#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

杠杆、力矩平衡和简单机械的机械优势计算作为API，本地确定性地计算。杠杆端点应用杠杆定律，力·力臂 = 负载·负载臂，并求解你省略的力、负载、力臂或负载臂中的任意一个，返回机械优势MA = 力臂/负载臂 = 负载/力，以及杠杆是增力还是增速。力矩端点计算单个力矩，M = F·d，或平衡一个绕支点的跷跷板：根据每侧的力和距离，告诉你是否平衡、净力矩和旋转方向，或者求解你省略的一个值以达到平衡。机械端点给出简单机械的理想机械优势——斜面（长度/高度）、螺丝（2πR/螺距）、轮轴（R/r）、楔子（长度/厚度）或滑轮系统（支撑绳数）——并在给定效率和力的情况下，给出实际机械优势和输出力。所有计算都在本地确定性地进行，因此即时且私密。非常适合物理和工程教育工具、力学和静力学应用、机械设计和DIY计算器。纯本地计算——无需密钥，无需第三方服务，即时。实时，不存储任何内容。3个端点。这是杠杆和简单机械的机械优势；对于齿轮和皮带传动比，请使用齿轮或皮带传动API。

api.oanor.com/lever-api