# Simple Machines Simulator - Levers, Pulley Systems, Gear Ratios, Screw & Wedge

> Drag a lever’s fulcrum, lift loads with pulleys, mesh gear trains and bike gears, and compare inclines, screw jacks and wedges: force and efficiency.

- URL: https://qilingtools.com/en/math/simple-machines
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Hands-on animations of the simple machines and the rule they all share: what you save in force you pay in distance. In Lever you drag the triangular fulcrum, the coloured loads and the effort arrow; the tool solves for the balancing effort and identifies class 1, 2 or 3, or you set the effort yourself, let go and watch the beam tip — with seesaw, crowbar, wheelbarrow, nutcracker and forearm presets. Pulleys covers a fixed pulley, a movable pulley, an n-strand block and tackle and cascaded movable pulleys; pull the rope and the load rises in proportion, with per-sheave efficiency, the weight of the moving blocks and the tension in every strand. Gears chains up to five gears, including compound gears on a shared shaft, with teeth that mesh at the right phase; drag the first gear to turn the train by hand. A bicycle mode turns chainring, cog, wheel size and cadence into speed and a full gear chart. Incline / screw / wedge gives the force needed, ideal and actual mechanical advantage, efficiency and self-locking.

## How to use

1. Pick a machine: lever, pulleys, gears or incline / screw / wedge
2. Drag the fulcrum, loads or gears, or set masses, teeth, angles and friction with sliders and presets
3. Press play: let the lever tip, pull the rope, spin the gears or push the block up the slope
4. Read the force needed, mechanical advantage, gear ratio, efficiency and self-locking, with the formulas

## Features

- Draggable lever with automatic class detection, balancing effort, torque bars and tipping animation
- Fixed, movable, block-and-tackle and cascaded pulleys with sheave efficiency, block weight and strand tensions
- Gear train of up to 5 gears: compound shafts, correctly meshing teeth, direction and torque
- Bicycle gearing: ratio, gear inches, development and a full speed chart
- Incline force and efficiency, screw-jack torque and handle force, wedge splitting force
- Ideal and actual mechanical advantage and a self-locking check for every machine

## FAQ

### How do you tell the three classes of lever apart?

Look at what sits in the middle. With the fulcrum in the middle it’s class 1 — seesaw, crowbar, scissors — and whether it saves force depends on the two arms. With the load in the middle it’s class 2 — wheelbarrow, nutcracker, bottle opener — and since the effort arm is always longer it always saves force. With the effort in the middle it’s class 3 — your forearm, tweezers, a fishing rod — which costs force but makes the load end move further and faster.

### Why is a block and tackle’s mechanical advantage the number of strands?

Ideally one continuous rope has the same tension F everywhere. The moving block hangs from n strands, so the upward force on it is nF and F = W/n. The price is distance: to raise the load by h every one of the n strands must shorten by h, so you pull out nh of rope, and the work F·nh equals Wh. Real sheaves have friction — the tension is multiplied by an efficiency η at each one — and the moving block must be lifted too, so the actual advantage is below n.

### How do gear ratios work, and what happens to torque?

Meshing gears share the same speed at the pitch circle, so ω₁N₁ = ω₂N₂: a small gear driving a large one slows down and turns the opposite way, while gears on one shaft share the same speed. The overall ratio of a multi-stage train is the product of driven/driving teeth for each mesh. With no losses power P = τω is constant, so cutting the speed by some factor multiplies the torque by the same factor — that’s why a reduction gearbox “gains force”.

### Why doesn’t a screw jack lower itself when you let go?

A thread is an inclined plane wrapped around a cylinder, with a lead angle λ given by tanλ = P/(πd), usually just a few degrees. When the thread friction μ ≥ tanλ, the component of the load trying to slide back down the thread can’t overcome friction — the screw is self-locking. The price is efficiency: tanλ / tan(λ + φ) with φ = arctan μ, typically below 50% for a self-locking screw. Inclines and wedges behave the same way: with μ ≥ tanθ a block won’t slide down by itself.

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