Maharashtra HSC Engineering Drawing (Technical Science) cheat sheet

Standard drawing sheet sizes (ISO 216 / IS 10713): A0 = 1189 × 841 mm; each successive size halves the longer side, so A1 = 841 × 594, A2 = 594 × 420, A3 = 420 × 297, A4 = 297 × 210 mm.

IS 10714 (based on ISO 3098) governs lettering: nominal height h of capitals; ratio of height to stroke width = 14:1 for style A (d/h = 1/14) and 10:1 for style B (d/h = 1/10); lowercase x-height = 7h/10 for style B.

Recommended lettering heights: 2.5, 3.5, 5, 7, 10, 14, 20 mm; minimum 2.5 mm for titles and notes, 3.5 mm or larger for drawing numbers and headings.

IS 10713 / ISO 5457 layout: drawing space bounded by border lines; filing margin 20 mm on the left edge (for binding), 10 mm on the other three edges for A4–A1; centring marks and a grid reference system are optional.

Title block per IS 11669 / ISO 7200 sits at the bottom-right corner of the drawing space and carries drawing title, drawing number, scale, sheet size, projection symbol, and revision.

Standard scales: full size 1:1; enlarging 2:1, 5:1, 10:1; reducing 1:2, 1:5, 1:10, 1:20, 1:50, 1:100, 1:200, 1:500, 1:1000. A scale is written as ratio (1:5) with no units.

Line types per IS 10714 / ISO 128: continuous thick (visible outlines, 0.5–0.7 mm), continuous thin (dimension, extension, hatching, leader lines, ~0.25 mm), dashed (hidden edges), chain thin (centre lines, pitch circles), chain thick at ends (cutting-plane lines), and freehand (irregular boundaries).

Dimensioning rules: dimension line is continuous thin, terminated by 3 mm long arrowheads at 3:1 length-to-width ratio; figures placed above the dimension line and read from the bottom or right-hand edge; extension line starts 1 mm clear of the object and extends 2 mm beyond the dimension line.

Geometric construction facts: to bisect an angle of any size, strike equal arcs from the vertex on both arms and intersect arcs of equal radius from those points; to divide a line into n equal parts, draw an inclined auxiliary line of n equal segments and project parallels.

Regular polygon construction: for an n-sided polygon inscribed in a circle of radius R, side length s = 2R·sin(180°/n); for a circumscribed polygon, s = 2R·tan(180°/n). Interior angle = (n − 2)·180°/n.

To construct a regular hexagon in a circle, step the radius R around the circumference six times (side = R); for an octagon, bisect the four quadrants and join the eight arc points.

To draw a regular pentagon in a circle, construct the midpoint M of radius OA, strike arc from M through the top point to the horizontal diameter; the resulting segment gives the side length.

To draw a tangent from an external point P to a circle centre O radius r: bisect OP to get M, draw a semicircle on OP, and its intersection with the given circle is the tangent point; tangent length = √(OP² − r²).

To draw an arc of radius R tangent externally to two given circles of radii r₁ and r₂, locate the arc centre at the intersection of arcs of radii (R − r₁) and (R − r₂); for internal tangency use (R + r₁) and (R + r₂).

Conic sections: eccentricity e = distance of focus from directrix divided by focal distance relation; e = 1 parabola, e < 1 ellipse, e > 1 hyperbola. For an ellipse, major axis = 2a, minor axis = 2b, and focus distance from centre c = √(a² − b²).

Ellipse by concentric-circle (auxiliary-circle) method: divide the major and minor axis circles into the same number of equal parts, project from each circle onto vertical and horizontal lines, and intersect corresponding projections.

Involute of a circle: divide the circle into equal parts, draw tangents at each point, and step off along each tangent the arc length of the corresponding sector (arc length = r·θ in radians).

Cycloid: a point on a circle of radius r rolling on a straight line traces an arch of height 2r and base length 2πr; the generating circle in the mid-position is drawn to locate intermediate points.

First-angle projection (IS practice): the object lies between the observer and the plane, so the view from the front is placed below the top view, and the view from the left is placed on the right of the front view.

Second-angle: top view above front view, left view on the left. Third-angle: top view above front view, right view on the right. Fourth-angle: top view below front view, right view on the left.

Notation: a point in space is a (or A); its front view is a′ and its top view is a. Coordinates are written (distance from VP, distance from HP); a point in the first quadrant has both distances positive.

A point on the HP has its top view on the XY line; a point on the VP has its front view on XY; a point in both planes coincides with XY in both views.

True length of a line inclined at θ to the HP and φ to the VP satisfies: (TL)² = (front-view length)² + (difference of end heights)² = (top-view length)² + (difference of end distances from VP)².

Rule: sin θ = (difference in heights)/(true length) and sin φ = (difference in distances from VP)/(true length); the front view foreshortens by cos θ, the top view foreshortens by cos φ.

A line parallel to both HP and VP appears true length in both front and top views; a line perpendicular to HP appears as a point in the top view and true length in the front view.

Traces: the horizontal trace (HT) is where the line meets the HP, found by extending the front view to XY and projecting down to the extended top view; the vertical trace (VT) is found by extending the top view to XY and projecting up.

