Computerized determination of singularities and envelopes to families of contact lines on gear tooth surfaces Original Research Article

A family of tooth surfaces ∑Φ represented in parametric form is considered. The contents of the paper covers determination of envelope ∑2 to family ∑Φ, singularities on ∑2 and sufficient conditions of existence of envelopes E1 and E2 to characteristics on generating and generated tooth surfaces ∑1 and ∑2. Necessary condition of coincidence of E2 with the edge of regression on ∑2 is provided.