Abstract
Over the past few decades, there has been extensive research conducted in both academia and industry on conventional parallel manipulators. However, the exploration of generalized parallel mechanisms with coupling sub-chains has received limited attention. This paper introduces a novel approach to synthesizing parallel mechanisms with additional connecting sub-chains, focusing on number synthesis and graph representation. To develop manipulators with additional constraints, this study constructs contracted graphs with different loops. The contracted graphs are represented by arrays, which denote the connectivity relationships among associated linkages, leading to the discovery of new contracted graphs. Besides, the connective array is introduced to identify isomorphic and invalid contracted graphs, while also analyzing specific contracted graph variations. Furthermore, this paper deduces the evolutionary process of contracted graphs, resulting in the derivation of all available topological arrangements. This innovative method for graph synthesis of parallel mechanisms with coupling sub-chains has the potential to expand the range of available options within the family of generalized parallel mechanisms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Gogu, G.: Structural Synthesis of Parallel Robots. Springer (2008)
Huang, Z., Li, Q., Ding, H.: Theory of Parallel Mechanisms. Springer, Netherlands, Dordrecht (2013)
Wang, Z., Zhang, W., Ding, X.: A family of RCM mechanisms: type synthesis and kinematics analysis. Int. J. Mech. Sci. 231, 107590 (2022)
Meng, Z., Cao, W., Ding, H., Chen, Z.: A new six degree-of-freedom parallel robot with three limbs for high-speed operations. Mech. Mach. Theory 173, 104875 (2022)
Tian, C., Zhang, D.: A new family of generalized parallel manipulators with configurable moving platforms. Mech. Mach. Theory 153, 103997 (2020)
Guo, S., Fang, Y., Qu, H.: Type synthesis of 4-DOF nonoverconstrained parallel mechanisms based on screw theory. Robotica 30, 31–37 (2012)
Tian, C., Zhang, D., Tang, H., Wu, C.: Structure synthesis of reconfigurable generalized parallel mechanisms with configurable platforms. Mech. Mach. Theory 160, 104281 (2021)
Zeng, Q., Fang, Y.: Structural synthesis and analysis of serial–parallel hybrid mechanisms with spatial multi-loop kinematic chains. Mech. Mach. Theory 49, 198–215 (2012)
Zoppi, M., Bruzzone, L., Molfino, R., et al.: A novel 5-DoF Interconnected-Chains PKM for manufacturing of revolute surfaces. In: 4th Chemnitzer Parallel Kinematik Seminar, pp. 20–21. Chemnitz (2004)
Cao, W., Ding, H., Chen, Z., Zhao, S.: Mobility analysis and structural synthesis of a class of spatial mechanisms with coupling chains. Robotica 34, 2467–2485 (2016)
Tian, C., Fang, Y., Ge, Q.J.: Structural synthesis of parallel manipulators with coupling sub-chains. Mech. Mach. Theory 118, 84–99 (2017)
Tian, C., Fang, Y., Ge, Q.J.: Design and analysis of a partially decoupled generalized parallel mechanism for 3T1R motion. Mech. Mach. Theory 140, 211–232 (2019)
L.-W. Tsai, Mechanism Design: Enumeration of Kinematic Structures According to Function. CRC press (2000)
Gogu, G.: Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations. Eur. J. Mech.-A/Solids 23, 1021–1039 (2004)
Vucina, D., Freudenstein, F.: An application of graph theory and nonlinear programming to the kinematic synthesis of mechanisms. Mech. Mach. Theory 26, 553–563 (1991)
Lu, Y., Leinonen, T.: Type synthesis of unified planar–spatial mechanisms by systematic linkage and topology matrix-graph technique. Mech. Mach. Theory 40, 1145–1163 (2005)
Lu, Y., Ye, N.: Type synthesis of parallel mechanisms by utilizing sub-mechanisms and digital topological graphs. Mech. Mach. Theory 109, 39–50 (2017)
Huang, Z., Li, Q.C.: General methodology for type synthesis of symmetrical lower-mobility parallel manipulators and several novel manipulators. Int. J. Robot. Res. 21, 131–145 (2002)
Tsai, L.-W.: Robot Analysis: The Mechanics of Serial and Parallel Manipulators. Wiley, New York (1999)
Zeng, Q., Fang, Y.: Algorithm for topological design of multi-loop hybrid mechanisms via logical proposition. Robotica 30, 599–612 (2012)
Lu, Y., Lu, Y., Ye, N., Mao, B., Han, J., Sui, C.: Derivation of valid contracted graphs from simpler contracted graphs for type synthesis of closed mechanisms. Mech. Mach. Theory 52, 206–218 (2012)
Xia, Z., Zhang, D., Chen, Y., Tian, C., Liu, J., Wu, C.: A novel 6 DOFs generalized parallel manipulator design and analysis based on humanoid leg. Mech. Mach. Theory 176, 105029 (2022)
Acknowledgements
This work is founded by National Nature Science Foundation of China (grants 52150710538).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Tian, C., Li, L., Xia, Z., Zhang, D. (2023). Graph Synthesis of Generalized Parallel Mechanisms with Coupling Sub-chains. In: Yang, H., et al. Intelligent Robotics and Applications. ICIRA 2023. Lecture Notes in Computer Science(), vol 14275. Springer, Singapore. https://doi.org/10.1007/978-981-99-6504-5_7
Download citation
DOI: https://doi.org/10.1007/978-981-99-6504-5_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-6503-8
Online ISBN: 978-981-99-6504-5
eBook Packages: Computer ScienceComputer Science (R0)