Geometry design of roller gear cams with hyperboloid rollers

Hong-Sen Yan, Chen Hsin-Hung

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

This paper studies the surface geometry of roller gear cams with hyperboloid rollers as meshing elements. The surface equation of the hyperboloid roller is established. Coordinate systems and coordinate transformation matrices corresponding to the roller gear cam are defined. The mathematical expressions for the surface geometry of the roller gear cam, by applying the theory of conjugate surfaces, differential geometry, and coordinate transformation, are derived. Based on available surface geometry of the roller gear cam, the unit normal of the cam surface is obtained by differential geometry. The contact lines of the conjugate surfaces are defined according to the equation of meshing and the specified input-output relation. Once the contact line is transformed to the coordinate system which is rigidly connected to the globoidal cam, the surface profiles of the globoidal cam are obtained. Two design examples are given.

Original language English 107-117 11 Mathematical and Computer Modelling 22 8 https://doi.org/10.1016/0895-7177(95)00160-4 Published - 1995 Jan 1

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Rollers (machine components)
Cams
Gears
Geometry
Contact Line
Coordinate Transformation
Meshing
Differential Geometry
Unit normal vector
Surface Profile
Transformation Matrix
Design
Output

All Science Journal Classification (ASJC) codes

• Modelling and Simulation
• Computer Science Applications

Cite this

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abstract = "This paper studies the surface geometry of roller gear cams with hyperboloid rollers as meshing elements. The surface equation of the hyperboloid roller is established. Coordinate systems and coordinate transformation matrices corresponding to the roller gear cam are defined. The mathematical expressions for the surface geometry of the roller gear cam, by applying the theory of conjugate surfaces, differential geometry, and coordinate transformation, are derived. Based on available surface geometry of the roller gear cam, the unit normal of the cam surface is obtained by differential geometry. The contact lines of the conjugate surfaces are defined according to the equation of meshing and the specified input-output relation. Once the contact line is transformed to the coordinate system which is rigidly connected to the globoidal cam, the surface profiles of the globoidal cam are obtained. Two design examples are given.",
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Geometry design of roller gear cams with hyperboloid rollers. / Yan, Hong-Sen; Hsin-Hung, Chen.

In: Mathematical and Computer Modelling, Vol. 22, No. 8, 01.01.1995, p. 107-117.

Research output: Contribution to journalArticle

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