Summary: ``A parametric family $\Sigma_\phi$ of planar curves generated by the tool profile $\Sigma_r$ is considered. The generated profile $\Sigma_\rho$ of the workpiece (gear) is the envelope to the family $\Sigma_\phi$. We propose simplified approaches for the determination of the envelope, its singularities and conditions of existence of a point of regression. The proposed developments are illustrated by the design and generation of Root's blowers.''