A plane parallel to the VP appears true shape in the front view and as an edge (line) in the top view; a plane perpendicular to both HP and VP appears as a line in both views.

Solids are classified as polyhedra (prism, pyramid, cube, tetrahedron) and solids of revolution (cylinder, cone, sphere); a solid is positioned by its axis and its base.

For a right regular prism or pyramid with base side a and n sides: circumradius R = a/(2·sin(180°/n)); apothem (in-circle radius) r = a/(2·tan(180°/n)).

A right circular cone with base radius r and height h has slant height l = √(r² + h²); a right circular cylinder has no apex and its development is a rectangle of width 2πr.

A sphere rests on the HP at one point; its front and top views are circles of true diameter, with the equator and great-circle centre lines shown as chain lines.

Section plane parallel to the HP on a cone gives a circle; parallel to a generator gives a parabola; inclined to the axis more steeply than the generator gives an ellipse; parallel to the axis gives a hyperbola.

A section plane perpendicular to the VP and inclined to the HP shows the true shape of the section in the auxiliary view projected from the front view; the section is hatched with continuous thin lines at 45°.

When drawing a sectional view, omit hidden lines behind the cutting plane and hatch only the cut surface; visible edges beyond the plane remain as continuous thick lines.

Frustum of a cone or pyramid: obtained by a section plane parallel to the base; volume of a frustum = (h/3)(A₁ + A₂ + √(A₁A₂)) where A₁, A₂ are base areas.

Development is the true-shape unfolding of a surface onto a plane; only developable surfaces (prisms, cylinders, pyramids, cones) have exact developments - a sphere is developed only approximately.

Development of a right cylinder: rectangle of width 2πr and height h; of an oblique cylinder: divide the base circle into equal parts, project each generator true length, and join the ends with a smooth curve.

Development of a right cone: sector of radius equal to slant height l, with sector angle θ = 360°·(r/l); arc length equals the base circumference 2πr.

Development of a right pyramid: as many equal isosceles triangles as base sides, each with base a and slant edge true length; for an oblique pyramid the slant edges differ and each must be found by the true-length method.

Development of a truncated prism or cylinder: draw the stretch-out line, mark the base division points, erect perpendiculars of true length taken from the front view, and join the ends of the perpendiculars.

Methods of finding the intersection of two solids: (a) line method - draw a series of cutting planes and find where corresponding edges cut; (b) face method - find lines of intersection of individual faces; (c) sphere method for solids of revolution with intersecting axes.

When a cylinder penetrates a cylinder of equal diameter at right angles, the line of intersection in the front view is two straight lines forming a cross; unequal diameters give a curved line.

A vertical cylinder meeting a horizontal cylinder: the curve of intersection is projected by drawing a series of vertical cutting planes, transferring widths from the top view to the front view.

Points on an intersection curve are located where the same cutting plane meets both surfaces; the curve must pass through points where the surfaces' outlines cross in each view.

Isometric projection: the three axes are inclined at 120° to one another and at equal angles to the plane of projection; the three foreshortening factors are equal, 0.816.

Isometric drawing (isometric scale): true lengths are used along the isometric axes; the isometric length = 0.816 × true length, or approximately 82% of the true length.

Angle between an isometric axis and the horizontal in the drawing is 30°; vertical edges remain vertical; all lines parallel to the three axes are drawn parallel to them.

Non-isometric lines (lines not parallel to the axes) are drawn by locating their end points on the isometric axes and joining them; angles are not transferred directly.

Isometric circles (ellipses): on each isometric face the circle appears as an ellipse with major axis = 1.22d and minor axis = 0.71d, with the major axis perpendicular to the axis normal to that face.

The four-centre method approximates an isometric ellipse: locate the mid-points of the sides of the isometric square and strike four arcs from the corners and the centre of the square.

Oblique projection: the front face is drawn true shape and true size; receding edges are drawn at an angle, usually 30°, 45°, or 60° to the horizontal.

Cavalier oblique uses full scale (1:1) along the receding axis; cabinet oblique uses half scale (1:2) along the receding axis to reduce distortion; cavalier is chosen for short depths.

In oblique projection the receding axis is drawn at 45° for equal foreshortening appearance; the front face is chosen as the most complex or characteristic face of the object.

A full section removes one half of the object by a single cutting plane through the whole length; a half section removes one quarter and shows half in section, half in outside view, separated by a chain thin centre line.

An offset section uses a cutting plane bent at right angles to pass through features not in one plane; the bend is shown as a thick chain line in the view and the section is drawn as one continuous view.

A revolved section is drawn on the view itself by rotating the cross-section 90° about its axis; a removed section is drawn outside the view and labelled.

A broken-out section is bounded by a freehand (irregular) break line and shows only a small portion of the interior; a part section (local section) is used for a single feature such as a keyway.

Hatching: continuous thin lines at 45° to the principal outlines, spacing 2–4 mm; adjacent parts in an assembly are hatched in opposite directions or at different spacings.

