On the synthesis of spatial cycloidal gears

Figliolini, Giorgio; Stachel, Hellmuth; Ángeles, Jorge

doi:10.1007/s11012-012-9664-9

Cited by 7 publications

(3 citation statements)

References 13 publications

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“…Thus, the choice of the auxiliary surface is not free, since the spatial version of Camus's theorem must be satisfied, but there are infinitely many canditates, which should be evaluated in terms of specific critera, as reported in [20][21][22][23][24][25].…”

Section: Synthesis Of the Orthogonal Helicoidmentioning

confidence: 99%

“…However, in addition to these geometric properties and in agreement with screw theory, each axis of the Plücker conoid is also associated with a specific pitch p = v / , where v and  are the point and angular velocities, along and around the same axis, respectively. As reported in [19][20][21][22], the only two axes with zero pitch are represented by the I 2 and I 3 axes of the gear pair. Thus, the pitch p 32 of the ISA is given by Eqs.…”

Section: Synthesis Of the Orthogonal Helicoidmentioning

confidence: 99%

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The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

Figliolini

Stachel

Ángeles

2014

Volume 5A: 38th Mechanisms and Robotics Conference

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Camus’ concept of Auxiliary Surface (AS) is extended to the case of involute gears with skew axes. In the case at hand, we show that the AS is an orthogonal helicoid whose axis a) lies in the cylindroid and b) is normal to the instant screw axis of one gear with respect to its meshing counterpart; in general, the helicoid axis is skew with respect to the latter. According to the spatial version of Camus’ Theorem, any line attached to the AS, in particular any generator g of AS itself, can be chosen to generate a pair of conjugate flanks with line contact. While the pair of conjugate flanks is geometrically feasible, as they always share a line of contact and the tangent plane at each point of this line, there are poses where the flanks even have a common Disteli axis. Then there is a G2-contact at the striction point and the two surfaces penetrate each other. The outcome is that the surfaces are not realizable as tooth flanks. Nevertheless, this is a fundamental step towards the synthesis of the flanks of involute gears with skew axes.

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Section: Synthesis Of the Orthogonal Helicoidmentioning

confidence: 99%

Section: Synthesis Of the Orthogonal Helicoidmentioning

confidence: 99%

The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

Figliolini

Stachel

Ángeles

2014

Volume 5A: 38th Mechanisms and Robotics Conference

Self Cite

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“…It can be seen that research on gear transmission design is mostly concentrated in the field of cylindrical gear, and there is relatively little knowledge about bevel gear transmission design. The derivation of meshing equation of bevel gear tooth surface based on bevel gear meshing principle and accurate modeling of bevel gear pair are a challenge faced by the machinery industry [25].…”

Section: Introductionmentioning

confidence: 99%

Transmission Design of Bevel Gear with Arbitrary Crossed Axes and Its Application in the Knotter

Yin

Han

Zheng

et al. 2021

Preprint

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The bevel gear transmission with crossed axes is widely used, but there are the difficulty of tooth profile calculation and modeling in the design and manufacturing process. This paper analyzes firstly the parameter solving equation of the bevel gear pair with arbitrary crossed axes. Based on the meshing principle of the bevel gear pair and numerical analysis method, the meshing equations of the bevel gear pair with crossed axes are derived, which provide the calculation models for the design of spatial bevel gear tooth surface. Taking the bevel gear pair with crossed axes in two kinds of the knotter as two design examples, the geometric parameters of the bevel gear pair in the knotter are solved, and the mathematical models of the tooth surface are programmed and calculated by using MATLAB. Through the graphic display of the tooth surface point set under MATLAB software and the 3D modeling function of Pro/Engineering software, the accurate 3D models of the bevel gear tooth surface are established. The meshing transmission simulations of the established bevel gear pair are respectively carried out by using ADAMS, and their physical prototype and transmission tests are also implemented. The test results showed that the transmission of the designed bevel gear pair is accurate and stable, which proves the correctness of the derived calculation model of the tooth surface of the bevel gear with crossed axes.

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Kinematics of Machines: Contributions from Meccanica

Belfiore

Pennestrı̀

2022

50+ Years of AIMETA

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On the synthesis of spatial cycloidal gears

Cited by 7 publications

References 13 publications

The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

Transmission Design of Bevel Gear with Arbitrary Crossed Axes and Its Application in the Knotter

Kinematics of Machines: Contributions from Meccanica

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