Mathematical Models, Oriented to the Synthesis of Hyperboloid Gear Drives with Eliminated Singularity on the Mesh Region

The study illustrates the mathematical models, applied to the synthesis of hyperboloid gear drives. The kinematic approach for registration and elimination singularity from the vicinity of the pitch contact point at the mesh region of the synthesized spatial transmissions is shown. Analytical dependencies are illustrated in order to provide the definition and control of the singularity of first order on the conjugated active tooth surfaces, when hyperboloid gear sets are synthesized by applying two approaches for their synthesis: “synthesis upon a pitch contact point” and “synthesis upon region of mesh”.