Structure Functions Of Normal Ruled Surface

The ruled surface is formed by straight line trajectory.The cylindrical surface,conical surface,hyperboloid of one sheet and hyperbolic paraboloid are all ruled surfaces.The ruled surface is widely used in engineering practice,such as components of the aircraft wing and the steam turbine impeller often with ruled surface as surface;a part of groove surfaces of gear hob,some special revolving tools are the ruled surface;for some surfaces with slightly larger absolute value of normal curvature,can also be approximated to the ruled surface for processing.This paper focuses on the normal surfaces of curves in Euclidean 3-space.A ruled surface generated by the principal normal of the curve is called normal ruled surface.It is a kind of non-developable ruled surface,therefore,the research on the normal surface can enrich the related content of the non-developable ruled surface.The structure of this paper is arranged as follows:In Chapter 1,we introduce the research background,the main mathematical concepts and formulae of this paper.In Chapter 2,we review the definition,standard equation and structure functions of the non-developable ruled surface,and summarize the main conclusions of the structure functions of the non-developable ruled surface.In Chapter 3,we study the structure functions of the normal surface.First of all,we give the definition and standard equation of the normal surface.Secondly,we give the relation of the structure functions of the normal surface,and the relation between the structure functions,the striction line and the guide line of the normal surface.In Chapter 4,we discuss the normal surface of the Mannheim curve and the general helix.The normal surface of a Mannheim curve is a binormal surface of the companion line,and the normal surface of a general helix is a right helicoid.In Chapter 5,we summarize and prospect our work.