Standard items never shown in section (conventional practice): shafts, bolts, nuts, screws, rivets, pins, keys, and the solid parts of spokes, ribs, and webs cut longitudinally.

Sections of thin parts such as gaskets, sheet metal, and packing are shown solid black (filled) instead of hatched.

A cutting plane is shown by a chain thick line with arrows at the ends showing the direction of sight, and labelled with capital letters (A–A, B–B) matching the section view title.

In a sectional view, hidden lines behind the cutting plane are generally omitted unless needed for clarity; visible lines behind the plane are drawn as continuous thick lines.

Thread notation: M20 × 2.5 means ISO metric thread, nominal (major) diameter 20 mm, pitch 2.5 mm; a coarse thread omits the pitch, so M20 is coarse and M20 × 1.5 is fine.

ISO metric coarse pitch examples: M6 = 1.0, M8 = 1.25, M10 = 1.5, M12 = 1.75, M16 = 2.0, M20 = 2.5, M24 = 3.0 mm.

Thread drawing convention: the crest (major diameter) is a continuous thick line and the root (minor diameter) a continuous thin line, with the thin line drawn about 3/4 of the circle in end view.

A thread is shown in section by hatching to the crest line on the external thread and to the root line on the internal thread; the tapped hole's thin line is drawn outside the thick line.

Square thread: depth = 0.5 × pitch; ACME thread: included angle 29°; buttress thread: included angle 45° with one face vertical - used where thrust acts in one direction.

A key transmits torque between shaft and hub; a sunk key is half in the shaft and half in the hub; a Woodruff key is a segment of a cylinder seated in a milled keyway in the shaft.

A taper key has a taper of 1 in 100 on its top surface; a saddle key bears on the shaft surface by friction and is used for light loads.

A muff coupling consists of a cast-iron sleeve fitted over the two shaft ends and driven by a sunk key; a flange coupling has two flanges keyed to the shafts and bolted together.

A bush bearing (journal bearing) supports a rotating shaft in a bearing bush of bronze or white metal; a ball bearing is designated by bore number × 5 mm (e.g., 6205 has a 25 mm bore).

Fundamental deviation is the deviation nearer the zero line; the upper deviation is ES for holes and es for shafts; the lower deviation is EI for holes and ei for shafts.

Tolerance = upper limit − lower limit = ES − EI (hole) = es − ei (shaft); the tolerance zone is the region between the maximum and minimum limits.

Hole-basis system: the hole's lower deviation is zero (H), so the hole varies from nominal to nominal + tolerance; shaft-basis system: the shaft's upper deviation is zero (h).

Clearance fit: the hole's minimum size is larger than the shaft's maximum size (e.g., H7/g6, H7/h6 - the latter is a slide fit with zero minimum clearance).

Interference fit: the shaft's minimum size exceeds the hole's maximum size (e.g., H7/p6, H7/s6); transition fit: the tolerance zones overlap (e.g., H7/k6, H7/n6).

IT grades: IT01 to IT4 for gauges, IT5–IT11 for fits, IT12–IT16 for un-machined or coarse work; for a given nominal size the tolerance increases with the IT number.

Example: 40 H7/g6 means nominal 40 mm, hole with H7 tolerance and shaft with g6 tolerance; the limits are read from IS 919 tables for the 30–50 mm diameter step.

Maximum material condition (MMC) is the largest shaft / smallest hole; least material condition (LMC) is the smallest shaft / largest hole; virtual condition = MMC ± the geometric tolerance.

Surface roughness Ra is the arithmetic mean deviation of the profile; symbols: ✓ for any process, ✓ with a bar for material removal not permitted, a circle in the V for removal not required, and N1–N12 grade numbers from 0.025 µm to 50 µm Ra.

A building drawing set consists of the plan (view from above, cut at about 1.2 m above floor), the elevation (front, rear, side), and the section (cut vertically through the building, showing foundations and roof).

Standard scales: site plan 1:500 or 1:1000; building plan 1:100 or 1:50; detailed section and enlarged details 1:20 or 1:10.

Wall thickness conventions: 230 mm for a 9-inch brick wall (one brick), 115 mm for a half-brick wall, 345 mm for a 1½-brick wall; the module is 100 mm in metric building practice.

A door is shown in plan as a break in the wall with a quarter-circle arc of radius equal to the door width, indicating the swing; standard widths are 700, 800, 900, 1000 mm.

A window in plan is drawn as a thin rectangle inside the wall thickness with the sill and lintel lines; the notation W1, D1, V1 is used to label windows, doors, and ventilators in a schedule.

The section shows the foundation: a typical strip footing has a concrete bed (PCC) 1:4:8, then brick masonry in cement mortar in stepped courses, with the plinth level marked as GL + plinth height.

Levels are written in metres to three decimals (e.g., +0.450) with a level symbol (a small triangle) and a horizontal line; the floor level is usually ±0.000.

Line conventions: continuous thick for walls cut in plan/section, continuous thin for doors, windows, and fixtures, dashed for hidden or above-cut features such as a beam or loft.

A schedule of areas and a north arrow are placed on the plan; the scale is stated in the title block and the drawing is oriented with north at the top unless noted.