A possibility of application of Plückerʹs conoid for mathematical modeling of contact of two smooth regular surfaces in the first order of tangency

The purpose of the paper is to investigate a possibility of application of Plückerʹs conoid in engineering geometry of surfaces. The research reveals that Plückerʹs conoid itself is a complex 3D characteristic image. On the premises of Plückerʹs conoid, the 2D characteristic curves of novel kind are introduced. We refer to these characteristic curves as to the AnR (P)-indicatrix and Ank(P)-indicatrix of the surface P. The characteristic curves AnR(P) and Ank(P) in many cases are similar to the corresponding Dupinʹs indicatrices DupR(P) and Dupk(P). For two interacting surfaces the developed approach yields introducing of the Plückerʹs relative indicatrices PlR(P/T) and Plk(P/T). Finally, the 3D characteristic curves PlR(P/T) and Plk(P/T) reduced to the planar characteristic curves AnR(P/T) and Ank(P/T), i.e., to the so-called AnR(P/T)- and Ank(P/T)-relative indicatrices. The characteristic curves AnR(P/T) and Ank(P/T) could be employed.(a) alytical description of local topology of composite surfaces along the linkage curve; veloping of the optimal tool-paths for sculptured surface machining on multiaxis NC machine, as well as for analytical description of conditions of proper sculptured surface machining; proving accuracy of solution to the problem of contact of two elastic bodies, etc. characteristic curves reported in the paper in many cases are similar to the indicatrices of conformity CnfR(P/T) and Cnfk(P/T) of two smooth rugular surfaces earlier developed by the author. The obtained results perfectly correlate with the results obtained by other researchers, as well as with the results earlier developed by the author.