Function and Space Curve Interpolation

Based on space curve meshing theory, in this paper, we present a novel geometric design of a circular arc helical gear mechanism for parallel transmission with convex-concave circular arc profiles. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equations, and parameter equations for calculating the convex-concave circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was deduced, and the impact factors influencing the contact ratio are discussed. Using the deduced equations, several numerical examples were considered to validate the contact ratio equation. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance when considering practical applications, such as a pure rolling process, a high contact ratio, and a large comprehensive strength.

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C-shaped Hermite interpolation with circular precision based on cubic PH curve interpolation

Computer-Aided Design ◽

10.1016/j.cad.2012.04.007 ◽

2012 ◽

Vol 44 (11) ◽

pp. 1056-1061 ◽

Cited By ~ 9

Author(s):

Yajuan Li ◽

Chongyang Deng

Keyword(s):

Hermite Interpolation ◽

Curve Interpolation ◽

Ph Curve

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Research of NURBS curve interpolation algorithm

2014 IEEE Workshop on Electronics, Computer and Applications ◽

10.1109/iweca.2014.6845589 ◽

2014 ◽

Author(s):

Zhai Xiaoshuai ◽

Tong Chonglou

Keyword(s):

Interpolation Algorithm ◽

Nurbs Curve ◽

Curve Interpolation

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Special Bishop Motion and Bishop Darboux Rotation Axis of the Space Curve

Journal of Dynamical Systems and Geometric Theories ◽

10.1080/1726037x.2008.10698542 ◽

2008 ◽

Vol 6 (1) ◽

pp. 27-34 ◽

Cited By ~ 11

Author(s):

Bahaddin Bukcu ◽

Murat Kemal Karacan

Keyword(s):

Rotation Axis ◽

Space Curve

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Optimal sampling and curve interpolation via wavelets

Applied Mathematics Letters ◽

10.1016/j.aml.2013.03.002 ◽

2013 ◽

Vol 26 (7) ◽

pp. 774-779 ◽

Cited By ~ 1

Author(s):

Heeyoung Kim ◽

Xiaoming Huo

Keyword(s):

Optimal Sampling ◽

Curve Interpolation

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Designing and Mapping Trimming Curves on Surfaces Using Orthogonal Projection

16th Design Automation Conference: Volume 1 — Computer Aided and Computational Design ◽

10.1115/detc1990-0029 ◽

1990 ◽

Author(s):

Joseph Pegna ◽

Franz-Erich Wolter

Keyword(s):

Differential Equation ◽

Orthogonal Projection ◽

Broad Class ◽

Design Tool ◽

Space Curve ◽

Computationally Efficient ◽

Curves On Surfaces ◽

Surface Representations ◽

Differential Properties ◽

Surface Curve

Abstract In the design and manufacturing of shell structures it is frequently necessary to construct trimming curves on surfaces. The novel method introduced in this paper was formulated to be coordinate independent and computationally efficient for a very general class of surfaces. Generality of the formulation is attained by solving a tensorial differential equation that is formulated in terms of local differential properties of the surface. In the method proposed here, a space curve is mapped onto the surface by tracing a surface curve whose points are connected to the space curve via surface normals. This surface curve is called to be an orthogonal projection of the space curve onto the surface. Tracing of the orthogonal projection is achieved by solving the aforementionned tensorial differential equation. For an implicitely represented surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This method has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations. Orthogonal projection of a curve onto a surface was also developed in the context of surface blending. The orthogonal projection of a curve onto two surfaces to be blended provides not only a trimming curve design tool, but it was also used to construct smooth natural maps between trimming curves on different surfaces. This provides a coordinate and representation independent tool for constructing blend surfaces.

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