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Journal ArticleDOI

Linkage model and manufacturing process of shaping non-circular gears

Fangyan Zheng1, Hua Lin1, Han Xinghui1, Bo Li1, Dingfang Chen1 
01 Feb 2016-Mechanism and Machine Theory (Pergamon)-Vol. 96, Iss: 96, pp 192-212
TL;DR: In this article, a linkage model for non-circular gear shaping is presented, and the entire process is demonstrated in a CNC gear-shaping machine, thus proving the accuracy of the mathematical model and providing a valid reference for shaping noncircular gears.
About: This article is published in Mechanism and Machine Theory.The article was published on 2016-02-01. It has received 46 citations till now. The article focuses on the topics: Gear shaping & Hobbing.
Citations
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Journal ArticleDOI
Fangyan Zheng1, Hua Lin1, Han Xinghui1, Bo Li1, Dingfang Chen1 
TL;DR: In this article, the gear ratios and pitch surfaces of non-circular gear are synthetized using the indexing motion laws and three types of noncircular planetary gear trains.

38 citations

Journal Article
TL;DR: In this article, a mathematical model for elliptical gears with circular-arc teeth is developed according to gear theory, and the influence of the design parameters, such as the number of teeth, gear module, pressure angle at the pitch point and the major axis, are investigated.
Abstract: This study describes rack cutters with circular-arc profile teeth to generate elliptical gears which rotate about one of their foci. A mathematical model for elliptical gears with circular-arc teeth is developed according to gear theory. The influence of the design parameters, such as the number of teeth, gear module, pressure angle at the pitch point and the major-axis, are investigated. The effects of the circular-arc radius of the rack cutter on both the undercutting of teeth and on pointed teeth of the generated circular-arc elliptical gear are also studied. Three numerical examples are presented to elucidate the generation of gear tooth profiles using the proposed mathematical model, and to investigate the phenomena of tooth undercutting and pointed teeth.

34 citations

Journal ArticleDOI
TL;DR: Based on the face-milling cutting method and noncircular gear meshing theory, the authors investigates into curvilinear non-circular cylindrical gear generation, including the mathematical model for design and the linkage model for manufacture.

32 citations

Journal ArticleDOI
TL;DR: In this paper, the meshing equations for non-circular gear contacting with helical curve face gear without misalignment are obtained based on the theory of gear meshing and coordinate transmission.

22 citations

References
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Book
01 Jan 1994
TL;DR: In this paper, the theory, design, geometry, and manufacture of all types of gears and gear drives are discussed, including modified spur and helical gears, face-gear drives, and cycloidal pumps.
Abstract: This revised, expanded, edition covers the theory, design, geometry and manufacture of all types of gears and gear drives. This is an invaluable reference for designers, theoreticians, students, and manufacturers. This edition includes advances in gear theory, gear manufacturing, and computer simulation. Among the new topics are: 1. New geometry for modified spur and helical gears, face-gear drives, and cycloidal pumps. 2. New design approaches for one stage planetary gear trains and spiral bevel gear drives. 3. An enhanced approach for stress analysis of gear drives with FEM. 4. New methods of grinding face gear drives, generating double crowned pinions, and improved helical gear shaving. 5. Broad application of simulation of meshing and TCA. 6. New theories on the simulation of meshing for multi-body systems, detection of cases wherein the contact line on generating surfaces may have its own envelope, and detection and avoidance of singularities of generated surfaces.

1,574 citations

Book
01 Sep 1998
TL;DR: The theory of screws in non-Euclidian space has been studied extensively in the literature, see as mentioned in this paper for an introduction to the theory of screw co-ordinates and a survey.
Abstract: 1. Twists and wrenches 2. The cylindroid 3. Reciprocal screws 4. Screw co-ordinates 5. The representation of the cylindroid by a circle 6. The equilibrium of a rigid body 7. The principal screws of inertia 8. The potential 9. Harmonic screws 10. Freedom of the first order 11. Freedom of the second order 12. Plane representation of dynamical problems concerning a body with two degrees of freedom 13. The geometry of the cylindroid 14. Freedom of the third order 15. The plane representation of freedom of the third order 16. Freedom of the fourth order 17. Freedom of the fifth order 18. Freedom of the sixth order 19. Homographic screw systems 20. Emanants and pitch invariants 21. Developments of the dynamical theory 22. The geometrical theory 23. Various exercises 24. The theory of screw-chains 25. The theory of permanent screws 26. An introduction to the theory of screws in non-Euclidian space Appendices Bibliographical notes Index.

707 citations

Journal ArticleDOI
TL;DR: In this paper, the authors presented a concept of epicyclical gear train able to generate a variable gear ratio law, which is useful when the synthesis of a specific torque curve or the design of a function generator involve a highly variable input/output relationship.

93 citations

Journal ArticleDOI
TL;DR: In this paper, the design and generation of non-circular gear drives with noncircular gears is discussed. But the authors focus on the design of a gear drive that is formed by an eccentric involute one and by a non-Circular gear.

85 citations

Journal ArticleDOI
TL;DR: In this article, the pitch curves of a conjugate noncircular gear pair are derived based on kinematic considerations and a method for considering the inverse mechanism relationship and the equation of meshing is proposed.
Abstract: Pitch curves of a conjugate noncircular gear pair are derived based on kinematic considerations. A method for considering the inverse mechanism relationship and the equation of meshing, is proposed here to derive a complete mathematical model of noncircular gears manufactured with involute-shaped shaper-cutters. The proposed method is similar to the contact line method and the envelope method, but is easier to apply to the determination of tooth profiles. A computer program is developed for generation the tooth profile with backlashes. Undercutting analysis is also investigated by considering the relative velocity and equation of meshing. Finally, modified elliptical gears are presented to illustrate the tooth profile generation when the proposed mathematical model is applied, and to investigate the phenomenon of tooth undercutting.

77 citations