Summary: We consider a parametric family $Σ_φ$ of planar curves generated by the tool profile $Σ_r$. The generated profile $Σ_ρ$ of the workpiece (gear) is the envelope to the family $Σ_φ$. A simplified approach is proposed for determination of the envelope, its singularities and conditions for existence of a point of regression. The proposed developments are illustrated with the design of Root’s blowers.