Feature generators

Feature generators

Feature generators turn a few engineering numbers into exact profiles or meshes: an involute gear from module and tooth count, an ISO thread from diameter and pitch, a helix from radius and pitch, a bent strip from a centre line and a thickness. Each is a pure function in packages/core/src/cad; the editor, the assistant and the CAM model call the same function, so all three see the same part.

Involute gears

Pitch radius m·z/2, tip radius pitch + m, root radius pitch − 1.25·m, flanks the involute of the base circle r_p·cos α (ISO 53 / DIN 867). The outline is one counter-clockwise ring about the origin with tooth 0 centred on +X. When the teeth would come to a point before the tip circle (few teeth, a large pressure angle), the tip is pulled in by bisection to where the tooth is still 2 % of a pitch wide.

gearOutline({ moduleValue: 2, teeth: 5 })
// RangeError: A gear needs a module > 0 and at least 6 whole teeth
gearOutline({ moduleValue: 2, teeth: 18, pressureAngle: 50 })
// RangeError: The pressure angle must be between 0 and 45 degrees

ISO metric threads

A modelled thread is real helical geometry: a core cylinder at the root united with a ridge swept along a helix with the profile kept radial, clipped to the thread length. External threads have their core at d₃ = d − 1.22687·P and a ridge up to d; internal ones are the tool that cuts a tapped hole, core at D₁ = D − 1.08253·P (the tap drill) and a groove out to D. The flank is cut square to the helix and the axial widths are corrected by the cosine of the helix angle so pitch and crest widths are exact.

Values are threadSizes(d, P, internal) output. Heights are 0.61343·P (external) and 0.54127·P (internal); the crest is P/8.

threadProblem({ diameter: 6, pitch: 4, length: 10, internal: false })
// "A pitch of 4 mm is too coarse for a 6 mm thread"       (pitch > d/2)
threadProblem({ diameter: 6, pitch: 0.1, length: 10, internal: false })
// "A thread has at most 58 turns (this one is 100.0 long: 10 mm at a pitch of 0.1 mm)"
threadProblem({ diameter: 6, pitch: 1, length: 10, internal: false })   // undefined: buildable

The 58-turn limit is COIL_MAX_TURNS − 2: the ridge starts one pitch before the thread and ends one after, so the flat end cuts meet the full profile.

Helices

Sheet metal

A sheet-metal profile is a centre line thickened to a strip of constant thickness, with the material on the left, right or both sides, and inside bend radius r on every corner. developedLength unbends it with a K-factor (default 0.44): each bend contributes (r + K·t)·θ and each straight run loses the setback of its neighbouring bends.

{"straight":70,
 "bends":[{"angle":1.5707963267948966,"allowance":6.094689747964199},
          {"angle":1.5707963267948966,"allowance":6.094689747964199}],
 "length":82.18937949592839}

Check: (3 + 0.44 × 2) × π/2 = 6.0947 per bend, and 70 + 2 × 6.0947 = 82.189 mm.

Troubleshooting