Machine Drawing

Given: Scale 1:1, Pitch P = 30 mm (enlarged), BSW (British Standard Whitworth) thread profile.

Standard proportions of BSW thread:
- Pitch P = 30 mm
- Depth of thread: $d = 0.6403P = 0.6403 \times 30 \approx 19.2$ mm
- Radius at crest and root: $r = 0.1373P = 0.1373 \times 30 \approx 4.1$ mm
- Flank angle: 55° (i.e., included angle = 55°, each side = 27.5° from vertical)

Steps:
1. Draw a thin horizontal centre (axis) line.
2. Mark pitch divisions of 30 mm along the axis.
3. Draw the crest line (outer boundary) and root line (inner boundary) parallel to the axis, separated by the depth $d \approx 19.2$ mm (half on each side = 9.6 mm from axis).
4. Draw the flanks at 27.5° to the vertical (included angle 55°) connecting crest to root.
5. Round off the crests and roots with radius $r \approx 4.1$ mm using a compass.
6. Apply hatching and mark all standard dimensions: P = 30 mm, depth = 19.2 mm, r = 4.1 mm, flank angle = 55°.

Final Answer: The BSW thread profile is a V-thread with 55° included angle, rounded crests and roots (r = 0.1373P ≈ 4.1 mm), and depth = 0.6403P ≈ 19.2 mm, drawn to scale 1:1 with P = 30 mm.

Given: Scale 1:1, Pitch P = 60 mm (enlarged), Metric external thread (V-thread, 60° included angle).

Standard proportions of Metric thread:
- Pitch P = 60 mm
- Depth of thread (theoretical): $H = 0.866P = 0.866 \times 60 = 51.96$ mm
- Actual depth (external): $d = 0.6134P = 0.6134 \times 60 \approx 36.8$ mm
- Crest: flat = $P/8 = 60/8 = 7.5$ mm
- Root: flat = $P/4 = 60/4 = 15$ mm (or rounded)
- Flank angle: 30° each side (included angle = 60°)

Steps:
1. Draw a thin horizontal centre line (axis).
2. Mark pitch divisions of 60 mm along the axis.
3. Draw crest line and root line parallel to the axis; total depth = 0.6134P ≈ 36.8 mm.
4. Draw flanks at 30° to the vertical on each side (60° included angle).
5. Truncate the crest with a flat of P/8 = 7.5 mm and the root with a flat of P/4 = 15 mm.
6. Apply hatching and dimension: P = 60 mm, depth ≈ 36.8 mm, crest flat = 7.5 mm, root flat = 15 mm, included angle = 60°.

Final Answer: Metric external thread profile — 60° V-thread, depth ≈ 36.8 mm, crest flat = 7.5 mm, root flat = 15 mm, drawn to scale 1:1 with P = 60 mm.

Given: Scale 1:1, Pitch P = 60 mm (enlarged), Metric internal thread.

Standard proportions (Metric internal thread):
- Pitch P = 60 mm
- Depth: $d = 0.6134P \approx 36.8$ mm
- Crest (internal = minor diameter side): flat = $P/4 = 15$ mm
- Root (internal = major diameter side): flat = $P/8 = 7.5$ mm
- Flank angle: 30° each side (60° included)

Note: For internal thread, the crest and root are interchanged compared to external thread — the crest is at the minor diameter (inside) and the root is at the major diameter.

Steps:
1. Draw a thin horizontal centre line.
2. Mark pitch divisions of 60 mm.
3. Draw the two boundary lines (major and minor diameter) separated by depth ≈ 36.8 mm.
4. Draw flanks at 30° to the vertical (60° included angle).
5. Crest flat (at minor diameter) = P/4 = 15 mm; Root flat (at major diameter) = P/8 = 7.5 mm.
6. Apply hatching and mark all dimensions.

Final Answer: Metric internal thread profile — 60° V-thread, depth ≈ 36.8 mm, crest flat (minor dia side) = 15 mm, root flat (major dia side) = 7.5 mm, drawn to scale 1:1 with P = 60 mm.

Given: Scale 1:1, Pitch P = 40 mm (enlarged), Square thread.

Standard proportions of Square thread:
- Pitch P = 40 mm
- Depth of thread = $P/2 = 40/2 = 20$ mm
- Width of thread (crest) = $P/2 = 20$ mm
- Width of space (root) = $P/2 = 20$ mm
- Flanks are perpendicular to the axis (90° flanks)

Steps:
1. Draw a thin horizontal centre line (axis).
2. Mark pitch divisions of 40 mm along the axis.
3. Draw crest line and root line parallel to the axis, each at a distance of P/2 = 20 mm from the axis (total depth = 20 mm on one side, giving full depth = 20 mm).
4. Draw vertical flanks (perpendicular to axis) at every P/2 = 20 mm interval, alternating between crest and root levels, forming perfect squares.
5. The thread width = space width = P/2 = 20 mm.
6. Apply hatching and dimension: P = 40 mm, depth = 20 mm, thread width = 20 mm.

Final Answer: Square thread profile — rectangular cross-section, depth = P/2 = 20 mm, thread width = space width = P/2 = 20 mm, flanks perpendicular to axis, drawn to scale 1:1 with P = 40 mm.

Given: Scale 1:1, Pitch P = 60 mm (enlarged), Knuckle thread.

Standard proportions of Knuckle thread (from table):
- Pitch P = 60 mm
- Half pitch = 0.5P = 30 mm
- Quarter pitch = 0.25P = 15 mm
- The profile consists of tangential semicircles (rounded crests and roots).
- Depth of thread = 0.5 × (0.5P) = 0.25P = 15 mm
- Radius of each semicircle = 0.25P = 15 mm

Steps:
1. Draw a thin horizontal centre line (axis).
2. Mark pitch divisions of P = 60 mm along the axis.
3. On either side of the centre line, draw rows of tangential semicircles of radius = 0.25P = 15 mm. The semicircles at the crest curve outward and those at the root curve inward, flowing smoothly into one another.
4. Ensure free-flowing tangential connection between consecutive semicircles (no sharp corners).
5. Apply hatching and mark dimensions: P = 60 mm, 0.5P = 30 mm, 0.25P = 15 mm.

Final Answer: Knuckle thread profile — rounded crests and roots formed by tangential semicircles of radius 0.25P = 15 mm, depth = 0.25P = 15 mm, drawn to scale 1:1 with P = 60 mm.

Given: Nominal diameter d = 30 mm.

Concept: As per BIS convention, threads are represented by continuous thick and thin lines instead of helical curves.

External Thread Representation:

*Front View:*
1. Draw the axis (centre line — thin chain line).
2. Draw two continuous thick lines at distance d = 30 mm apart (representing the crests).
3. Draw two continuous thin lines at distance 0.8d = 24 mm apart (representing the roots), inside the thick lines.
4. Draw a thick line perpendicular to the axis at the limit of useful thread length.
5. In the end view (side view): draw a thick full circle of diameter d = 30 mm (crest) and a thin incomplete (broken) circle of diameter 0.8d = 24 mm (root) — the thin circle is broken (approximately ¾ of the circle is drawn).

