Definition of an instrumental surface, generating gears of a parallel, circular and cycloid line of the tooth

The geometry of different types of instrumental surfaces, used in forming the profiles of the teeth of arcoidal gear wheels, is known.This geometry depends mostly on the peculiarities in the kinematics of cutting for getting a specified longitudinal tooth line.
In the paper are summerized all main parameteurs, indroduced buy the study of the various methods of forming of the teeth profiles and the producing surface(called a summerized one) is presented in a genral type.From the got equations, trought annuiment of some parameters are derived the instrumental surfaces knowntill now and some new ones.