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“Make a lever-operated ball valve in the 30° open position as 6 separate solids (body, ball, 2 seat rings, stem, handle). Coordinate system: flow axis = X axis, ball center = origin, stem axis = Z axis. Direction d = (cos30°, sin30°, 0) = (0.86603, 0.5, 0) is the direction of the ball bore and the handle, and e = (-0.5, 0.86603, 0) is the horizontal direction perpendicular to it. (1) Body (one solid): block X=-40~40, Y=-30~30, Z=-30~30. A Ø20 flow hole runs through the full length in the X direction, with Ø26 pipe counterbores at both ends (X=30~40, X=-40~-30). Internal cavity: Ø48 cylinder on the X axis, X=-22~22 (enclosed space). A Ø12 stem hole on the Z axis runs from the cavity to the top face Z=30. (2) Ball: Ø40 sphere (centered at the origin). A Ø20 ball bore runs through along an axis in direction d. Stem tang slot on the top: long in direction d, width 6 (±3) in direction e, from Z=15 to the sphere surface (through the full length in direction d). (3) 2 seat rings: each an annular cylinder on the X axis, outer diameter Ø48, inner diameter Ø20, one at X=15~22 and the other at X=-22~-15. The side facing the ball is cut to the ball's spherical surface (Ø40) so that it seats against the ball. (4) Stem (one solid): tang = cuboid with length 16 (±8) in direction d, thickness 6 (±3) in direction e, Z=15~21 (inside the ball's slot). Ø12 shaft at Z=21~45. Top-end 10×10 square (sides parallel to directions d and e) at Z=45~55. (5) Handle (one solid): plate at Z=46~52. Measured from the stem axis, it runs from -20 to +100 in direction d, width 20 (±10) in direction e, with a 10×10 square hole that the stem square fits into (sides parallel to d and e). That is, the handle points in the same 30° direction as the ball bore.”
“Model a swivel caster as seven separate solids: top plate, thrust washer, kingpin bolt, nut, fork, wheel, axle. Frame: the kingpin (swivel) axis is the Z axis; the floor is Z=0 and the wheel touches it. Top plate: X=-40..40, Y=-40..40, Z=100..105 (edges parallel to X and Y), Ø12 hole on the Z axis and four Ø9 holes at (±30, ±30), all through along Z. Thrust washer: Ø40, bore Ø12, Z=92..100, on the Z axis. Kingpin bolt: shank Ø12 from Z=78 to Z=105 on the Z axis, head Ø20 from Z=105 to Z=110. Nut: Ø20 cylinder, bore Ø12, Z=78..84. Fork, one solid, described in a fork frame whose origin is on the Z axis: its x axis is the horizontal direction (cos35°, sin35°, 0), its y axis is (-sin35°, cos35°, 0), z = world Z. Crown plate: x=-42..15, y=-23..23, Z=84..92, with a Ø12 hole on the Z axis. Two legs, 5 thick, at y=18..23 and y=-23..-18; each leg (in the x-Z plane) is the rectangle x=-42..-18, Z=37.5..84 united with a disc R12 centred on the axle point (x=-30, Z=37.5), and has a Ø10 axle hole there. So the axle sits 30 behind the kingpin toward the 215° direction, at world (X, Y) = (-24.575, -17.207), Z=37.5. Wheel: axis along the fork y axis through the axle point. Tyre Ø75 over y=-15..15, hub Ø30 over y=-18..18 (the hub faces touch the legs), bore Ø10. Axle: Ø10 along the fork y axis from y=-26 to y=26 through the legs and wheel, with Ø16 heads over y=23..26 and y=-26..-23 bearing on the outer faces of the legs.”
“Model a tie-rod hydraulic cylinder as eight separate solids: base cap, barrel, head cap, piston-and-rod (one solid) and four tie rods. Frame: the cylinder axis is parallel to X through Y=20, Z=35. Offsets 'u, v' below are Y and Z measured from that axis (Y = 20 + u, Z = 35 + v). Base cap: square block X=0..20, u, v = -40..40, with a spigot Ø60 from X=20 to X=25 entering the barrel. Port: a Ø10 hole drilled from the top face (v=40) straight down at X=10, u=0, to the axis, and a Ø8 axial passage on the axis from X=10 to X=25 (opening into the bore). Barrel: tube Ø70 outside, Ø60 inside, X=20..170. Head cap: square block X=170..190, u, v = -40..40, spigot Ø60 from X=165 to X=170, rod bore Ø25 through. Tie-rod holes: both caps have four Ø10 holes along X at (u, v) = (±30, ±30). Piston and rod (one solid): piston Ø60 from X=85 to X=105 (so the piston's base-side face is 60 from the spigot face X=25); rod Ø25 from X=105 to X=250 through the head cap; a Ø12 cross hole through the rod along Z at X=240. Tie rods (four, identical): Ø10 from X=0 to X=190 on (u, v) = (±30, ±30), with heads Ø17 from X=-5 to X=0 and from X=190 to X=195 bearing on the outer faces of the caps.”