Internal Thread Representation (Sectional view of threaded hole):

*Front View (section):*
1. Draw the axis (thin chain line).
2. Draw two continuous thick lines at 0.8d = 24 mm apart (crests of internal thread = minor diameter).
3. Draw two continuous thin lines at d = 30 mm apart (roots = major diameter).
4. Hatching (section lines) are extended up to the thick lines.
5. In the end (side) view: draw a thick full circle of diameter 0.8d = 24 mm (crest) and a thin incomplete circle of diameter d = 30 mm (root).

Dimensions to mark: d = 30 mm, 0.8d = 24 mm, thread length as assumed.

Final Answer: Freehand sketches of external thread (thick lines at d = 30 mm, thin lines at 0.8d = 24 mm) and internal thread in section (thick lines at 0.8d = 24 mm, thin lines at d = 30 mm, hatching up to thick lines) are drawn as per BIS convention.

Given: d = 30 mm, Length L = 120 mm, axis parallel to both H.P. and V.P., two opposite sides of hexagonal head parallel to V.P., Scale 1:1.

Standard Dimensions (Hexagonal Head Bolt):
$$d = 30\ \text{mm},\quad 0.8d = 24\ \text{mm (root diameter)},\quad \text{Across flats} = 1.5d+3 = 48\ \text{mm}$$
$$\text{Across corners} = \frac{2}{\sqrt{3}} \times 48 \approx 55.4\ \text{mm},\quad \text{Head height} = 0.7d = 21\ \text{mm}$$
$$\text{Threaded length} = 2d = 60\ \text{mm},\quad \text{Chamfer angle} = 30°$$

Steps — Front View (axis horizontal, two flats parallel to VP → two flats seen in front view):
1. Draw the axis as a horizontal centre line.
2. Draw the shank: two thick lines at distance d = 30 mm apart, length = L − head length = 120 − 21 = 99 mm from the head face.
3. Show threaded portion (last 2d = 60 mm): thick lines at d = 30 mm (crest), thin lines at 0.8d = 24 mm (root).
4. Draw the hexagonal head (two flats visible): a rectangle of width = across flats = 48 mm and height = 21 mm. Show chamfer arcs on top corners.
5. Draw chamfer arc on the head using radius = across corners/2 ≈ 27.7 mm.

Steps — Side View (end view of head):
1. Draw the hexagon with across-flats = 48 mm (two sides parallel to VP means in side view the hexagon appears with a vertex pointing toward viewer — across corners view).
2. Show the chamfering circle (inscribed circle of chamfer) touching mid-points of all six sides.
3. Show the shank as a circle of diameter d = 30 mm and root circle of 0.8d = 24 mm (broken).

Final Answer: Front view shows rectangular shank with threaded end and hexagonal head (two flats visible, chamfer arcs shown); Side view shows hexagon (across flats = 48 mm) with chamfer circle. All dimensions marked: d = 30, L = 120, head height = 21, threaded length = 60 mm.

Given: d = 20 mm, axis perpendicular to V.P. (axis is horizontal, pointing toward/away from VP — i.e., axis along the depth direction), Scale 1:1.

Standard Dimensions:
$$d = 20\ \text{mm},\quad 0.8d = 16\ \text{mm},\quad \text{Across flats} = 1.5d+3 = 33\ \text{mm}$$
$$\text{Head height} = 0.7d = 14\ \text{mm},\quad \text{Threaded length} = 2d = 40\ \text{mm}$$
$$\text{Total length} = 3.5d+6 = 76\ \text{mm (standard)}$$

Steps — Front View (axis perpendicular to VP → front view shows end/circular view of bolt):
1. Draw centre lines (horizontal and vertical).
2. Draw a circle of diameter d = 20 mm (shank/crest) — thick circle.
3. Draw a broken circle of diameter 0.8d = 16 mm (root of thread) — thin broken circle.
4. Draw the hexagon circumscribed about the circle of across-flats = 33 mm (two sides horizontal or as specified).
5. Draw the chamfering circle touching mid-points of all six sides.

Steps — Top View (plan, axis horizontal going into VP):
1. Project from front view.
2. Draw the shank as two horizontal lines d = 20 mm apart.
3. Show threaded portion: thick lines at 20 mm, thin lines at 16 mm.
4. Draw the head as a rectangle: width = across flats = 33 mm, length = head height = 14 mm.
5. Show chamfer arc on the visible face of the head.

Final Answer: Front view shows hexagonal end view with concentric circles (d = 20 mm thick, 0.8d = 16 mm thin broken) and hexagon (across flats = 33 mm). Top view shows shank with threaded end and rectangular head. All standard dimensions marked.

Given: d = 24 mm, L = 120 mm, Threaded length = 80 mm, axis parallel to both VP and HP, two opposite sides of hexagonal head perpendicular to VP, Scale 1:1.

Standard Dimensions:
$$d = 24\ \text{mm},\quad 0.8d = 19.2\ \text{mm},\quad \text{Across flats} = 1.5d+3 = 39\ \text{mm}$$
$$\text{Across corners} = \frac{39}{\cos 30°} \approx 45\ \text{mm},\quad \text{Head height} = 0.7d \approx 17\ \text{mm}$$

Steps — Front View (axis horizontal; two sides perpendicular to VP → one vertex points toward viewer in side view; in front view, a vertex is seen at top and bottom of head):
1. Draw horizontal axis (centre line).
2. Draw shank: two thick lines 24 mm apart, total length 120 mm.
3. Show threaded portion (80 mm from tip): thick lines at d = 24 mm, thin lines at 0.8d = 19.2 mm.
4. Draw hexagonal head: since two sides are perpendicular to VP, in the front view the head appears with a corner (vertex) at top and bottom. Width = across corners ≈ 45 mm, height = head height = 17 mm. Draw the outline showing two slanted sides and one vertical side on each half.
5. Show chamfer arc on the head.

Steps — Side View:
1. Project from front view.
2. Show hexagon with across-flats = 39 mm (two sides now parallel to VP in side view).
3. Show chamfer circle.
4. Show shank circle d = 24 mm (thick) and root circle 0.8d = 19.2 mm (thin broken).

Final Answer: Front view shows bolt with shank (L = 120 mm), threaded length = 80 mm, and hexagonal head with vertex at top/bottom (across corners ≈ 45 mm, height = 17 mm). Side view shows hexagon across flats = 39 mm. All dimensions marked.

Given: d = 24 mm, axis horizontal (parallel to HP and VP), Scale 1:1 (full size).

