Geometry of Surfaces pp 97-117 | Cite as

# Indicatrix of Conformity at Point of Contact of Two Smooth Regular Part Surfaces in the First Order of Tangency

## Abstract

In Chap. 5 a novel kind of characteristic curve for the purposes of analytical description of the contact geometry of two smooth regular part surfaces in the first order of tangency is discussed in detail. The discussion begins with preliminary remarks and follows with introduction and with derivation of an equation of the indicatrix of conformity at point of contact of two parts surfaces. Then, directions of extremum degree of conformity of two part surfaces in contact are specified and are described analytically. This analysis is followed by determination and by derivation of corresponding equations of asymptotes of the indicatrix of conformity. Capabilities of the indicatrix of conformity R point of contact of two smooth regular part surfaces in the first order of tangency are compared with the corresponding capabilities of “Dupin indicatrix” of the surface of relative curvature. Important properties of the indicatrix of conformity of two smooth regular part surfaces are outlined. Ultimately, the converse indicatrix of conformity at point of contact of two regular part surfaces in the first order of tangency is introduced and is briefly discussed as an alternative to the regular indicatrix of conformity.

## References

- 1.Pat. No. 1249787. (1984).
*A method of sculptured surface machining on multi-axis NC machine*. S.P. Radzevich, Int. Cl. B23c 3/16, Filed: December 27, 1984.Google Scholar - 2.Pat. No. 1185749. (1983).
*A Method of sculptured surface machining on multi-axis NC machine*. S.P. Radzevich, Int. Cl. B23c 3/16, Filed: October 24, 1983.Google Scholar