#mechanical-advantage

Pulley and block-and-tackle mechanics as an API, computed locally and deterministically. The advantage endpoint computes the mechanical advantage of a pulley system — the ideal MA equals the number of rope parts supporting the load, which is also the velocity ratio — and returns the effort needed to hold or raise a load, effort = load/(n·efficiency), the length of rope that must be pulled (n times the lift height) and the work in and out. The friction endpoint models a real block and tackle where every sheave loses a little tension: the mechanical advantage becomes MA = e·(1−eⁿ)/(1−e) for a per-sheave efficiency e (≈0.96 for a plain bearing, ≈0.98 for a ball bearing), so it returns the true MA, the overall efficiency and the extra effort friction costs you. The solve endpoint takes any two of the load, the effort and the number of rope parts and returns the third — for example, how many parts you need so a given person can raise a given load, or the heaviest load a winch can lift. Everything is computed locally and deterministically, so it is instant and private. Ideal for rigging, lifting and hoist-design tools, sailing, climbing and theatre-rigging apps, crane and winch sizing, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is pulley and block-and-tackle mechanics; for lever and moment balance use a lever API and for rope-around-a-drum capstan friction use a capstan API.

api.oanor.com/pulley-api

Lever, moment-balance and simple-machine mechanical-advantage maths as an API, computed locally and deterministically. The lever endpoint applies the lever law, effort·effort_arm = load·load_arm, and solves for whichever of the effort, the load, the effort arm or the load arm you leave out, returning the mechanical advantage MA = effort_arm/load_arm = load/effort and whether the lever multiplies force or speed. The moment endpoint computes a single moment of force, M = F·d, or balances a seesaw about a pivot: from the force and distance on each side it tells you whether it is balanced, the net moment and which way it rotates, or solves the one value you omit to bring it into equilibrium. The machine endpoint gives the ideal mechanical advantage of a simple machine — an inclined plane (length/height), a screw (2πR/pitch), a wheel and axle (R/r), a wedge (length/thickness) or a pulley system (number of supporting strands) — and, given an efficiency and an effort, the actual mechanical advantage and the output force. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics and engineering-education tools, mechanics and statics apps, and machine-design and DIY calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is levers and simple-machine mechanical advantage; for gear and belt drive ratios use a gear or belt-drive API.

api.oanor.com/lever-api