“Model a meshing spur gear pair as two separate solids. Frame: both gear axes are parallel to the X axis. The pinion axis passes through Y=20, Z=-10; the wheel axis passes through Y=99.674, Z=36, so the line of centres runs 30° from +Y toward +Z (centre distance 92). Angular positions about each axis are measured in the YZ plane from +Y toward +Z. Tooth form for both: involute, module 4, pressure angle 20°, no profile shift, addendum 1.0m, root diameter = pitch diameter - 2.5m, root fillets free. Backlash: circular tooth thickness on the pitch circle = pi*m/2 - 0.15 = 6.133, symmetric about the tooth centre line. Both toothed widths span X=0..30. Pinion (a gear shaft, one solid): 17 teeth, pitch Ø68, outside Ø76, root Ø58. Shaft Ø30 from X=-50 to X=0 and from X=30 to X=75. The X=30..75 end has a square-ended keyway 8 wide from X=48 to X=75 on the 90° side (+Z side of the shaft), floor 11 from the pinion axis. Phase: the pinion has a tooth SPACE centred on the 30° direction (toward the wheel). Wheel: 29 teeth, pitch Ø116, outside Ø124, root Ø106. Both side faces are recessed: an annular pocket from Ø56 out to Ø88, 9 deep, is cut into the X=0 face (X=0..9) and into the X=30 face (X=21..30), leaving a web X=9..21. Hub Ø56 from X=-10 to X=30 (it sticks out 10 on the -X side). Ø32 bore through X=-10..30 with a 10 wide keyway on the 90° side over the full length, keyway floor 20.3 from the wheel axis. A radial Ø6.8 set-screw hole at X=-5 runs from the hub surface into the bore on the 0° side (+Y side). Phase: the wheel has a TOOTH centred on the 210° direction from its own axis (toward the pinion), which sits in the pinion's tooth space.”
“Make a twisted blade lofted through 3 NACA symmetric airfoil sections, together with a root block, as a single solid. Coordinate system: blade span direction = +Z, twist axis = Z axis (the 1/4-chord point of each section lies on the Z axis). Section definition (local coordinates x, y within the section plane Z=z): the chord line lies on the local x axis, leading edge (LE) at x = -c/4, trailing edge (TE) at x = 3c/4. The thickness distribution follows the NACA 4-digit symmetric formula y = ±5·t·c·(0.2969·√ξ - 0.1260·ξ - 0.3516·ξ² + 0.2843·ξ³ - 0.1036·ξ⁴), ξ = (x + c/4)/c (0~1), and the trailing edge closes to a sharp point. The local coordinates are rotated counterclockwise by the twist angle, as seen looking down from +Z, and then placed in the world (local x axis = (cosθ, sinθ, 0)). - Section 1: Z=0, chord c=60, thickness ratio t=0.15 (NACA 0015), twist θ=0°. - Section 2: Z=60, c=48, t=0.12 (NACA 0012), θ=15°. - Section 3: Z=120, c=36, t=0.10 (NACA 0010), θ=30°. Blade = smooth loft passing through the three sections in order (Z=0~120, flat ends). Root block: cuboid X=-20~50, Y=-14~14, Z=-20~0 (the blade root face attaches to its top face), with a Ø10 hole through in the Y direction, axis at (X=15, Z=-10).”
“Make a bench vise in the assembled state as 6 separate solids (body, movable jaw, fixed jaw plate, movable jaw plate, screw, handle). Coordinate system: the jaw moves in the X direction, and the screw axis is the line (Y=0, Z=45) parallel to the X axis. Bottom face Z=0. (1) Body (one solid): base plate X=-60~100, Y=-40~40, Z=0~12. Fixed jaw block X=-60~-40, Y=-40~40, Z=12~60. Guide bar X=-40~90, Y=-15~15, Z=12~30. End plate X=90~100, Y=-25~25, Z=12~60, with a Ø14 hole through in the X direction on the screw axis. (2) Fixed jaw plate: X=-40~-36, Y=-38~38, Z=40~60 (attached to the +X face of the fixed jaw block). (3) Movable jaw (one solid): block X=5.5~35.5, Y=-40~40, Z=12~60 with a channel Y=-15~15, Z=12~30 that wraps around the guide removed over the full length in X (the channel top face contacts the guide top face Z=30, and its side faces contact the guide side faces). A Ø14 blind hole on the screw axis from the +X face (X=35.5), depth 12 (X=23.5~35.5, flat bottom). (4) Movable jaw plate: X=1.5~5.5, Y=-38~38, Z=40~60 (attached to the -X face of the movable jaw). Therefore the opening between the two jaw plates (X=-36~1.5) is 37.5. (5) Screw (one solid, a cylinder with the thread omitted): Ø14 at X=23.5~110 (its end touches the bottom of the movable jaw's blind hole and it passes through the end plate hole), head Ø24 at X=110~122. A Ø8 hole through the head in the Z direction at X=116. (6) Handle (one solid): Ø8 rod passing through the head hole in the Z direction, axis (X=116, Y=0), Z=0~90. Ø14 knobs at both ends: Z=-6~0 and Z=90~96.”