Standard Dimensions (Square Head Bolt):
$$d = 24\ \text{mm},\quad 0.8d = 19.2\ \text{mm},\quad \text{Side of square} = 1.5d = 36\ \text{mm}$$
$$\text{Head height} = 0.7d \approx 17\ \text{mm},\quad \text{Threaded length} = 2d = 48\ \text{mm}$$
$$\text{Total length} = 3.5d+6 = 90\ \text{mm (standard, or as given)}$$

Steps — Front View (axis horizontal, two faces of square head parallel to VP):
1. Draw horizontal centre line (axis).
2. Draw shank: two thick lines 24 mm apart.
3. Show threaded portion (48 mm from tip): thick lines at 24 mm, thin lines at 19.2 mm.
4. Draw square head: rectangle of width = 1.5d = 36 mm and height = 0.7d = 17 mm. Show chamfer (45°) on the top corners.
5. Draw chamfer arc on the head face.

Steps — Side View (end view of head):
1. Draw a square of side 1.5d = 36 mm.
2. Draw the chamfering circle (inscribed circle) of diameter = 36 mm touching all four sides.
3. Show shank circle d = 24 mm (thick) and root circle 0.8d = 19.2 mm (thin broken).

Final Answer: Front view shows rectangular shank with threaded end and square head (36 mm × 17 mm, chamfered corners). Side view shows square (36 mm side) with inscribed chamfer circle. All dimensions marked.

Given: d = 30 mm, axis perpendicular to HP (axis vertical), Scale 1:1.

Standard Dimensions:
$$d = 30\ \text{mm},\quad 0.8d = 24\ \text{mm},\quad \text{Side of square} = 1.5d = 45\ \text{mm}$$
$$\text{Head height} = 0.7d = 21\ \text{mm},\quad \text{Threaded length} = 2d = 60\ \text{mm}$$
$$\text{Total length} = 3.5d+6 = 111\ \text{mm (standard)}$$

Steps — Plan (Top View, axis vertical → plan shows end view of bolt):
1. Draw centre lines.
2. Draw circle of diameter d = 30 mm (shank crest) — thick.
3. Draw broken circle of diameter 0.8d = 24 mm (root) — thin broken.
4. Draw square of side 1.5d = 45 mm around the circles (head in plan).
5. Draw chamfering circle (diameter = 45 mm, inscribed in square) — this is the chamfer circle touching mid-points of all four sides.

Steps — Elevation (Front View, axis vertical):
1. Project from plan.
2. Draw the shank as two vertical thick lines 30 mm apart.
3. Show threaded portion (60 mm from tip): thick lines at 30 mm, thin lines at 24 mm.
4. Draw square head: rectangle of width = 45 mm, height = 21 mm at the top.
5. Show chamfer (45°) on top corners of the head.

Final Answer: Plan shows square (45 mm side) with inscribed chamfer circle and shank circles (d = 30 mm thick, 0.8d = 24 mm thin broken). Elevation shows vertical shank with threaded end and square head (45 mm wide, 21 mm high, chamfered). All dimensions marked.

Given: d = 24 mm, axis perpendicular to HP (vertical), Scale 1:1.

Standard Dimensions (Tee Head Bolt):
$$d = 24\ \text{mm},\quad 0.8d = 19.2\ \text{mm}$$
$$\text{Head width (flange)} = 3d = 72\ \text{mm},\quad \text{Head height} = 0.7d \approx 17\ \text{mm}$$
$$\text{Neck width} = 1.5d = 36\ \text{mm},\quad \text{Neck height} = 0.5d = 12\ \text{mm}$$
$$\text{Threaded length} = 2d = 48\ \text{mm},\quad \text{Total length} = 3.5d+6 \approx 90\ \text{mm}$$

Steps — Plan (Top View):
1. Draw centre lines.
2. Draw the T-shaped head in plan: a rectangle of 3d × 0.7d = 72 mm × 17 mm (the cross of the T) and a rectangle of 1.5d × 0.5d = 36 mm × 12 mm (the stem of the T).
3. Draw shank circle d = 24 mm (thick) and root circle 0.8d = 19.2 mm (thin broken) at centre.

Steps — Front Elevation (axis vertical):
1. Project from plan.
2. Draw shank as two vertical thick lines 24 mm apart.
3. Show threaded portion (48 mm from tip): thick lines at 24 mm, thin lines at 19.2 mm.
4. Draw T-shaped head at top: wide flange (72 mm wide, 17 mm high) with a narrower neck (36 mm wide, 12 mm high) below the flange.
5. Dimension all parts.

Final Answer: Front elevation shows vertical shank with threaded end and T-shaped head (flange 72 mm wide, 17 mm high; neck 36 mm wide, 12 mm high). Plan shows T-shape with shank circles. All dimensions marked.

Given: d = 25 mm, axis parallel to both VP and HP (horizontal), Scale 1:1.

Standard Dimensions (Hook Bolt / J-Bolt):
$$d = 25\ \text{mm},\quad 0.8d = 20\ \text{mm},\quad \text{Shank diameter} = d = 25\ \text{mm}$$
$$\text{Hook outer diameter} = 2d = 50\ \text{mm},\quad \text{Hook inner diameter} = 0.8d = 20\ \text{mm (approx)}$$
$$\text{Total length} = 3.5d+6 \approx 93.5\ \text{mm},\quad \text{Threaded length} = 2d = 50\ \text{mm}$$

Steps — Front View (axis horizontal):
1. Draw horizontal centre line (axis).
2. Draw the straight shank portion: two thick lines d = 25 mm apart.
3. Show threaded portion (2d = 50 mm from the threaded end): thick lines at 25 mm, thin lines at 20 mm.
4. At the other end, draw the hook (J-shape): a semicircle of outer radius = d = 25 mm curving downward (or upward), with the hook end returning parallel to the shank.
5. The hook cross-section is circular (diameter = d = 25 mm).

Steps — Side View (Top View / Plan):
1. Draw centre lines.
2. Draw outer circle of diameter d = 25 mm (shank cross-section) — thick.
3. Draw broken circle of diameter 0.8d = 20 mm (root of thread) — thin broken.
4. Show the hook in plan as a semicircular arc.
5. Mark thin cross lines on the head portion to indicate the circular cross-section.

Final Answer: Front view shows horizontal shank with threaded end and J-shaped hook at the other end (hook radius = d = 25 mm). Side/top view shows circular shank (d = 25 mm thick, 0.8d = 20 mm thin broken) and hook arc. All standard dimensions marked.

Given: d = 24 mm, axis vertical (perpendicular to HP), two opposite sides of hexagon parallel to VP, Scale 1:1.

