This section is from the book "The English And American Mechanic", by B. Frank Van Cleve. Also available from Amazon: The English And American Mechanic.
Wheels which act upon each other at an angle.
When the tooth of a wheel is made of a material different from that of the wheel, it is termed a Cog; in a pinion it is termed a Leaf, and in a trundle a Stave.
A wheel which impels another is termed the Spur, Driver, or Leader ; the one impelled is the Pinion, Driven, or Follower.
A series of wheels in connection with each other is termed a Train.
When two wheels act upon one another, the greater is termed the Wheel and the lesser the Pinion.
A Trundle, Lantern, or Wallower is when the teeth of a pinion are constructed of round brass or solid cylinders set into two discs.
A Trundle with less than eight staves cannot be operated uniformly by a wheel with any number of teeth.
The material of which cogs are made is about one-fourth the strength of cast iron. The product of their bd2 should be four times that of iron teeth.
Buchanan: Rules that to increase or diminish velocity in a given proportion, and with the least quantity of wheel-work, the number of teeth in each pinion should be to the number of teeth in its wheel as 1 : 3.59. Even to save space and expense, the ratio should never exceed 1 : 6.
The least number of teeth that it is practicable to give to a wheel is regulated by the necessity of having at least one pair always in action, in order to provide for the contingency of a tooth breaking.
The teeth of wheels should be as small and numerous as is consistent with strength.
When a Pinion is driven by a wheel, the number of teeth in the pinion should not be less than eight.
When a Wheel is driven by a pinion, the number of teeth in the pinion should not be less than ten.
The Number of teeth in a wheel should always be prime to the number of the pinion; that is, the number of teeth in the wheel should not be divisible by the number of teeth in the pinion without a remainder. This is in order to prevent the same teeth coming together so often as to cause an irregular wear of their faces. An odd tooth introduced into a wheel is termed a hunting tooth or cog.
 
Continue to: