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Difficulty: MediumGears and Gear Ratios

Review the following gear train configurations. Match each specific gear arrangement to its resulting mechanical outcome or primary functional advantage.

  • A small 15-tooth driving gear meshed directly with a large 60-tooth driven gear.Multiplies output torque by a factor of 4 while reducing rotational speed.
  • A large 60-tooth driving gear meshed directly with a small 15-tooth driven gear.Multiplies output speed by a factor of 4 while reducing output torque.
  • Two 30-tooth gears connected by a single intermediate idler gear.Transfers rotation in the same direction without changing the overall speed ratio.
  • A threaded worm driving a standard spur gear.Provides extreme speed reduction and creates a one-way, self-locking mechanism.

Answer

Match the small driving gear to torque multiplication, the large driving gear to speed multiplication, the idler setup to identical direction/speed, and the worm gear to extreme reduction/self-locking.
Each arrangement fundamentally alters mechanical power in a distinct way: small-to-large increases torque, large-to-small increases speed, idlers are strictly for directional matching, and worm gears provide self-locking high-reduction.

Step-by-Step Solution

1
Analyze the 15-tooth driving to 60-tooth driven gear arrangement.
It operates as a step-down gear system with a 1:4 ratio.
A smaller driving gear turning a larger driven gear inherently increases torque at the expense of rotational speed.
2
Analyze the 60-tooth driving to 15-tooth driven gear arrangement.
It operates as a step-up gear system with a 4:1 ratio.
A larger driving gear turning a smaller driven gear increases output rotational speed but reduces the available torque.
3
Analyze the two 30-tooth gears connected by an idler.
The output gear spins at the exact same speed as the input gear, and in the same rotational direction.
The intermediate idler gear reverses the rotational direction twice, ensuring input and output spin identically. The idler's size has no mathematical effect on the overall 1:1 ratio between the identical 30-tooth gears.
4
Analyze the worm and spur gear setup.
It drastically drops speed and cannot be easily back-driven.
A worm drive behaves like a continuous screw; a single full rotation of the worm may only advance the spur gear by one tooth, yielding massive reduction. Additionally, the angle typically prevents the spur gear from turning the worm.

Key Concept

Mechanical Advantage and Function of Gear Trains
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Topics

Gears and Gear Ratios

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