, BIM for livestock and storage buildings, and the interoperability of standards for machine data. You also judge where national standards lag practice and contribute to standards committees, and you teach graphics in a way that builds spatial reasoning, a skill that research links to success in engineering study.
This manual is text-only, and drawing is a visual and manual skill: it cannot replace hours of drawing practice with instruments and in CAD, and its questions describe views in words. It does not reproduce numerical tables of ISO 286 deviations, thread dimensions, nut and bolt sizes, key sizes or weld-preparation dimensions; questions give such values in the stem. It does not cover the projection symbol's exact geometry, perspective construction in detail, intersection of surfaces (interpenetration of solids) beyond a mention, gear and cam drawing in detail, piping and electrical schematics, GIS (which the NCEES specification groups with graphics; see the remote sensing and GIS subject), or any one CAD program's commands. Building-drawing symbols, plan-approval rules and recommended dimensions of farm buildings vary by country and are left to the national codes and to the building materials and structures subject. The ASME and ISO GD&T systems are summarised, not taught clause by clause.
Original practice questions written to the syllabus and pattern of the exams named in each question's examTags. They are not past papers and do not reproduce any board's questions. Views are described in words; sketch each object as you read.
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