“Make an internal ring gear, 2 planet gears and a carrier as 4 separate solids in the meshed, assembled state. Coordinate system: the ring gear axis is parallel to the Y axis and passes through (X=30, Z=25). Angles are measured around the ring axis in the XZ plane from +X toward +Z. The planet gear axes are also parallel to the Y axis. Common tooth form: involute, module 1.25, pressure angle 20°, no profile shift, root fillet unrestricted. (1) Ring gear: 84 teeth, pitch circle Ø105, internal tip circle Ø102.5, internal root circle Ø108.125, tooth space width on the pitch circle is the nominal π·m/2 = 1.963. The internal teeth span the full range Y=0~16, ring body outer diameter Ø122 (Y=0~16). Square flange at the back: Y=-8~0, 150×150 (±75 each in X and Z relative to the ring axis, sides parallel to the X and Z axes), central hole Ø100, 4 Ø9 holes through in the Y direction at (X, Z) = (±60, ±60) relative to the ring axis. Phase: the ring has a tooth space center at the 0° direction. (2) 2 planet gears (identical shape): 26 teeth, pitch circle Ø32.5, tip circle Ø35, root circle Ø29.375, face width Y=0.5~15.5, Ø10 through bore. Backlash: circular tooth thickness on the pitch circle π·m/2 - 0.08 = 1.883 (symmetric about the tooth centerline). At a center distance of 36.25, planet 1 is in the 0° direction from the ring axis and planet 2 is in the 135° direction. Planet 1 has a tooth center facing outward (0° direction) from its own axis, which enters a tooth space of the ring; planet 2 has a tooth space center facing outward (135° direction), which the ring tooth at that position enters. (3) Carrier (one solid): Ø100 disc on the ring axis, Y=16.5~22.5. On both planet gear axes, Ø9.8 pins protrude from the disc to Y=0.5 and enter the planet bores (radial clearance 0.1). On the +Y side of the disc, a Ø20 shaft on the ring axis at Y=22.5~45.”
“Make one screw conveyor shaft as a single solid (pipe, flange and helical flight in one body). Coordinate system: the axis is parallel to the Z axis and passes through (X=-10, Y=20). Angle θ is measured around this axis in the XY plane from +X toward +Y (in degrees, continuing to accumulate past one full turn). (1) Pipe: outer diameter Ø40, inner diameter Ø30 through, Z=0~300. (2) Flange: outer diameter Ø100, Z=0~10 (one body with the pipe, Ø30 through at the center), 4 Ø9 through holes on a Ø80 circle at 45°+k·90°. (3) Helical flight (right-hand, pitch 100, axial thickness 5, 2.5 turns): in every plane Z=z with 20 ≤ Z ≤ 270, the flight cross-section is an annular sector of radius 20~60, spanning the angle from θ0(z) - 18° to θ0(z). Here θ0(z) = 3.6·(z - 20) (degrees). That is, at Z=20 the sector is -18°~0°, it rotates one full turn counterclockwise (as seen from +Z) for every 100 increase in Z, and it ends at 162°~180° at Z=270. Both ends of the flight are faces cut by the planes Z=20 and Z=270. The inner edge of the flight is one body with the outer surface of the pipe.”
“Make one spherical dome (shower-head type) as a single solid. Coordinate system: the dome axis is parallel to the Z axis and passes through (X=15, Y=-5). Sphere center O = (15, -5, -20). Azimuth is measured around the dome axis in the XY plane from +X toward +Y, and the polar angle is measured from the +Z direction at O. (1) Shell: the Z≥0 portion of a spherical shell centered at O with outer radius 60 and inner radius 55 (cut at the Z=0 plane, apex (15, -5, 40)). (2) Base flange: annular plate on the dome axis, outer diameter Ø144, inner diameter Ø102, Z=-6~0 (one body with the lower end of the shell). 6 Ø6.6 through holes at radius 64 from the dome axis, azimuth 30°+k·60°. (3) Shell holes: all Ø4, through the shell along radial axes pointing to the sphere center O. - 1 apex hole: polar angle 0° (on the dome axis). - Ring A: polar angle 15°, 6 holes, azimuth 0°+k·60°. - Ring B: polar angle 30°, 12 holes, azimuth 15°+k·30°. - Ring C: polar angle 45°, 18 holes, azimuth 10°+k·20°.”
“Model a ratchet-and-pawl mechanism as five separate solids: base plate, shaft, ratchet wheel, pawl and pawl pin. Frame: all axes parallel to Z; angles in the XY plane from +X toward +Y about the ratchet axis, which passes through (10, 0). Base plate: X=-50..60, Y=-45..60, Z=0..6, with a Ø16 hole on the ratchet axis, a Ø6 hole on the pawl axis (below) and four Ø6.6 holes at (X, Y) = (-42, -37), (52, -37), (-42, 52), (52, 52), all through along Z. Shaft: Ø16 from Z=0 to Z=20 on the ratchet axis (sits in the base hole), with a collar Ø24 from Z=20 to Z=24. Ratchet wheel: 16 sawtooth teeth, Z=8..20, bore Ø16 on the shaft, and a spacer hub Ø26 from Z=6 to Z=8 under it. Tooth outline: tip radius 40, root radius 32. For k = 0..15 let a_k = 5° + k·22.5°. Tooth k has a RADIAL face along the ray at a_k from r=32 to r=40, and a straight back flank from the root point (r=32 at a_k) to the tip point (r=40 at a_(k+1)). So every radial face faces counter-clockwise (toward increasing angle) and the wheel can only turn clockwise seen from +Z. Pawl (Z=8..20): a straight bar, outline = quadrilateral (7.101, 33.135), (6.368, 41.511), (-29.714, 49.800), (-31.505, 42.003) (world XY), plus a boss Ø14 from Z=6 to Z=20 centred on the pawl axis (-30.609, 45.902), with a Ø6.2 hole on that axis. The edge (7.101, 33.135)-(6.368, 41.511) lies on the ray at 95° from the ratchet axis, so the pawl's end face bears flat on the radial face of tooth k=4; the bar's lower edge runs 1.2 above the back flank of tooth k=4. Pawl pin: Ø6 on the pawl axis from Z=0 to Z=20 (in the base hole), head Ø10 from Z=20 to Z=23.”
