#machine-design

Helical compression-spring maths as an API, computed locally and deterministically. The rate endpoint computes the spring rate from the wire diameter, the mean coil diameter and the number of active coils using k = G·d⁴/(8·D³·n), where the shear modulus G is taken from the material (music wire and spring steel, stainless, phosphor bronze, beryllium copper, titanium and more) or supplied directly — and it reports the rate in newtons per millimetre, newtons per metre and pounds per inch, along with the spring index C = D/d. The force endpoint relates force and deflection through F = k·x in both directions, taking the rate directly or deriving it from the geometry. The stress endpoint computes the shear stress in the wire, τ = 8·F·D·Kw/(π·d³), applying the Wahl correction factor Kw = (4C−1)/(4C−4) + 0.615/C for curvature and direct shear, and also reports the uncorrected stress. Lengths are in millimetres, force in newtons and stress in megapascals. Everything is computed locally and deterministically, so it is instant and private. A design aid — keep the spring index between about 4 and 12 and confirm against the material's allowable stress. Ideal for mechanical-design and CAD tools, spring-selection and prototyping apps, maker and robotics projects, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is helical-spring design; for beam deflection use a beam API.

api.oanor.com/springcoil-api

Spur-gear geometry as an API, computed locally and deterministically for standard full-depth involute teeth. The geometry endpoint takes a module and a number of teeth (and an optional pressure angle, default 20°) and returns the complete tooth geometry: the pitch diameter (module × teeth), the base, tip (outside) and root diameters, the addendum, dedendum, whole and working depth, the circular and base pitch, the diametral pitch and the tooth thickness — all in millimetres. The module can be given directly or derived from a diametral pitch or a circular pitch. The pair endpoint meshes two gears of the same module and returns each gear's pitch and tip diameter, the centre distance (module × (z1 + z2) ÷ 2) and the gear ratio. The module endpoint converts freely between module, diametral pitch and circular pitch, or derives the module from a pitch diameter and tooth count. Everything is computed locally and deterministically, so it is instant and private. Ideal for machine-design and CAD tools, gear and gearbox calculators, maker, robotics and 3D-printing projects, and mechanical-engineering apps. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is spur-gear geometry; for bicycle gear ratios and development use a bike-gear API and for belt-and-pulley drives use a belt-drive API.

api.oanor.com/spurgear-api