Gear Train & Mechanical Advantage Designer
Build a real two-stage compound gear train, watch the gears mesh and turn, and read off the true speed and torque the math predicts.
Drag the four tooth-count sliders to build a two-stage compound gear train, then watch the gears mesh and turn at their true computed speeds.
overall ratio = (N2/N1) × (N4/N3), ωout = ωin / ratio, τout = τin × ratio × ηAbout the Gear Train & Mechanical Advantage Designer
Free gear train & mechanical advantage designer. Build a real two-stage compound gear train, watch the gears mesh and turn, and read off the true speed and torque the math predicts. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for engineering, the gear train & mechanical advantage designer runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Build a real two-stage compound gear train, watch the gears mesh and turn, and read off the true speed and torque the math predicts. Use it to explore engineering ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Gear Train & Mechanical Advantage Designer
- Use the controls to change Driver gear N1 (teeth), Idler/driven N2 (teeth), Output gear N4 (teeth), Input speed (rpm), Input torque (N·m), and more. The simulation reacts instantly.
- Press "Reset to defaults", "Lab report" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Set N1=20, N2=50, N3=20, N4=40 and confirm the overall ratio is exactly 5:1.
- Keep the input speed fixed and see how far you can drop the output speed by raising N2 and N4.
- Try the 5:1 mechanical-advantage challenge.
- Try the 60 rpm output-speed challenge at a fixed 900 rpm input.
Key ideas you can learn
- Gear ratio is inversely proportional to tooth count: a small driver gear turning a large driven gear slows the speed down and multiplies the torque.
- A compound gear train stacks two (or more) stages on shared shafts, so the overall ratio is the product of each stage's ratio.
- Torque and speed trade off through a gear train: whatever factor speed is divided by, torque is multiplied by (minus friction losses).
- Real gear meshes are not perfectly efficient; each mesh typically loses a few percent, so a two-stage train loses roughly twice as much as one stage.
Where this is used in the real world
Compound gear trains like this appear in car transmissions, bicycle drivetrains, wind-up clocks, power drills and wind-turbine gearboxes, anywhere a motor's natural speed needs to be traded for more torque or vice versa.
Who is this simulation for?
Engineering and technology students, makers, robotics clubs and teachers of design and technology. It gives a hands-on feel for how machines behave before you build a real one.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
Why does a compound gear train multiply the ratios of each stage instead of adding them?
Each stage independently divides speed (and multiplies torque) by its own ratio, and since the output of stage one becomes the input of stage two, the two scaling factors apply one after another - which is multiplication, not addition.
Why is the output torque slightly less than N times the input torque even though the gear ratio is exactly N?
Every real gear mesh has friction between the meshing teeth, so a small fraction of the input power is lost as heat at each mesh; the efficiency factors for each mesh multiply together and slightly reduce the torque the ideal ratio alone would predict.
Is the Gear Train & Mechanical Advantage Designer free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Gear Train & Mechanical Advantage Designer work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.