Standard Dimensions (Hexagonal Nut):
$$d = 24\ \text{mm},\quad 0.8d = 19.2\ \text{mm (root/thread diameter)}$$
$$\text{Across flats} = 1.5d+3 = 39\ \text{mm},\quad \text{Across corners} = \frac{39}{\cos 30°} \approx 45\ \text{mm}$$
$$\text{Height (thickness) of nut} = 0.8d = 19.2\ \text{mm},\quad \text{Chamfer angle} = 30°$$

Steps — Plan (Top View, axis vertical):
1. Draw centre lines.
2. Draw chamfering circle of diameter = across flats = 39 mm.
3. Circumscribe a regular hexagon about this circle with two sides horizontal (parallel to VP means in plan two sides are horizontal).
4. Draw a thick circle of diameter 0.8d = 19.2 mm (crest of internal thread — minor diameter) — shown as full thick circle.
5. Draw a thin broken circle of diameter d = 24 mm (root — major diameter).

Steps — Front Elevation (axis vertical):
1. Project from plan.
2. Two opposite sides are parallel to VP → in front elevation, two flat faces are seen (rectangle view).
3. Draw the nut outline: width = across flats = 39 mm, height = 0.8d = 19.2 mm.
4. Show chamfer arcs on the top two corners (chamfer angle 30°). The chamfer arc is drawn using radius = across corners/2 ≈ 22.5 mm.
5. Show the threaded hole: thick lines at 0.8d = 19.2 mm apart (crest), thin lines at d = 24 mm apart (root) — since it is a sectional or conventional representation.

Final Answer: Plan shows hexagon (across flats = 39 mm, two sides horizontal) with thick circle (0.8d = 19.2 mm) and thin broken circle (d = 24 mm). Front elevation shows rectangle (39 mm wide, 19.2 mm high) with chamfer arcs on top corners. All dimensions marked.

Given: d = 30 mm, axis perpendicular to HP (vertical), two opposite sides of hexagon perpendicular to VP, Scale 1:1.

Standard Dimensions:
$$d = 30\ \text{mm},\quad 0.8d = 24\ \text{mm},\quad \text{Across flats} = 1.5d+3 = 48\ \text{mm}$$
$$\text{Across corners} \approx 55.4\ \text{mm},\quad \text{Nut height} = 0.8d = 24\ \text{mm}$$

Steps — Plan (Top View):
1. Draw centre lines.
2. Draw chamfering circle (diameter = across flats = 48 mm).
3. Circumscribe hexagon with two sides perpendicular to VP (i.e., two sides are vertical in plan — two sides parallel to the left-right direction).
4. Draw thick circle d = 0.8×30 = 24 mm (minor diameter/crest of internal thread).
5. Draw thin broken circle d = 30 mm (major diameter/root).

Steps — Front View:
1. Project from plan.
2. Two sides perpendicular to VP → in front view, a corner (vertex) of the hexagon faces the viewer — across corners view.
3. Width of front view = across corners ≈ 55.4 mm, height = nut height = 24 mm.
4. Draw the outline showing two slanted sides meeting at a top vertex and two slanted sides at bottom, with vertical sides at the extreme left and right.
5. Show chamfer arc on top.
6. Show threaded hole conventionally.

Final Answer: Plan shows hexagon (across flats = 48 mm, two sides vertical) with concentric circles. Front view shows hexagon in across-corners orientation (width ≈ 55.4 mm, height = 24 mm) with chamfer arc. All dimensions marked.

Given: d = 30 mm, axis perpendicular to HP (vertical), two opposite sides of square perpendicular to VP, Scale 1:1.

Standard Dimensions (Square Nut):
$$d = 30\ \text{mm},\quad 0.8d = 24\ \text{mm},\quad \text{Side of square} = 1.5d = 45\ \text{mm}$$
$$\text{Nut height} = 0.8d = 24\ \text{mm},\quad \text{Chamfer angle} = 45°$$

Steps — Top View (Plan):
1. Draw centre lines.
2. Draw chamfering circle of diameter = side of square = 45 mm (inscribed circle).
3. Draw square of side 45 mm with two sides perpendicular to VP (i.e., two sides are vertical in plan).
4. Draw thick circle of diameter 0.8d = 24 mm (crest of internal thread).
5. Draw thin broken circle of diameter d = 30 mm (root).

Steps — Front View:
1. Project from plan.
2. Two sides perpendicular to VP → in front view, two flat faces are seen (rectangle).
3. Width = side of square = 45 mm, height = nut height = 24 mm.
4. Show chamfer (45°) on the top two corners.
5. Show threaded hole: thick lines at 0.8d = 24 mm, thin lines at d = 30 mm.

Final Answer: Top view shows square (45 mm side, two sides vertical) with inscribed chamfer circle and concentric thread circles. Front view shows rectangle (45 mm × 24 mm) with 45° chamfered top corners. All dimensions marked.

Given: d = 30 mm, axis perpendicular to HP (vertical), diagonal of square face parallel to VP, Scale 1:1.

Standard Dimensions:
$$d = 30\ \text{mm},\quad 0.8d = 24\ \text{mm},\quad \text{Side of square} = 1.5d = 45\ \text{mm}$$
$$\text{Diagonal of square} = 45\sqrt{2} \approx 63.6\ \text{mm},\quad \text{Nut height} = 0.8d = 24\ \text{mm}$$

Steps — Plan (Top View):
1. Draw centre lines.
2. Draw the square of side 45 mm rotated 45° so that the diagonal is parallel to VP (i.e., one corner points toward VP — the square appears as a diamond shape in plan).
3. Draw chamfering circle (diameter = 45 mm, inscribed in square).
4. Draw thick circle 0.8d = 24 mm and thin broken circle d = 30 mm.

Steps — Front View:
1. Project from plan.
2. Diagonal parallel to VP → in front view, a corner (vertex) faces the viewer on left and right.
3. Width of front view = diagonal = 45√2 ≈ 63.6 mm, height = 24 mm.
4. The outline shows a pointed/diamond shape: two slanted lines meeting at a point on each side.
5. Show chamfer arc on top.
6. Show threaded hole conventionally.

Final Answer: Plan shows square (45 mm side) rotated 45° (diamond orientation) with inscribed chamfer circle and thread circles. Front view shows diamond-shaped outline (width ≈ 63.6 mm, height = 24 mm) with chamfer arc. All dimensions marked.

Given: d = 30 mm, hexagonal bolt + hexagonal nut + washer, axis parallel to both VP and HP, Scale 1:1.

Standard Dimensions:
$$d = 30\ \text{mm},\quad 0.8d = 24\ \text{mm},\quad \text{Across flats} = 1.5d+3 = 48\ \text{mm}$$
$$\text{Bolt head height} = 0.7d = 21\ \text{mm},\quad \text{Nut height} = 0.8d = 24\ \text{mm}$$
$$\text{Threaded length} = 2d = 60\ \text{mm},\quad \text{Total bolt length} = 3.5d+6 = 111\ \text{mm}$$
$$\text{Washer: outer dia} = 2d = 60\ \text{mm},\quad \text{inner dia} = d+1.5 \approx 31.5\ \text{mm},\quad \text{thickness} = 0.12d \approx 3.6\ \text{mm}$$

Steps — Front View (axis horizontal):
1. Draw horizontal centre line.
2. Draw the bolt shank (d = 30 mm) with threaded portion (60 mm) showing thick and thin lines.
3. Draw hexagonal bolt head on the left: width = 48 mm (two flats visible), height = 21 mm, with chamfer arcs.
4. Place washer next to the nut side: outer dia = 60 mm shown as rectangle (60 mm wide, 3.6 mm thick), inner hole = 31.5 mm.
5. Draw hexagonal nut on the right of the washer: width = 48 mm, height = 24 mm, with chamfer arcs.
6. Show the bolt protruding slightly beyond the nut.

