Gears and Mechanisms Simulation

About this experiment

Mesh two external gears and compare their rotation, angular speeds and transmitted torque. Change tooth counts or use ratio presets, then track a marker on each pitch circle. The driven gear turns in the opposite direction. A larger driven gear rotates more slowly but transmits a greater torque magnitude in this ideal lossless model.

Learning goals

Relate tooth counts to angular speed and direction
Compare torque multiplication with speed reduction
Verify equal pitch-line speed and ideal power conservation
Explain how bicycles, clocks and drills use gear ratios to trade speed for force

How to use it

1Play the default 16-tooth driver and 32-tooth driven gear. Compare speed magnitudes and torque magnitudes.
2Turn the driver by one tooth and observe the corresponding tooth movement of the driven gear.
3Compare the 1:1, 1:2 and 2:1 tooth-count presets at a fixed input torque and speed.
4Set input speed to zero. Explain why transmitted power is zero even though the ideal torque ratio still has a value.
5Count how many turns of the driver it takes for the 32-tooth gear to turn exactly once in the 1:2 preset.

The model

\frac{ω _{2}}{ω _{1}} = - \frac{N _{1}}{N _{2}}

Opposite rotation directions for two external gears

\frac{∣ τ _{2} ∣}{∣ τ _{1} ∣} = \frac{N _{2}}{N _{1}}

Ideal torque magnitude ratio

P = τ_{1} ω_{1} = ∣ τ_{2} ω_{2} ∣, v = r_{1} ω_{1} = r_{2} ∣ ω_{2} ∣

Power conservation and equal pitch-line speed

d = m N, m = 2 mm

Pitch diameter from the fixed gear module and tooth count

Assumptions

The gears are ideal external spur gears with fixed parallel axes, module 2 mm and no slip.
Tooth outlines are schematic rather than exact involute profiles. Pitch-circle kinematics give the quantitative rotation ratios.
Friction, backlash, shaft deformation, rotational inertia and motor-load dynamics are omitted. The source supplies the selected input speed and torque.
Output torque is reported as a magnitude. The negative output speed indicates the opposite rotation direction. Feedback tones are UI cues, not a recording of gear noise.

Try this in class

Q1If the driven tooth count doubles while driver count stays fixed, what happens to output speed and torque?
Q2Why can the tangential speeds match even when the angular speeds differ?
Q3Why does speed reduction not create extra power?
Q4On a bicycle, why do you change to a gear with a large rear sprocket to climb a hill?
Q5How could you make the output turn in the same direction as the input using gears only?

Frequently asked questions

Why do external gears rotate in opposite directions?

At the contacting pitch point the two surfaces must move together without slipping. With centers on opposite sides of that point, their angular rotation directions must be opposite.

Can real gears achieve the exact torque increase shown?

Real mechanisms lose power through friction and other effects, and their behavior also depends on loads and inertia. The displayed values isolate the ideal ratio and power relationship.

What is an idler gear?

A gear placed between the driver and the driven gear. It reverses the direction a second time so input and output turn the same way, but it does not change the overall speed ratio.