Determination of envelope to family of planar parametric curves and envelope singularities

摘要

A parametric family A of planar curves generated by the tool profile X is considered. The generated profile 4, of the work piece (gear) is the envelope to the family Σ_φ. The authors propose simplified approaches for determination of the envelope, its singularities and conditions of existence of a point of regression. The proposed developments are illustrated with the design and generation of Root's blowers.