Gear Reduction Torque
Output torque after gear reduction, allowing for efficiency.
Formula
Variables
Example
τ_in=0.5 N·m, GR=50, η=0.9: τ_out = 22.5 N·m
How it works
A gear reduction trades speed for torque: when the gears slow the rotation down, the output shaft can deliver more turning force. In an ideal gearbox, torque increases in proportion to the gear ratio, but real gears lose some power to friction, heat, and vibration, so efficiency reduces the result. This formula captures both effects by multiplying the input torque by the gear ratio and then by the efficiency factor.
When to use it
Use this when estimating the torque available after a gearbox in robots, machines, actuators, or drivetrain systems. It is especially useful when you know the motor torque and gear ratio and want to check whether the output can move a load.
Worked example, step by step
Given: τ_in = 1.2 N·m, GR = 12, η = 0.85 Step 1: Multiply input torque by gear ratio τ_in × GR = 1.2 × 12 = 14.4 N·m Step 2: Account for efficiency τ_out = 14.4 × 0.85 Step 3: Calculate final output torque τ_out = 12.24 N·m
Common mistakes to avoid
- Using the gear ratio backward and dividing torque instead of multiplying
- Forgetting to include efficiency, which makes the torque estimate too high
- Mixing up torque units or comparing torque values from different shafts without checking the gear direction
Did You Know?
Gear reduction trades speed for torque — how a small motor lifts a heavy robotic limb.
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