Formation by branches of envelope to parametric families of surfaces and curves

The existence of envelope to family of surfaces (cur;es in planar gearing) is usually discussed as existence of envelope formed by one branch of a regular surface (curve in planar gearing). The authors consider cases of formation of envelopes formed by several branches. Existence of such envelopes is represented for the cases of cycloidal pumps and conventional worm gear drives. The formation of envelope by several branches is represented analytically, rules for discovery of different envelope branches are proposed, and the existence of branches is illustrated graphically. The obtained results are important For computerized design of generation of surfaces and curves and enable to separate real and false branches of envelope. (C) 2001 Elsevier Science B.V. All rights reserved.