Synthesis of hyperboloid gear sets based on the pitch point approach

The pitch configurations (circles and surfaces) are the foundation, upon which the mathematical models for synthesis of spatial gears with crossed axes of rotation are worked out. These mathematical models are created on the approach for synthesis based on one common point of contact between the operating tooth surfaces of the mating gears, this point being at the same time a common point of the pitch configurations. This point is named a pitch contact point.When the pitch circles are in a static position, they are treated as geometric characteristics of the designed gears, and determine not only the basic parameters of their structure but also the dimensions of the gears' blanks. If the pitch configurations are put in a rotation according to a given law of motions transformation, then the dimensions and the mutual position of the configurations serve to define the dimensions and the longitudinal and the profile geometry of the tooth surfaces contacting in the pitch point.

► Synthesis of spatial gear mechanisms with crossed rotation axes. ► Essence and definitions of pitch configurations: pitch circles and pitch surfaces. ► Mathematical model for synthesis of geometric pitch configurations. ► Determination of the dimensions and mutual position of the pitch configurations.