1. Understanding the difference between simple and compound gear trains and the gear ratios

2. Simple Gear Train
Shaft
Each shaft in a simple gear train is attached to one spur gear only.

3. Compound Gear Train System
Two or more spur gears added together to the same shaft form a compound gear. The different gears that make a compound gear all rotate at the same speed. Gear trains with compound gears are called compound gear trains.

4. What’s the advantage of compound gear train over simple gear train ?

5. A B C Simple Gear Train 120 Teeth 60 Teeth 30 Teeth Driver Driven
If gear A is running at 100 revs/min, gear B will run at 200 revs/min. This is because the no. of teeth is inversely proportional to the speed. The smaller the gear the faster it turns. Similarly gear C turns at 400 revs/min as Gear C is twice as small as gear A.
The gear ratio (velocity ratio) for the gear train above is Velocity of Gear A(Driver): Velocity of Gear C(Driven) which is 1:4. This gear ratio means that the driven gear is 4 times faster than the driver gear.

6. Compound Gear Train A C B 30 Teeth 60 Teeth 120 Teeth
If gear A is running at 100 revs/min, compound gear B will run at 200 revs/min as it has twice the teeth and will be twice as slow (inversely proportional). The larger teeth gear in compound gear B (120 teeth) is attached to Gear C (30 teeth), which is 4 times smaller and therefore 4 times faster. Gear C’s speed will be 800 revs/min. The strategy here to mesh the smaller gear (30 teeth) in compound gear B to A and the larger(120 teeth) to C to achieve the greatest increase in speed. This is the advantage of a having a compound gear.
The gear ratio (velocity ratio) for the gear train above is Velocity of Gear A(Driver): Velocity of Gear C(Driven) which is 1:8 as A is running at 100 revs/min and C is running at 800 revs/min. You get 2 times better output speed compared to the simple gear train used just now.

7. Now compare the space taken up by the simple gear train and compound gear train
Look at the compound gear train, it has one more 30 teeth gear, and the other 3 gears are the same. Yet the length occupied by the compound gear is less, this is because of the overlap of A with B. So you have 2 advantages, takes up less space and at the same time achieves a better speed increase or reduction (in above case its speed increase of course). No wonder watches use compound gear trains as a great speed reduction is needed within a small space !!

8. Worm Gear
Worm Gear systems always has a gear ratio of No. of tooth in worm wheel : 1. And worm gears are used to reduce speed. The worm gear is the driver and the worm wheel is the driven. The driver rotates 1 full turn just for the worm wheel to move 1 teeth.
In the above example the worm gear rotates 12( since there are 12 teeth in worm wheel) times for the wheel to turn once. Hence gear ratio (velocity ratio) is 12: 1.