Steps — Side View:
1. Show hexagonal head as hexagon (across flats = 48 mm) with chamfer circle.
2. Show washer as annular ring (outer circle 60 mm, inner circle 31.5 mm).
3. Show nut as hexagon (across flats = 48 mm) with chamfer circle.
4. Show shank circles (d = 30 mm thick, 0.8d = 24 mm thin broken).

Final Answer: Front view shows complete assembly — hexagonal bolt head (48 mm wide, 21 mm high), shank (d = 30 mm, L = 111 mm), washer (60 mm OD, 3.6 mm thick), and hexagonal nut (48 mm wide, 24 mm high) — all with chamfer arcs. Side view shows hexagonal end views and washer ring. All dimensions marked.

Given: d = 24 mm (M24), square head bolt + square nut + washer, axis parallel to VP and HP, Scale 1:1.

Standard Dimensions:
$$d = 24\ \text{mm},\quad 0.8d = 19.2\ \text{mm},\quad \text{Side of square} = 1.5d = 36\ \text{mm}$$
$$\text{Bolt head height} = 0.7d \approx 17\ \text{mm},\quad \text{Nut height} = 0.8d \approx 19.2\ \text{mm}$$
$$\text{Threaded length} = 2d = 48\ \text{mm},\quad \text{Total length} = 3.5d+6 = 90\ \text{mm}$$
$$\text{Washer: OD} = 2d = 48\ \text{mm},\quad \text{ID} \approx d+1.5 = 25.5\ \text{mm},\quad \text{thickness} = 0.12d \approx 2.9\ \text{mm}$$

Steps — Front View (axis horizontal, two faces of square head and nut parallel to VP):
1. Draw horizontal centre line.
2. Draw shank (d = 24 mm) with threaded portion (48 mm): thick lines at 24 mm, thin lines at 19.2 mm.
3. Draw square bolt head on left: rectangle 36 mm wide × 17 mm high, with 45° chamfer on top corners.
4. Draw washer: rectangle 48 mm wide × 2.9 mm thick.
5. Draw square nut: rectangle 36 mm wide × 19.2 mm high, with 45° chamfer on top corners.

Steps — Side View:
1. Show square head as a square (36 mm side) with inscribed chamfer circle.
2. Show washer as annular ring (OD = 48 mm, ID = 25.5 mm).
3. Show square nut as a square (36 mm side) with inscribed chamfer circle.
4. Show shank circles.

Final Answer: Front view shows complete M24 assembly — square bolt head (36 mm × 17 mm), shank (L = 90 mm), washer (48 mm OD), and square nut (36 mm × 19.2 mm). Side view shows square end views and washer ring. All dimensions marked.

Given: d = 30 mm, square head bolt + hexagonal nut + washer, axis parallel to VP and HP, two opposite sides of square head and hexagonal nut parallel to VP, Scale 1:1.

Standard Dimensions:
$$d = 30\ \text{mm},\quad 0.8d = 24\ \text{mm}$$
$$\text{Square head side} = 1.5d = 45\ \text{mm},\quad \text{Bolt head height} = 0.7d = 21\ \text{mm}$$
$$\text{Hex nut across flats} = 1.5d+3 = 48\ \text{mm},\quad \text{Nut height} = 0.8d = 24\ \text{mm}$$
$$\text{Threaded length} = 2d = 60\ \text{mm},\quad \text{Total length} = 3.5d+6 = 111\ \text{mm}$$
$$\text{Washer: OD} = 2d = 60\ \text{mm},\quad \text{thickness} = 0.12d \approx 3.6\ \text{mm}$$

Steps — Front View (axis horizontal):
1. Draw horizontal centre line.
2. Draw shank (d = 30 mm) with threaded portion (60 mm).
3. Draw square head on left: rectangle 45 mm wide × 21 mm high (two sides parallel to VP → two flat faces visible), 45° chamfer on top corners.
4. Draw washer: rectangle 60 mm wide × 3.6 mm thick.
5. Draw hexagonal nut on right of washer: two opposite sides parallel to VP → two flat faces visible, width = across flats = 48 mm, height = 24 mm, with chamfer arcs.

Steps — Side View:
1. Show square head as square (45 mm side) with inscribed chamfer circle.
2. Show washer as annular ring (OD = 60 mm).
3. Show hexagonal nut as hexagon (across flats = 48 mm) with chamfer circle.
4. Show shank circles (d = 30 mm thick, 0.8d = 24 mm thin broken).

Final Answer: Front view shows complete assembly — square bolt head (45 mm × 21 mm, chamfered), shank (L = 111 mm, threaded 60 mm), washer (60 mm OD), and hexagonal nut (48 mm wide, 24 mm high, chamfered). Side view shows respective end views. All dimensions marked.

Given: d = 25 mm, Plain stud, axis parallel to VP and HP (horizontal), freehand sketch.

Standard Dimensions (Plain Stud):
$$d = 25\ \text{mm},\quad 0.8d = 20\ \text{mm (root diameter)}$$
$$\text{Metal end (plant end) threaded length} = d = 25\ \text{mm}$$
$$\text{Nut end threaded length} = 2d = 50\ \text{mm}$$
$$\text{Plain shank length} = 1.5d = 37.5\ \text{mm}$$
$$\text{Total length} = d + 1.5d + 2d = 4.5d = 112.5\ \text{mm}$$

Steps — Front Elevation (axis horizontal):
1. Draw horizontal centre line.
2. Draw the plain shank: two thick lines d = 25 mm apart, length = 1.5d = 37.5 mm in the middle.
3. On the left (metal/plant end): show threaded portion of length d = 25 mm — thick lines at 25 mm, thin lines at 20 mm.
4. On the right (nut end): show threaded portion of length 2d = 50 mm — thick lines at 25 mm, thin lines at 20 mm.
5. Both ends are chamfered (45°).

Steps — Side View:
1. Draw a circle of diameter d = 25 mm (thick) — shank cross-section.
2. Draw a thin broken circle of diameter 0.8d = 20 mm (root of thread).

Final Answer: Front elevation shows horizontal stud with plain shank (37.5 mm) flanked by threaded metal end (25 mm) and threaded nut end (50 mm), both with chamfers. Side view shows concentric circles (d = 25 mm thick, 0.8d = 20 mm thin broken). All dimensions marked.

Given: d = 20 mm, Stud with square neck, axis perpendicular to HP (vertical), freehand sketch.

