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A novel planar motion generation method based on the synthesis of planetary gear train with noncircular gears

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Abstract

Four-bar linkage has been used in motion generation synthesis for a long time, but there are inevitably some shortcomings such as order defects and poor design flexibility. In this work, a planetary gear train with noncircular gears is proposed to realize planar motion generation synthesis. Compared with the four-bar linkage, it has the advantages of a compact structure, full rotatability, and flexible design. The planetary gear train with noncircular gears is composed of two interrelated parts: a two-stage noncircular gear pair and the RR dyad. The synthesis method is divided mainly into three steps: First, the constraint equation of RR dyad for planar motion generation is established, and a solution region of the double revolute joint (RR) dyads is calculated by kinematic mapping theory. Second, after the full rotatability identification of RR dyads and the determination of each transmission ratio, the centrodes of two-stage noncircular gear pairs, which correspond to the specific RR dyad, are obtained. Finally, the planetary gear train with noncir-cular gears is established to pass the given poses. This method has a universal significance and can be applied to many practical cases.

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Abbreviations

a :

Center distance

θ 1 :

Angle between the rotating planetary frame 5 and the horizontal line

θ 2 :

Angle between the execution component 6 and the horizontal line

φ 15 :

Rotor angle of central noncircular gear 1 relative to planetary frame 5

φ 25 :

Rotor angle of planetary noncircular gear 2 relative to planetary frame 5

φ 35 :

Rotor angle of second-stage active noncircular gear 3 relative to planetary frame 5

φ 45 :

Rotor angle of second-stage driven noncircular gear 4 relative to planetary frame 5

r 1 :

Radius of central noncircular gear 1

r 2 :

Radius of planetary noncircular gear 2

r 3 :

Radius of second-stage active noncircular gear 3

r 4 :

Radius of second-stage driven noncircular gear 4

i :

Total gear ratio

\(i_{21}^5\) :

Gear ratio of first-stage noncircular gear pair relative to planetary frame 5

\(i_{43}^5\) :

Gear ratio of second-stage noncircular gear pair relative to planetary frame 5

\(i_{41}^5\) :

Gear ratio of two-stage noncircular gear pair relative to planetary frame 5

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Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 51975536, No. 51775512, and No. 51675486), Zhejiang Key Research and Development Program (2018C02046).

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Jun Ye, Xiong Zhao, XinCheng Sun, JianNeng Chen & XuDong Xia

  2. Faculty of Mechanical Engineering, Zhejiang Industry Polytechnic College, Shaoxing, 312000, China

    Jun Ye & XinCheng Sun

  3. Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo, 315211, China

    Ying Wang

Authors
  1. Jun Ye
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  2. Xiong Zhao
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  3. Ying Wang
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  4. XinCheng Sun
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  5. JianNeng Chen
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  6. XuDong Xia
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Corresponding authors

Correspondence to Xiong Zhao or JianNeng Chen.

Additional information

Recommended by Associate Editor Yongho Jeon

Jun Ye is a Lecturer in Mechanical Engineering, Zhejiang Industry Polytechnic College, Shaoxing, China. He is studying for his Ph.D. from Zhejiang Sci-Tech University. His research interests include mechanism synthesis, mechanism optimization design.

Xiong Zhao is an Associate Professor of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, China. He received his Ph.D. in Mechanical Engineering from Zhejiang Sci-Tech University. His research interests include mechanism synthesis, mechanism optimization design and development of transplanting equipment.

JianNeng Chen is a Professor of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, China. He received his Ph.D. from Zhejiang University. His research interests include mechanism synthesis, mechanism optimization design and agricultural machinery equipment.

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Ye, J., Zhao, X., Wang, Y. et al. A novel planar motion generation method based on the synthesis of planetary gear train with noncircular gears. J Mech Sci Technol 33, 4939–4949 (2019). https://doi.org/10.1007/s12206-019-0933-6

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  • DOI: https://doi.org/10.1007/s12206-019-0933-6

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