Type the numbers, watch the blueprint move.

Feed D₁, D₂, L and R; get tangency point T₁ (flank side) and T₂ (face side), with the direction chosen by standard G18 coordinates.

Tap drill ⌀ = D − P, external minor diameter and radial thread depth, laid out as a two-block G76 with radial μm values.

Ellipse interpolation in FANUC Macro B, with the upper bound of the chord error so you can pick a step that suits the tolerance.

Large end D, small end d, taper length L and Z end: half angle for the compound rest, taper C and a G90 cycle with a 2 mm approach allowance.

Solve a right triangle from any two known values, with a quick reference of the angles you keep using.

Convert between across-flats and the circumscribed circle for square, hex and octagon — turn the round first, then index to form.

Bar, tube and plate: volume × density, with the formula and density shown in the result. Add a unit price for a cost check.

Best wire size d₀ = P/√3, theoretical pitch diameter d₂ = D − 0.6495P, measurement over wires M and Δd₂ = ΔM.

Pick material and tool (brazed YT15 / coated insert / HSS W18) to get v, then n = 1000v/πD rounded and capped by your machine speed limit.

R = ⌀S/2 and h = R − √(R² − (d/2)²), followed by three turning plans for single-slide, two-slide or batch work.

The GB/T 1800 table: tap a size segment for the recommended gauge, then jump to GB/T 3177 acceptance limits with safety margin A = T/10.