Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-12T10:46:56.588Z Has data issue: false hasContentIssue false
  • English
  • Français

Algorithm for topological design of multi-loop hybrid mechanisms via logical proposition

Published online by Cambridge University Press:  26 July 2011

Qiang Zeng and
Yuefa Fang
Qiang Zeng*
Affiliation:
Robotics Research Lab., School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, PR China
Yuefa Fang
Affiliation:
Robotics Research Lab., School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, PR China
*
*Corresponding author. E-mail: 07116302@bjtu.edu.cn
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper introduces the mathematical logical proposition into kinematics and presents a novel method for topological design and representation of mechanisms. The six-value non-classical logical matrix in three orders is proposed to represent spatial basic motions, relations, and selection of moving reference frame. The combinatorial logical sets of mechanisms are built and axiomatized to analyze serial–parallel hybrid mechanisms. In accordance to the logical relations, the mapping between topological arrangement and topological geometry is developed, and algorithm of decomposition synthesis is presented. Furthermore, the higher dimensional topological arrangement of multi-loop hybrid mechanism can be obtained by mapping of higher dimensional geometry. At last, four typical examples are developed to illustrate application of method of logical proposition in topological design of mechanisms. The method is helpful for topological design and analysis of multi-loop hybrid mechanisms.

Keywords

Logical propositionLogical matrixTopological designMulti-loop kinematic chainsHybrid mechanisms

Information

Type
Articles
Information
Robotica , Volume 30 , Issue 4 , July 2012, pp. 599 - 612
Copyright
Copyright © Cambridge University Press 2011

References

1.Kong, X. and Gosselin, C. M., “Type synthesis of 3-DOF spherical parallel manipulators based on screw theory,” ASME J. Mech. Des. 126, 101–108 (2004).CrossRefGoogle Scholar
2.Kong, X. and Gosselin, C. M., “Type synthesis of 3-DOF PPR-equivalent parallel manipulators based on screw theory and the concept of virtual chain,” ASME J. Mech. Des. 127, 1113–1121 (2005).CrossRefGoogle Scholar
3.Kong, X. and Gosselin, C. M., “Type synthesis of 4-DOF SP-equivalent parallel manipulators: A virtual chain approach,” Mech. Mach. Theory 41, 1306–1319 (2006).CrossRefGoogle Scholar
4.Hervé, J. M., “The Lie group of rigid body displacements, a fundamental tool for mechanism design,” Mech. Mach. Theory 34, 719–730 (1999).CrossRefGoogle Scholar
5.Rico, J. M., Cervantes-Sanchez, J. J., Tadeo-Chavez, A., et al. , “New considerations on the theory of type synthesis of fully parallel platforms,” ASME J. Mech. Des. 130 (11), 112302 (2008).CrossRefGoogle Scholar
6.Lee, C.-C. and Hervé, J. M., “Type synthesis of primitive Schoenflies-motion generators,” Mech. Mach. Theory 44, 1980–1997 (2009).CrossRefGoogle Scholar
7.Jin, Q. and Yang, T.-L., “Theory for topology synthesis of parallel manipulators and its application to three-dimension translation parallel manipulators,” ASME J. Mech. Des. 126, 625–639 (2004).CrossRefGoogle Scholar
8.Yang, T.-L., Liu, A.-X., Jin, Q., et al. , “Position and orientation characteristic equation for topological design of robot mechanisms,” ASME J. Mech. Des. 131, 021001 (2009).CrossRefGoogle Scholar
9.Wang, X., Baron, L. and Cloutier, G., “Topology of serial and parallel manipulators and topological diagrams,” Mech. Mach. Theory 43, 754–770 (2008).CrossRefGoogle Scholar
10.Ding, H. and Huang, Z., “A unique representation of the kinematic chain and the atlas database,” Mech. Mach. Theory 42, 637–651 (2007).CrossRefGoogle Scholar
11.Gogu, G., “Structural synthesis of fully isotropic parallel robots with Schönflies motions via theory of linear transformations and evolutionary morphology,” Eur. J. Mech. A/Solids 26, 242–269 (2007).CrossRefGoogle Scholar
12.Bribiesca, E., “3D-curve representation by means of a binary chain code,” Math. Comput. Modell. 40, 285–295 (2004).CrossRefGoogle Scholar
13.Dai, J.S. and Jones, J. Rees, “Matrix representation of topological configuration transformation of metamorphic mechanisms,” ASME J. Mech. Des. 127, 837–840 (2005).CrossRefGoogle Scholar
14.Tanev, T. K., “Kinematics of a hybrid (parallel–serial) robot manipulator,” Mech. Mach. Theory 35, 1183–1196 (2000).CrossRefGoogle Scholar
15.Tsai, L.-W. and Joshi, S., “Kinematic analysis of 3-DOF position mechanisms for use in hybrid kinematic machines,” ASME J. Mech. Des. 124, 245–253 (2002).CrossRefGoogle Scholar
16.Campos, A., Budde, C. and Hesselbach, J., “A type synthesis method for hybrid robot structures,” Mech. Mach. Theory 43, 984–995 (2008).CrossRefGoogle Scholar
17.Alizade, R. and Bayram, C., “Structural synthesis of parallel manipulators,” Mech. Mach. Theory 39, 857–870 (2004).CrossRefGoogle Scholar
18.Alizade, R., Can, F. C. and Gezgin, E., “Structural synthesis of Euclidean platform robot manipulators with variable general constraints,” Mech. Mach. Theory 43, 1431–1449 (2008).CrossRefGoogle Scholar
19.Rico, J. M. and Ravani, B., “On mobility analysis of linkages using group theory,” ASME J. Mech. Des. 125, 70–80 (2003).Google Scholar
20.Rico, J. M. and Ravani, B., “On calculating the degrees of freedom or mobility of overconstraint linkages: Single-loop exceptional linkages,” ASME J. Mech. Des. 129, 301–311 (2007).CrossRefGoogle Scholar
21.Chaudhary, H. and Saha, S. K., “Constraint wrench formulation for closed-loop systems using two-level recursions,” ASME J. Mech. Des. 129, 1234–1242 (2007).CrossRefGoogle Scholar
22.Gogu, G., “Chebychev-Grubler-Kutzbach's criterion for mobility calculation of multi-loop mechanisms revisited via theory of linear transformations,” Eur. J. Mech. A/Solids 24, 427–441 (2005).CrossRefGoogle Scholar
23.Kovacs, P. and Hommel, G., “An algorithm for the kinematic analysis and optimal input joint assignment of recursive mechanisms,” Mech. Mach. Theory 34, 615–635 (1999).CrossRefGoogle Scholar
24.Liberati, A. and Belfiore, N. P., “A method for the identification of the connectivity in multi-loop kinematic chains: Analysis of chains with total and partial mobility,” Mech. Mach. Theory 41, 1443–1466 (2006).CrossRefGoogle Scholar
25.Mao, D., Luo, Y. and You, Z., “Planar closed loop double chain linkages,” Mech. Mach. Theory 44, 850–859 (2009).CrossRefGoogle Scholar
26.Zeng, Q. and Fang, Y., “Structural synthesis of serial–parallel hybrid mechanisms based on representation and operation of logical matrix,” ASME J. Mech. Robot. 1, 041003 (2009).CrossRefGoogle Scholar
27.Zeng, Q. and Fang, Y., “Structural Synthesis of Serial–Parallel Hybrid Mechanisms via Group Theory and Representation of Logical Matrix,” In: IEEE International Conference on Information and Automation, Zhuhai, China (June 22–24, 2009) 1392–1397.Google Scholar