#mechanism

Slider-crank (piston-crank) mechanism kinematics as an API, computed locally and deterministically. The position endpoint takes the crank radius, the connecting-rod length and the crank angle from top dead centre and returns the exact piston displacement from TDC, x = r(1−cosθ) + l(1 − √(1−λ²sin²θ)) with λ = r/l, the piston-pin distance from the crank axis, the connecting-rod swing angle φ = asin(λ·sinθ), the stroke (2r), the rod ratio n = l/r and the fraction of stroke travelled. The velocity endpoint adds the crank speed (as rpm or angular velocity) and returns the exact piston velocity, v = ω·[r·sinθ + r·λ·sinθcosθ/√(1−λ²sin²θ)], and the piston acceleration from the standard two-term approximation a ≈ r·ω²·(cosθ + λ·cos2θ) — the inertia term engine designers use for balancing. The geometry endpoint summarises the whole mechanism: the stroke, the rod ratio, the top- and bottom-dead-centre positions, the maximum connecting-rod angle asin(λ), and — with a speed — the mean piston speed 2·stroke·(rev/s). Everything is computed locally and deterministically, so it is instant and private. Ideal for engine, compressor and pump-mechanism design tools, robotics and linkage simulation, CNC and animation, and mechanical-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is slider-crank linkage kinematics; for rotational energy use a flywheel API and for shaft torsion use a torsion API.

api.oanor.com/crankslider-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.

api.oanor.com/screwjack-api