“Model two roller-chain sprockets for ISO 606 06B single-strand chain as two separate solids on a fixed centre distance; the chain itself is not modelled. Chain pitch p = 9.525, roller Ø6.35. Frame: both axes parallel to Z; sprocket A's axis passes through (20, -30), sprocket B's through (164, 78), so the line of centres from A to B points at 36.870° (centre distance 180). Both tooth plates occupy Z=0..5.3 (one chain line). Angles are measured in the XY plane from +X toward +Y about each sprocket's own axis. Tooth form, ISO 606 construction with these exact values: pitch diameter d = p / sin(180°/z). Around each roller centre on the pitch circle, a roller-seat arc of radius ri spans the seating angle, symmetric about the line from the roller centre to the sprocket centre. From each end of the seat arc a convex flank arc of radius re continues tangentially; its centre lies on the line from the roller centre through that seat-arc end, re beyond the end. The flanks are cut off by the tip circle da. Root diameter = d - 2ri. No tooth side chamfer. Sprocket A: 21 teeth, d = 63.908, ri = 3.30, seating angle 124°, re = 24, da = 68, root Ø57.308. Hub Ø32 from Z=5.3 to Z=25. Ø15 bore through Z=0..25 with a 5 wide keyway on the 90° side, floor 9.8 from the axis. A radial Ø5 set-screw hole at Z=15 runs from the hub surface into the bore on the 270° side. Phase: a TOOTH of A is centred on the 36.870° direction (pointing at B), so A's roller seats sit at 36.870° ± 8.571°. Sprocket B (plate type, no hub): 45 teeth, d = 136.546, ri = 3.30, seating angle 126°, re = 60, da = 141, root Ø129.946. Centre hole Ø60 through the plate; six Ø6.6 bolt holes through the plate on a Ø76 circle about B's axis at 0° + k·60°. Phase: a roller seat of B is centred on the 216.870° direction from B's axis (pointing at A).”
“Model a torsion spring as ONE solid (wire and legs in one piece). Frame: coil axis parallel to Z through (X=8, Y=-6); angles about it are measured in the XY plane from +X toward +Y. Wire: round, Ø3, swept along the path below (section perpendicular to the path). Coil: helix of radius 12 (wire centre), pitch 4, LEFT-hand, 4.75 turns, from Z=0 to Z=19. It starts at Z=0 on the 0° side, at (20, -6, 0). Left-hand: the angle DEcreases as Z increases (clockwise seen from +Z), angle = -90°·Z, so at Z=1 the wire centre is on the 270° side (8, -18, 1) and at Z=19 it ends on the 90° side at (8, 6, 19). Leg 1: straight, in the plane Z=0, tangent to the coil at its start: from (20, 34, 0) to the start point (20, -6, 0), i.e. it runs along -Y into the coil. Leg 2: straight, in the plane Z=19, tangent to the coil at its end: from the end point (8, 6, 19) along +X to (48, 6, 19). At both joints the wire is continuous (fill the joint with a Ø3 sphere); leg ends are flat.”
“Model a rocker-arm valve train as seven separate solids: pedestal, rocker shaft, rocker arm, valve, spring retainer, valve spring, pushrod. Frame: the rocker shaft axis is parallel to Y through X=0, Z=60; Z is up. Pedestal (one solid): base plate X=-60..60, Y=-30..30, Z=-8..0; two cheeks X=-12..12, Z=0..70, at Y=15..25 and Y=-25..-15, each with a Ø16 hole on the shaft axis. The base plate has a Ø8 hole for the valve stem and a Ø10 clearance hole for the pushrod (axes below), both through along Z. Rocker shaft: Ø16 along Y from Y=-30 to Y=30. Rocker arm (one solid, Y=-7..7), defined in an arm frame with origin on the shaft axis, arm x along the arm and arm z across it: a hub Ø28 with a Ø16 bore on the shaft, united with a beam x=-30..40, z=-6..6. The arm is rotated about the shaft axis by 8° so that its +X end goes DOWN: arm x = (cos8°, 0, -sin8°), arm z = (sin8°, 0, cos8°). Valve (one solid): vertical stem Ø8 whose axis is X=34.258, Y=0, from Z=-40 up to Z=45.087, capped by a hemisphere R4 centred at (34.258, 0, 45.087); this tip touches the arm's lower face (arm z=-6) at arm x=36. Head: disc Ø28 from Z=-44 to Z=-40. Spring retainer: disc Ø24, bore Ø8, Z=20..24 on the valve axis. Valve spring: round wire Ø2.5 swept along a helix around the valve axis, coil radius 9, right-hand, 4 turns from Z=1.25 to Z=18.75 (pitch 4.375), starting on the +X side of the valve axis; it rests on the base plate (Z=0) and touches the retainer (Z=20). Pushrod (one solid): vertical rod Ø6 with axis X=-25.158, Y=0, from Z=-40 up to Z=53.437, with a ball Ø8 centred at (-25.158, 0, 53.437); the ball touches the arm's lower face at arm x=-24.”
