Determination of envelope to family of planar parametric curves and envelope singularities Original Research Article

A parametric family Σφ of planar curves generated by the tool profile Σr is considered. The generated profile Σp of the workpiece (gear) is the envelope to the family Σφ. 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 Rootʹs blowers.