Curvature continuous connections of cones and cylinders

Aumann, Günter

doi:10.1016/0010-4485(95)91139-c

Cited by 22 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is difficult to directly solve the sixth-order partial differential equations (5) subjected to the blending boundary constraints (1). In order to simplify the solution, we examine the boundary functions…”

Section: Approximate Analytical Solution Of Mathematical Modelmentioning

confidence: 99%

“…Tangent and curvature continuities are most frequently applied in mechanical engineering. For example, discontinuous curvature causes problems in NC milling and leads to break points of reflection lines [5] which are widely used in automotive industry [6]. A cam with second-order discontinuity creates abrupt changes in acceleration, and the design of streamlined surfaces of aircraft, ship, and submarine requires curvature continuity to avoid flow separation and turbulence [7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

C2 Continuous Blending of Time-Dependent Parametric Surfaces

You

Tian

Tang

2019

Journal of Computing and Information Science in Engineering

View full text Add to dashboard Cite

Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.

show abstract

Section: Approximate Analytical Solution Of Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

C2 Continuous Blending of Time-Dependent Parametric Surfaces

You

Tian

Tang

2019

Journal of Computing and Information Science in Engineering

View full text Add to dashboard Cite

show abstract

“…The theoretical conditions for the smoothness of spine curves are established by Lukacs [4] who has also demonstrated that if the geodesic curvature of the spine curve on the Voronoi surface is too large the blend surface may have singularities even if at any of the contact points the surfaces enclose the rolling ball and the spine curve is smooth. The existence of singular points on the blending surfaces is also discussed in reference [8]. Warren [2] demonstrated the possibility of blending several algebraic surfaces simultaneously.…”

Section: Singularities Blendingmentioning

confidence: 99%

Surface blending for machining purposes: A brief survey and application for machining compound surfaces

Hatna

Grieve

Broomhead

2001

Proceedings of the Institution of Mechanical Engineers, Part B:

View full text Add to dashboard Cite

Rolling ball blending techniques are widely used for rounding edges and corners of mechanical parts in computer aided design. The techniques of computing trim curves for blending are used in this paper to delimit the domains of machinability of parametric surfaces. Whereas the principle of the rolling ball can be used for machining single or compound surfaces, the focus here is only on compound surfaces. A survey of existing methods is given followed by an application for a new approach for the generation of¯ow line tool paths.

show abstract

“…Pratt [Pra90, Pra95] shows how to make piecewise cyclide blending surfaces, and extends the symmetric cyclide blends to include asymmetric problems, the particular case of the computation of double cyclide blends between two cones is given as an example of possible blending applications. Aumann [Aum95] investigates curvature continuous blending of cones and cylinders using normal ringed surfaces which are generated, like cyclides, by a circle of variable radius sweeping through space. Allen and Dutta [AD98] present a method to generate nonsingular transition surfaces between natural quadrics using either Dupin cyclides or parabolic cyclides, necessary and sufficient conditions for the existence of the cyclide transition surface are given.…”

Section: Introductionmentioning

confidence: 99%