“Model a cycloidal-reducer disc as ONE solid. Frame: disc axis parallel to Z through (X=5, Y=-8); disc coordinates (x, y) are measured from that point with x parallel to world X and y parallel to world Y. Thickness Z=0..12. Outline: the curve for t = 0..2·pi (the standard cycloidal-disc profile for N = 12 ring pins on a pin circle of radius R = 40, pin radius Rr = 3, eccentricity E = 1.5, giving N-1 = 11 lobes): x(t) = R·cos t - Rr·cos(t + psi) - E·cos(N·t) y(t) = -R·sin t + Rr·sin(t + psi) + E·sin(N·t) psi(t) = atan2( sin((1-N)·t), R/(E·N) - cos((1-N)·t) ). At t = 0 this gives the point (35.5, 0): a valley (minimum radius 35.5) on +x; the lobe tips (radius 38.5) are halfway between valleys, the first at 16.364° (360°/22) from +x. Holes through Z=0..12: a Ø22 centre bore on the disc axis, and six Ø12 output-pin holes on a Ø48 circle at 30° + k·60° (angles from +x toward +y).”
“Model a perforated conical shell as ONE solid. Frame: cone axis parallel to Z through (X=12, Y=12); azimuth phi is measured about that axis in the XY plane from +X toward +Y. Shell: the outer surface is the cone r_o(z) = 70 - (2/3)·z for z = 0..60 (radius 70 at Z=0, 30 at Z=60). The wall is 4 thick measured normal to that surface, so the inner surface is r_i(z) = 65.193 - (2/3)·z. The shell is cut by the planes Z=0 and Z=60. Bottom ring: annulus inner Ø124, outer Ø164, Z=-6..0. Top ring: annulus inner Ø48, outer Ø72, Z=60..66. Both are merged with the shell. Holes: Ø6, each drilled through the wall along the outward surface normal of the outer cone at a point P on the outer surface, i.e. along the direction (cos phi, sin phi, 2/3)/1.20185 (tilted up 33.69° from horizontal): - Row 1: P at z=15 (r_o=60), 16 holes at phi = 0° + k·22.5°. - Row 2: P at z=30 (r_o=50), 12 holes at phi = 15° + k·30°. - Row 3: P at z=45 (r_o=40), 8 holes at phi = 22.5° + k·45°.”
“Make a housing and shaft fitted with a deep groove ball bearing in the assembled state as 12 separate solids (housing, outer ring, inner ring, 8 balls, shaft). Coordinate system: the common axis is parallel to the X axis and passes through (Y=-15, Z=35). Angles are measured around the axis in the YZ plane from +Y toward +Z. The radii below are measured from this axis. (1) Housing (one solid): square flange X=0~10, ±40 each in Y and Z relative to the axis (80×80, sides parallel to the Y and Z axes), 4 Ø9 bolt holes through in the X direction at (Y, Z) = (±30, ±30) relative to the axis. Boss Ø64 at X=10~26. Bore: Ø38 at X=0~5 (shoulder supporting the outer ring), Ø47 at X=5~26 (bearing seat). (2) Outer ring: outer diameter Ø47, inner diameter Ø40, X=5~19 (width 14), the X=5 face contacts the housing shoulder. (3) Inner ring: inner diameter Ø20, outer diameter Ø27, X=5~19. Raceway grooves: grooves of circular section with radius 4.1 on the inside of the outer ring and the outside of the inner ring. The centers of the groove section circles lie on a circle of radius 16.75 in the X=12 plane (i.e. both rings are cut by a torus running around the radius 16.75 pitch circle). (4) 8 balls: each a Ø8 sphere, centers at X=12 on the pitch circle of radius 16.75, in the directions 20° + k·45° (k=0..7). That is, one ball center lies in the 20° direction. The balls have 0.1 clearance to both raceway grooves. (5) Shaft (one solid): Ø20 at X=-30~19 (fits against the inner ring bore, and passes through the housing shoulder hole Ø38 without touching it), collar Ø26 at X=19~28 (a shaft shoulder whose X=19 face contacts the inner ring's X=19 face), Ø22 at X=28~70. In the Ø22 section, a keyway of width 6 on the 0° side (+Y side) at X=40~62 (square ends), with the keyway bottom 8.5 from the axis.”