Standard Dimensions (Stud with Square Neck):
$$d = 20\ \text{mm},\quad 0.8d = 16\ \text{mm}$$
$$\text{Square neck side} = 1.5d = 30\ \text{mm},\quad \text{Square neck height} = 0.5d = 10\ \text{mm}$$
$$\text{Metal end threaded length} = d = 20\ \text{mm}$$
$$\text{Nut end threaded length} = 2d = 40\ \text{mm}$$
$$\text{Plain shank length} = 1.5d = 30\ \text{mm}$$

Steps — Top View (Plan, axis vertical):
1. Draw centre lines.
2. Draw a square of side 1.5d = 30 mm (square neck in plan).
3. Draw circle of diameter d = 20 mm (thick) inside the square.
4. Draw thin broken circle of diameter 0.8d = 16 mm.

Steps — Front View (axis vertical):
1. Project from top view.
2. Draw the stud vertically: metal end (threaded, d = 20 mm, length = 20 mm) at bottom, plain shank (30 mm) in middle, square neck (30 mm wide, 10 mm high) above shank, nut end (threaded, 40 mm) at top.
3. Show thread conventions on metal end and nut end.
4. Show square neck as rectangle (30 mm wide, 10 mm high) with chamfer.

Final Answer: Top view shows square (30 mm side) with concentric circles. Front view shows vertical stud with metal end thread (20 mm), plain shank (30 mm), square neck (30 mm × 10 mm), and nut end thread (40 mm). All dimensions marked.

Given: d = 20 mm, Stud with collar, axis vertical, freehand sketch.

Standard Dimensions (Stud with Collar):
$$d = 20\ \text{mm},\quad 0.8d = 16\ \text{mm}$$
$$\text{Collar diameter} = 1.5d = 30\ \text{mm},\quad \text{Collar height} = 0.5d = 10\ \text{mm}$$
$$\text{Metal end threaded length} = d = 20\ \text{mm}$$
$$\text{Nut end threaded length} = 2d = 40\ \text{mm}$$
$$\text{Plain shank length} = 1.5d = 30\ \text{mm}$$

Steps — Plan (Top View, axis vertical):
1. Draw centre lines.
2. Draw outer circle of collar: diameter = 1.5d = 30 mm (thick).
3. Draw circle of diameter d = 20 mm (thick) — shank.
4. Draw thin broken circle of diameter 0.8d = 16 mm (root).

Steps — Front View (axis vertical):
1. Draw the stud vertically.
2. Metal end (bottom): threaded, length = d = 20 mm, thick lines at 20 mm, thin lines at 16 mm.
3. Plain shank: length = 1.5d = 30 mm, diameter = d = 20 mm.
4. Collar: diameter = 1.5d = 30 mm, height = 0.5d = 10 mm — shown as a wider cylinder.
5. Nut end (top): threaded, length = 2d = 40 mm, thick lines at 20 mm, thin lines at 16 mm.
6. Both ends chamfered.

Final Answer: Plan shows three concentric circles (collar OD = 30 mm thick, shank d = 20 mm thick, root 0.8d = 16 mm thin broken). Front view shows vertical stud with metal end thread (20 mm), plain shank (30 mm), collar (30 mm dia × 10 mm high), and nut end thread (40 mm). All dimensions marked.

Given: d = 10 mm (M10), Round head machine screw, axis horizontal, freehand sketch.

Standard Dimensions (Round Head Screw):
$$d = 10\ \text{mm},\quad 0.8d = 8\ \text{mm}$$
$$\text{Head diameter} = 2d = 20\ \text{mm},\quad \text{Head height} = 0.7d = 7\ \text{mm}$$
$$\text{Slot width} = 0.2d = 2\ \text{mm},\quad \text{Slot depth} = 0.25d = 2.5\ \text{mm}$$
$$\text{Length of screw} = 3d = 30\ \text{mm (assumed standard)}$$

Steps — Front View (axis horizontal):
1. Draw horizontal centre line.
2. Draw the shank: two thick lines d = 10 mm apart (threaded throughout — thick lines at 10 mm, thin lines at 8 mm).
3. Draw the round head: a dome/semi-ellipse shape of diameter 2d = 20 mm and height 0.7d = 7 mm at the left end.
4. Show the slot on the head: a rectangle of width 0.2d = 2 mm and depth 0.25d = 2.5 mm at the top of the head.
5. Chamfer the tip of the screw at 45°.

Steps — Side View (end view):
1. Draw a circle of diameter 2d = 20 mm (head outline).
2. Draw a circle of diameter d = 10 mm (shank/crest) — thick.
3. Draw thin broken circle of diameter 0.8d = 8 mm (root).
4. Show the slot as a rectangle across the diameter of the head.

Final Answer: Front view shows round-headed screw (head dia = 20 mm, height = 7 mm, slot 2 mm × 2.5 mm) with threaded shank (d = 10 mm, L = 30 mm). Side view shows circular head (20 mm dia) with slot and shank circles. All dimensions marked.

Given: d = 10 mm (M10), Cheese head machine screw, axis horizontal and parallel to VP and HP, freehand sketch.

Standard Dimensions (Cheese Head Screw):
$$d = 10\ \text{mm},\quad 0.8d = 8\ \text{mm}$$
$$\text{Head diameter} = 1.5d = 15\ \text{mm},\quad \text{Head height} = 0.7d = 7\ \text{mm}$$
$$\text{Slot width} = 0.2d = 2\ \text{mm},\quad \text{Slot depth} = 0.25d = 2.5\ \text{mm}$$
$$\text{Length} = 3d = 30\ \text{mm (assumed)}$$

Steps — Front View (axis horizontal):
1. Draw horizontal centre line.
2. Draw threaded shank: thick lines at d = 10 mm, thin lines at 0.8d = 8 mm, length = 30 mm.
3. Draw cheese head (cylindrical head): rectangle of width = 1.5d = 15 mm and height = 0.7d = 7 mm at the left end. The head is a plain cylinder (flat top and bottom).
4. Show slot on top of head: width = 0.2d = 2 mm, depth = 0.25d = 2.5 mm.
5. Chamfer tip at 45°.

Steps — Side View:
1. Draw circle of diameter 1.5d = 15 mm (head outline).
2. Draw circle of diameter d = 10 mm (shank crest) — thick.
3. Draw thin broken circle of diameter 0.8d = 8 mm (root).
4. Show slot as a rectangle across the head diameter.

Final Answer: Front view shows cylindrical cheese head (15 mm dia, 7 mm high, slot 2 mm × 2.5 mm) with threaded shank (d = 10 mm, L = 30 mm). Side view shows circular head (15 mm dia) with slot and shank circles. All dimensions marked.

Given: d = 10 mm (M10), 90° flat countersunk head machine screw, axis vertical, freehand sketch.

