New method for determining singularities on enveloped surface and its application to study curvature interference theory of involute worm drive

In this paper, a more computationally convenient singularity condition of the enveloped surface is proposed using theory linear algebra. Its preconditions are only tangential vector enveloping surface, relative velocity vector, and total differential meshing function. It avoids calculating curvature parameters surface. proved that conditions from different references equivalent to each other relational equations among them obtained. The interference for involute worm drive established condition. equation trajectory calculation method its numerical result influence design on studied theory. study results show risk high when transmission ratio too small, especially in case single-threaded large modulus. can also be applied mechanism types undercutting machining drive.