“Model a plate cam as ONE solid. Frame: cam axis parallel to Z through (X=10, Y=5); the polar angle phi is measured about that axis in the XY plane from +X toward +Y, in the cam's own (fixed) frame as modelled. Pitch curve (path of the centre of an in-line roller follower of radius 8): r(phi) = 38 + s(phi), with s in mm and phi in degrees: - 0 <= phi < 120: cycloidal rise, s = 14·(phi/120 - sin(2·pi·phi/120)/(2·pi)). - 120 <= phi < 180: dwell, s = 14. - 180 <= phi < 300: simple-harmonic return, s = 7·(1 + cos(pi·(phi-180)/120)). - 300 <= phi < 360: dwell, s = 0. Cam profile: the inner envelope of the roller circle (radius 8) moving along the pitch curve, i.e. the pitch curve offset inward by 8 along its normal (base circle radius 30, maximum radius 44). The profile is extruded from Z=0 to Z=15. Hub: Ø34 from Z=15 to Z=25 on the cam axis. Bore Ø16 through Z=0..25 with a 5 wide keyway on the 270° side (phi = 270°), full length, floor 10.3 from the axis.”
“Make a universal joint (cardan) in the assembled state as 3 separate solids (yoke A, yoke B, cross). Coordinate system: joint center (cross center) C = (10, -5, 60). (1) Cross (one solid): a 16×16×16 cube centered at C (edges parallel to the X, Y and Z axes), with 4 trunnions extending from it: a Ø10 cylinder in the X direction from C at X=-22~+22 (relative to C), and a Ø10 cylinder in the Y direction from C at Y=-22~+22 (relative to C). (2) Yoke A (input, shaft below C in the -Z direction): its 2 ears are plates of thickness 6 that hold the X-direction trunnions. The ears are at X=13~19 and X=-19~-13 relative to C, Y=-10~10, with an outline formed by a rectangle from Z=-26 at the bottom up to the height of C, combined with an R10 semicircle around the X axis (trunnion axis). Each ear has a Ø10.2 hole on the trunnion axis. The two ears are joined by a bottom block X=-19~19, Y=-10~10, Z=-34~-26 (all relative to C), and below the block is a Ø20 shaft at Z=-64~-34 (relative to C; the shaft is on the vertical line through C). (3) Yoke B (output): same dimensions as yoke A, but it holds the Y-direction trunnions (ears at Y=13~19 and Y=-19~-13 relative to C), and its shaft direction is w = (sin25°, 0, cos25°) = (0.42262, 0, 0.90631), i.e. bent 25° toward +X going upward from C (rotated 25° around the cross's Y trunnion). In yoke B's own coordinates: the ears span -10~26 in direction w (R10 semicircle around the trunnion axis + rectangle), with width ±10 in direction e = (cos25°, 0, -sin25°); the bottom block spans 26~34 in direction w, ±10 in direction e and ±19 in the Y direction; the Ø20 shaft spans 34~64 in direction w. Radial clearance 0.1 between all holes and trunnions. The parts do not interpenetrate each other.”
“Model a six-slot Geneva drive, assembled, as 2 separate solids: the driver (crank + drive pin) and the Geneva wheel. Frame: both axes parallel to Z; driver axis through (-20, 15), wheel axis through (40, 15) (centre distance 60). Angles in the XY plane from +X toward +Y about each part's own axis. Geneva wheel: plate Ø104, Z=0..8, with six radial slots 8.2 wide, one every 60°. Each slot runs along its centre line from the rim inward and ends in a semicircle whose centre is 28 from the wheel axis. Hub Ø30 on top, Z=8..18; Ø12 bore through Z=0..18. Driver: crank arm 14 wide, Z=-7..-1 (1 below the wheel), from the driver axis to the pin centre, 30 long between centres, both ends rounded R7. Hub Ø24 under the arm, Z=-20..-7, Ø10 bore through Z=-20..-1. Drive pin Ø8 on the arm end, from Z=-1 up to Z=8, one solid with the arm. Position: the crank points at 20° (measured from the line of centres, which points at 0°), so the pin centre is at (8.191, 25.261). The wheel is turned so that one slot's centre line passes through the pin centre: that slot points at 162.122° from the wheel axis (the pin centre is 33.423 from the wheel axis), and the other slots are at 162.122° + k·60°. The pin sits in the slot with 0.1 clearance each side.”
“Make one 3-lobe Roots blower rotor as a single solid. Coordinate system: the rotor axis is parallel to the Z axis and passes through (X=-20, Y=15). Section coordinates (x, y) are measured from this axis (x ∥ +X, y ∥ +Y), and angles are measured from +x toward +y. Z=0 section profile: 6 arcs generated by a circle of radius a=5 rolling on the pitch circle of radius R=30 (each covering a 60° segment of the pitch circle): - Lobe arc = epicycloid: x = (R+a)·cosθ - a·cos((R+a)·θ/a), y = (R+a)·sinθ - a·sin((R+a)·θ/a), θ = 0~60°. 3 copies of this arc rotated by 0°, 120°, 240° (lobe tip radius 40 in the directions 30°, 150°, 270°). - Root arc = hypocycloid: x = (R-a)·cosθ + a·cos((R-a)·θ/a), y = (R-a)·sinθ - a·sin((R-a)·θ/a), θ = 0~60°. 3 copies of this arc rotated by 60°, 180°, 300° (root bottom radius 20 in the directions 90°, 210°, 330°). Rotor body: this profile swept helically from Z=0 to Z=90. As Z increases, the section rotates counterclockwise as seen from +Z, and at Z=90 it has rotated 60° (rotation angle = 60°·Z/90, uniform). Shaft: Ø20 journals at Z=-40~0 and Z=90~130 (one body with the rotor). At Z=115, a Ø6 cross hole runs through the journal in the X direction.”