Standard Dimensions (90° Flat CSK Head Screw, scaled from M20 example proportionally):
$$d = 10\ \text{mm},\quad 0.8d = 8\ \text{mm}$$
$$\text{Head diameter} = 1.8d = 18\ \text{mm},\quad \text{Head height} = 0.5d = 5\ \text{mm (approx)}$$
$$\text{Slot width} = 0.2d = 2\ \text{mm},\quad \text{Slot depth} = 0.25d = 2.5\ \text{mm}$$
$$\text{Countersink angle} = 90°,\quad \text{Length} = 3d = 30\ \text{mm}$$

Steps — Front View (axis vertical):
1. Draw vertical centre line.
2. Draw threaded shank: thick lines at d = 10 mm, thin lines at 0.8d = 8 mm, length = 30 mm.
3. Draw countersunk head at top: a trapezoid (inverted V shape) with top width = 1.8d = 18 mm, tapering to shank diameter at bottom, with 90° included angle (45° each side from vertical).
4. Show slot: width = 0.2d = 2 mm, depth = 0.25d = 2.5 mm at the top.
5. Chamfer tip at 45°.

Steps — Top View (Plan, axis vertical):
1. Draw centre lines.
2. Draw outer circle of head: diameter = 1.8d = 18 mm (thick).
3. Draw circle of diameter d = 10 mm (shank crest) — thick.
4. Draw thin broken circle of diameter 0.8d = 8 mm (root).
5. Show slot as a rectangle across the head.

Final Answer: Front view shows 90° CSK head (top dia = 18 mm, 45° flanks) with threaded shank (d = 10 mm, L = 30 mm) and slot (2 mm × 2.5 mm). Top view shows concentric circles (18 mm, 10 mm, 8 mm) with slot. All dimensions marked.

Given: d = 20 mm (M20), Hexagonal socket head machine screw, axis parallel to VP and HP (horizontal), freehand sketch.

Standard Dimensions (Hex Socket Head Screw):
$$d = 20\ \text{mm},\quad 0.8d = 16\ \text{mm}$$
$$\text{Head diameter} = 1.5d = 30\ \text{mm},\quad \text{Head height} = d = 20\ \text{mm}$$
$$\text{Socket (hex) across flats} = d = 20\ \text{mm},\quad \text{Socket depth} = 0.5d = 10\ \text{mm}$$
$$\text{Length} = 3d = 60\ \text{mm (assumed)}$$

Steps — Front View (axis horizontal):
1. Draw horizontal centre line.
2. Draw threaded shank: thick lines at d = 20 mm, thin lines at 0.8d = 16 mm, length = 60 mm.
3. Draw cylindrical head: rectangle of width = d = 20 mm (head height) and height = 1.5d = 30 mm at the left end.
4. Show hexagonal socket on the head face: a regular hexagon of across-flats = d = 20 mm, depth = 0.5d = 10 mm (shown as a hexagonal recess).
5. Chamfer tip at 45°.

Steps — Side View (end view):
1. Draw circle of diameter 1.5d = 30 mm (head outline).
2. Draw the hexagonal socket as a hexagon of across-flats = 20 mm inside the head circle.
3. Draw circle of diameter d = 20 mm (shank crest) — thick.
4. Draw thin broken circle of diameter 0.8d = 16 mm (root).

Final Answer: Front view shows cylindrical head (30 mm dia, 20 mm high) with hexagonal socket recess (across flats = 20 mm, depth = 10 mm) and threaded shank (d = 20 mm, L = 60 mm). Side view shows circular head (30 mm dia) with hexagonal socket and shank circles. All dimensions marked.

Given: d = 10 mm (M10), Grub screw (headless set screw), axis vertical, freehand sketch.

Standard Dimensions (Grub Screw):
$$d = 10\ \text{mm},\quad 0.8d = 8\ \text{mm}$$
$$\text{Length} = 2d = 20\ \text{mm (standard)}$$
$$\text{Slot width} = 0.2d = 2\ \text{mm},\quad \text{Slot depth} = 0.25d = 2.5\ \text{mm}$$
$$\text{Cone point angle} = 90°\ \text{(or flat/cup point)}$$

Note: A grub screw has no head — it is threaded throughout its length. One end has a slot (for screwdriver) and the other end has a cone/cup point.

Steps — Front View (axis vertical):
1. Draw vertical centre line.
2. Draw the screw body: two thick lines d = 10 mm apart, length = 2d = 20 mm (threaded throughout — thick lines at 10 mm, thin lines at 8 mm).
3. At the top end: show the slot — a rectangle of width 0.2d = 2 mm and depth 0.25d = 2.5 mm.
4. At the bottom end: show the cone point — a V-shape with 90° included angle (45° each side).

Steps — Top View (Plan, axis vertical):
1. Draw centre lines.
2. Draw circle of diameter d = 10 mm (crest) — thick.
3. Draw thin broken circle of diameter 0.8d = 8 mm (root).
4. Show the slot as a rectangle across the diameter.

Final Answer: Front view shows headless threaded screw (d = 10 mm, L = 20 mm) with slot at top (2 mm × 2.5 mm) and cone point at bottom (90°). Top view shows concentric circles (d = 10 mm thick, 0.8d = 8 mm thin broken) with slot. All dimensions marked.

Given: Single riveted lap joint, plate thickness t = 9 mm, Scale 1:1 (full size).

Standard Dimensions (Lap Joint):
$$t = 9\ \text{mm}$$
$$\text{Rivet diameter: } d = 1.9\sqrt{t} = 1.9\sqrt{9} = 1.9 \times 3 = 5.7\ \text{mm} \approx 6\ \text{mm (standard)}$$
$$\text{Pitch: } p = 3d = 3 \times 6 = 18\ \text{mm}$$
$$\text{Margin: } m = 1.5d = 1.5 \times 6 = 9\ \text{mm}$$
$$\text{Rivet head diameter: } D = 1.6d = 9.6\ \text{mm}$$
$$\text{Rivet head height: } h = 0.7d = 4.2\ \text{mm (snap/round head)}$$

Steps — Full Sectional Front View:
1. Draw the two overlapping plates in section: each plate is t = 9 mm thick. The overlap length = p + 2m = 18 + 18 = 36 mm. Show hatching on both plates (in opposite directions to distinguish).
2. Draw the rivet in the hole: rivet shank diameter = d = 6 mm, passing through both plates (total thickness = 2t = 18 mm).
3. Draw snap heads on both sides of the joint: diameter = 1.6d = 9.6 mm, height = 0.7d = 4.2 mm (hemispherical/snap head shape).
4. Mark all dimensions: t = 9 mm, d = 6 mm, p = 18 mm, m = 9 mm, D = 9.6 mm, h = 4.2 mm.

Final Answer: Full sectional front view shows two overlapping plates (t = 9 mm each, hatched) with one rivet (d = 6 mm) passing through both, with snap heads on both sides (D = 9.6 mm, h = 4.2 mm). Pitch = 18 mm, margin = 9 mm. All dimensions marked.

