Screw Jack API

Power-screw (lead-screw and screw-jack) mechanics as an API, computed locally and deterministically. The torque endpoint computes the torque to raise and to lower a load on a power screw from the load, the mean thread diameter, the lead (given directly or as pitch × starts) and the coefficient of friction: T_raise = (W·dm/2)·(L + π·μ′·dm)/(π·dm − μ′·L), with the matching lower torque, the lead angle, the efficiency (W·L ÷ 2π·T_raise) and whether the screw is self-locking (it is when the effective friction is at least the tangent of the lead angle). Square threads are the default; pass a thread angle (for example 29° for an ACME thread) and it applies the effective friction μ/cos(half-angle). The effort endpoint turns that torque into the hand force on a lever or handle and the resulting mechanical advantage. The travel endpoint relates turns, lift distance and — with an rpm — the linear speed and time. Lengths are in millimetres, load in newtons and torque in newton-metres. Everything is computed locally and deterministically, so it is instant and private. Thread friction only — add collar/thrust friction separately. Ideal for machine-design and mechanism tools, jack, press, vice and clamp design, maker and robotics projects, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is power-screw mechanics; for the geometry of a screw thread use a thread API and for bolt tightening torque use a torque API.