“Make a ball joint in the assembled state as 5 separate solids (housing, cap, ball stud, lever plate, nut). Coordinate system: ball center C = (15, -10, 30). The housing axis is the vertical line through C (parallel to the Z axis). Stud axis direction s = (sin20°, 0, cos20°) = (0.34202, 0, 0.93969), i.e. tilted 20° from vertical toward +X. t = (cos20°, 0, -sin20°) is the direction in the XZ plane perpendicular to s. (1) Housing (one solid): Ø50 cylinder on the C axis, Z=5~35, with a Ø16 shank below at Z=-30~5. Inside: a spherical socket of radius 12.5 centered at C (the hemisphere below C) and a Ø25 cylindrical bore at Z=30~35. (2) Cap (one solid): Ø50 disc on the C axis, Z=35~43. The inside is cut by a sphere of radius 12.5 centered at C, with a Ø30 through hole at the center. (3) Ball stud (one solid): ball Ø25 (center C), neck Ø14 at distance 0~30 from C in direction s, shank Ø12 at distance 30~60 (all on the s axis). (4) Lever plate: a plate perpendicular to s, at distance 30~40 in direction s (seated on the shoulder face of the neck). Within the plate, -15~45 in direction t and ±15 in the Y direction. A Ø12 hole for the shank on the s axis. (5) Nut: Ø22 cylinder on the s axis, bore Ø12, distance 40~48 in direction s (resting on the lever plate). The ball contacts the spherical surfaces of the socket and the cap, and no parts interpenetrate each other.”
“Make a spring latch (slide latch) with the bolt engaged in the keeper, as 4 separate solids (housing, bolt, compression spring, keeper). Coordinate system: the bolt axis is parallel to the X axis and passes through (Y=12, Z=10). Angles around the axis are measured in the YZ plane from +Y toward +Z. (1) Housing (one solid): block X=0~60, Y=0~24, Z=0~20. Bottom mounting plate Z=0~3 over X=0~60, Y=-10~34, with 4 Ø4.5 holes in the Z direction at (X, Y) = (10, -5), (50, -5), (10, 29), (50, 29). A Ø12.2 bore on the bolt axis at X=4~60 (open at the X=60 end; X=0~4 is a closed end wall). Top slot: width 4.2 (Y=9.9~14.1), X=18~44 (square ends), through from the bore to the top face Z=20. (2) Bolt (one solid): Ø12 cylinder on the bolt axis at X=20~70. A Ø4 handle pin at X=24 from the bolt axis toward +Z up to Z=26 (passing through the slot), with a Ø8 knob above it at Z=26~32. (3) Compression spring: wire diameter Ø1.6 (circular section), mean coil diameter Ø9 (wire center at radius 4.5 from the axis), right-hand wound, 4 turns. The helix of the wire center runs from X=4.8 to X=19.2 (pitch 3.6); the ends are left as cut, not ground, and the wire touches the end wall at X=4 and the back face of the bolt at X=20. Start point: at X=4.8 the wire center is on the +Z side of the axis (Y=12, Z=14.5). Because it is right-hand wound, the wire center angle increases in the direction from +Y toward +Z as X increases (180° at X=5.7, i.e. (Y=7.5, Z=10)). (4) Keeper (one solid): block X=64~78, Y=0~24, Z=0~20, bottom plate Z=0~3 over X=64~78, Y=-10~34, with 2 Ø4.5 holes in the Z direction at (71, -5), (71, 29). A Ø12.4 blind hole on the bolt axis at X=64~74. The bolt end (X=70) is inserted by 6.”
“Model an in-line slider-crank mechanism, assembled at one crank angle, as 4 separate solids: crank, connecting rod, slider and guide. Frame: the crank axis is parallel to Y through X=10, Z=5. The slider moves along the line parallel to X through Z=5 (in line with the crank axis). Angles are measured in the XZ plane from +X toward +Z. Crank (one solid): hub Ø30 on the crank axis from Y=-16 to Y=0; arm Y=0..8, a straight 24 wide bar from the crank axis to the crank-pin centre 25 away, both ends rounded R12 about those two centres; crank pin Ø10 from Y=8 to Y=15. Ø12 bore on the crank axis through Y=-16..8 with a 4 wide keyway pointing away from the crank pin (230°), floor 7.8 from the axis. Position: the crank points at 50°, so the crank-pin centre is at X=26.070, Z=24.151. Connecting rod: Y=8.2..14.2, 80 between centres. Big eye Ø24 with a Ø10.2 hole on the crank pin; small eye Ø18 with a Ø8.2 hole on the wrist pin; the eyes are joined by a straight shank 10 wide centred on the line between the centres. Slider (one solid, wrist pin included): the wrist-pin centre is on the slide line at X=103.744 (so the rod length is exactly 80). Block X=87.744..119.744 (wrist pin -16..+16), Z=-6..16, Y=2..20. A slot for the rod, Y=7.7..14.7, runs through the full block height and from the block's -X face to X=114.744 (wrist pin +11), leaving a 5 thick bridge at the +X end. Wrist pin Ø8 along Y from Y=2 to Y=20 on the wrist-pin centre, bridging the slot. Guide (one solid): base plate X=60..150, Y=-6..28, Z=-16..-6 (the slider rests on its top face Z=-6), and two side walls X=60..150, Z=-6..8, at Y=-6..2 and Y=20..28, touching the slider's Y=2 and Y=20 faces.”