Given: Single riveted lap joint, plate thickness t = 25 mm, Scale 1:1.

Standard Dimensions:
$$t = 25\ \text{mm}$$
$$\text{Rivet diameter: } d = 1.9\sqrt{t} = 1.9\sqrt{25} = 1.9 \times 5 = 9.5\ \text{mm} \approx 10\ \text{mm (standard)}$$
$$\text{Pitch: } p = 3d = 30\ \text{mm}$$
$$\text{Margin: } m = 1.5d = 15\ \text{mm}$$
$$\text{Rivet head diameter: } D = 1.6d = 16\ \text{mm}$$
$$\text{Rivet head height: } h = 0.7d = 7\ \text{mm}$$

Steps — Front View in Section:
1. Draw two overlapping plates in section: each t = 25 mm thick, with hatching. Overlap = p + 2m = 30 + 30 = 60 mm.
2. Draw rivet shank (d = 10 mm) passing through both plates (total = 2t = 50 mm).
3. Draw snap heads on both sides: D = 16 mm, h = 7 mm.
4. Mark all dimensions.

Steps — Plan (Top View):
1. Draw the top plate as a rectangle (show the overlap region).
2. Show the rivet hole as a circle of diameter d = 10 mm.
3. Show the rivet head (top) as a circle of diameter D = 16 mm.
4. Mark pitch p = 30 mm and margin m = 15 mm.

Final Answer: Front sectional view shows two plates (t = 25 mm each, hatched) with rivet (d = 10 mm, snap heads D = 16 mm, h = 7 mm). Plan shows top plate with rivet head circle (D = 16 mm) and pitch/margin dimensions. All standard dimensions marked: t = 25, d = 10, p = 30, m = 15, D = 16, h = 7 mm.

Given: Shaft diameter D = 60 mm, Rectangular taper key, freehand sketch.

Standard Dimensions (Rectangular Taper Key):
$$D = 60\ \text{mm}$$
$$\text{Width: } W = D/4 = 60/4 = 15\ \text{mm}$$
$$\text{Thickness (mean): } T = D/6 = 60/6 = 10\ \text{mm}$$
$$\text{Length: } L = 1.5D = 1.5 \times 60 = 90\ \text{mm}$$
$$\text{Taper: } 1:100\ \text{(1 mm in 100 mm on top face)}$$
$$\text{Gib head height} = 1.75T = 17.5\ \text{mm (if gib head type; plain taper has no gib head)}$$

Steps — Front View:
1. Draw a rectangle of length L = 90 mm and height = T = 10 mm.
2. Show the taper on the top face: one end is slightly thicker than the other (taper 1:100 — difference over 90 mm = 0.9 mm, shown exaggerated in sketch).
3. The bottom face is parallel to the axis.

Steps — Side View (end view):
1. Draw a rectangle of width W = 15 mm and height T = 10 mm.

Steps — Plan (Top View):
1. Draw a rectangle of length L = 90 mm and width W = 15 mm.
2. Show taper lines (converging slightly) on the top surface.

Final Answer: Front view shows tapered rectangle (L = 90 mm, T = 10 mm, taper 1:100). Side view shows rectangle (W = 15 mm × T = 10 mm). Plan shows rectangle (L = 90 mm × W = 15 mm) with taper indicated. All dimensions marked: D = 60, W = 15, T = 10, L = 90 mm.

Given: Shaft diameter D = 60 mm, Woodruff key, freehand sketch.

Standard Dimensions (Woodruff Key):
$$D = 60\ \text{mm}$$
$$\text{Width: } W = D/4 = 15\ \text{mm}$$
$$\text{Diameter of key (circular part): } d_k = 2.5W = 2.5 \times 15 = 37.5\ \text{mm} \approx 38\ \text{mm}$$
$$\text{Thickness: } T = D/6 = 10\ \text{mm}$$
$$\text{Height above shaft: } h = 0.5T = 5\ \text{mm (approx)}$$

Note: A Woodruff key is a semicircular key. Its cross-section is a segment of a circle.

Steps — Front View:
1. Draw a semicircle of diameter $d_k \approx 38$ mm (the full circular disc shape — actually a segment).
2. The flat top of the key has width W = 15 mm.
3. The curved bottom fits into the circular key seat on the shaft.
4. Height of key = T = 10 mm.

Steps — Side View (end view):
1. Draw a rectangle of width W = 15 mm and height T = 10 mm.

Steps — Plan (Top View):
1. Draw a rectangle of length = $d_k \approx 38$ mm and width W = 15 mm.
2. Show the curved ends (semicircular) of the key.

Final Answer: Front view shows semicircular/segment-shaped key (diameter ≈ 38 mm, width W = 15 mm, height T = 10 mm). Side view shows rectangle (15 mm × 10 mm). Plan shows rectangle with semicircular ends (38 mm × 15 mm). All dimensions marked.

Given: Shaft diameter D = 40 mm, Double head gib (feather) key, freehand sketch.

Standard Dimensions (Double Head Feather/Gib Key):
$$D = 40\ \text{mm}$$
$$\text{Width: } W = D/4 = 40/4 = 10\ \text{mm}$$
$$\text{Thickness: } T = D/6 = 40/6 \approx 6.5\ \text{mm} \approx 7\ \text{mm}$$
$$\text{Length: } L = 1.5D = 1.5 \times 40 = 60\ \text{mm (shank only)}$$
$$\text{Gib head height: } H = 1.75T \approx 1.75 \times 7 = 12.25\ \text{mm} \approx 12\ \text{mm}$$
$$\text{Gib head width: } = W = 10\ \text{mm}$$
$$\text{Total length (with both gib heads): } L_{total} = L + 2 \times H = 60 + 24 = 84\ \text{mm}$$

Note: A double head gib key has gib heads (projecting heads) on both ends, unlike a single gib head key.

Steps — Front View:
1. Draw the shank as a rectangle: length L = 60 mm, height T = 7 mm.
2. On the left end: draw the gib head — a rectangular projection of width W = 10 mm and height H = 12 mm, with a 45° chamfer at the top corner.
3. On the right end: draw an identical gib head.
4. The key has uniform thickness (no taper — it is a feather key).

Steps — Top View (Plan):
1. Draw a rectangle of total length $L_{total}$ = 84 mm and width W = 10 mm.
2. Show the gib head projections at both ends (wider portions).

Steps — Side View (Right Side):
1. Draw a rectangle of width W = 10 mm and height T = 7 mm (shank cross-section).
2. Show the gib head profile: height H = 12 mm, width W = 10 mm.

Final Answer: Front view shows double-headed key with shank (L = 60 mm, T = 7 mm) and gib heads on both ends (H = 12 mm, chamfered). Top view shows full length rectangle (84 mm × 10 mm). Side view shows rectangular cross-section (10 mm × 7 mm) with gib head. All dimensions marked: D = 40, W = 10, T = 7, L = 60, H = 12 mm.