“Model a scissor link, assembled, as 3 separate solids: bar A, bar B and the pivot pin. Frame: the pivot axis is parallel to Z through X=15, Y=20. Angles in the XY plane from +X toward +Y. Distances along a bar are measured from the pivot axis along that bar's direction. Both bars have the same stadium outline in plan: 16 wide, straight sides, semicircular ends of radius 8 centred at -60 and +60 along the bar (overall length 136), with a Ø8.2 pivot hole on the pivot axis. Bar A: 5 thick, Z=0..5, its direction points at 35°. It has a Ø6.2 hole at -60 and, at the + end, a slot 6.2 wide along the bar with semicircular ends whose centres are at +48 and +60. Bar B: 5 thick, Z=5.2..10.2 (0.2 above bar A), its direction points at 145°, so the bars cross at 110°. It has Ø6.2 holes at -60 and +60. Pivot pin: Ø8 shank on the pivot axis from Z=-4 to Z=10.2, head Ø14 from Z=10.2 to Z=12.2 seated on bar B's top face, and a Ø2.5 split-pin hole through the shank along the X direction at Z=-1.5.”
“Make an assembly of 2 telescoping round tubes fixed with a cross pin as 3 separate solids (outer tube, inner tube, pin). Coordinate system: the common axis of the two tubes is parallel to the Z axis and passes through (X=12, Y=-8). Angles are measured in the XY plane from +X toward +Y. The pin axis is perpendicular to the tube axis at height Z=130, with direction d = (cos30°, sin30°, 0) = (0.86603, 0.5, 0). Below, s is the distance from the tube axis measured in direction d. (1) Outer tube (one solid): outer diameter Ø40, inner diameter Ø34, Z=0~150. Square base plate at the bottom end, Z=-8~0, 70×70 (±35 each in X and Y relative to the tube axis, sides parallel to the X and Y axes); the base plate is closed, with 4 Ø7 holes through in the Z direction at (±25, ±25) relative to the tube axis. A Ø8.4 pin hole through both walls in direction d at Z=130. (2) Inner tube (one solid): outer diameter Ø33.8 (radial clearance 0.1 to the outer tube), inner diameter Ø27.8, Z=60~260. The top end is closed by a cap of thickness 8 (Z=252~260, with a Ø10 hole through the center; the hollow part is Z=60~252). 6 pairs of Ø8.4 pin holes through both walls in direction d, at heights 20 + k·25 (k=0..5) from the bottom end, i.e. Z=80, 105, 130, 155, 180, 205. The third hole from the bottom (k=2, Z=130) is aligned with the pin hole of the outer tube. (3) Pin (one solid): Ø8 shank on the pin axis at s=-24~27, head Ø14 at s=-28~-24 (the head is on the negative side of d, and the inner face of the head is clear of the outer tube surface). A Ø2.5 hole for a clip through the shank in the Z direction at s=24 at the tip end.”
“Model a control knob on a D-shaft potentiometer mounted in a panel, assembled, as 4 separate solids: panel, potentiometer (body, bushing and shaft as one solid), knob, set screw. Frame: the shaft axis is parallel to Y through X=-30, Z=40; the knob is on the -Y side of the panel. Angles are measured about the shaft axis in the XZ plane from +X toward +Z; radii are from the shaft axis. Panel: plate Y=0..3, X=-70..10, Z=0..80, with a Ø10 hole on the shaft axis. Potentiometer (one solid): body Ø24 from Y=3 to Y=15 (against the panel's back face), bushing Ø10 from Y=0 to Y=3 filling the panel hole, shaft Ø6 from Y=0 to Y=-20. D-flat: from Y=-10 to the shaft tip Y=-20 the shaft is cut by a plane 1.5 from the axis whose outward normal points at 225°. Knob (one solid): cylinder Ø30 from Y=-6 to Y=-24 (6 clear of the panel). Twelve grip flutes: semicircular grooves R2 along Y over the full knob length, their centres on radius 15 at 0° + k·30°. Pointer: a raised rib on the front face, 3 wide, Y=-26..-24, running radially from radius 5 to radius 15 along the 45° direction (diametrically opposite the flat). Blind bore Ø6.1 on the axis from Y=-6 to Y=-21. A Ø3 radial set-screw hole at Y=-14 runs from the bore to the knob surface along the 225° direction. Set screw: a plain Ø3 cylinder in that hole, on the 225° line at Y=-14, from radius 1.5 (its flat end bearing on the shaft's D-flat) out to radius 12 (3 below the knob surface).”
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