A new method for automatic layered sketching of topological graphs based on the optimized branch chain matrix

Abstract

The automatic sketching of kinematic chain topological graphs can provide an effective method for the computerized graphical representation of mechanism models in quantity. It is also helpful to establish a visual atlas database for mechanism optimization and selection. Due to the defects of line crossings and point-line overlaps for the existing methods of topological graph sketching, this paper proposes a new method for automatic layered sketching of topological graphs based on the optimized branch chain matrix. First, a tree-structured diagram is employed to illustrate the internal connected relations of the kinematic chain, and the concepts of the main chain, branch chains, and branch chain matrix are introduced. Then, the branch chain matrix is established by searching connection relationships between links. Based on the proposed definition of the proximity between branch chains, as well as the decision rules and calculation method of intersections, the optimized branch chain matrix corresponding to the diagram is further acquired, with no intersections or the least number of intersections. Moreover, the method for obtaining the outermost-loop links is formulated. Finally, based on the point distribution of the regular polygon for the outermost loop and combined with a layer-by-layer sketching approach, the bicolor topological graph is obtained with no or minimal intersections of kinematic chains, which avoids the point-line overlaps. According to the case analysis, it is demonstrated that the topological graph sketching method proposed in this paper has several advantageous features, including no or minimal intersections, high symmetry, avoidance of point-line overlaps, and improved visibility.

Keywords

topological graph tree-structured diagram intersection branch chain matrix proximity

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References

Zhu

Yao

Shen

, et al. Structural synthesis based on POC set for lower-mobility non-overconstrained parallel mechanisms//Advances in reconfigurable mechanisms and Robots II. Springer, 2016, pp.327–338.

Fan

Liu

Zhang

Type synthesis of 2T2R, 1T2R and 2R parallel mechanisms. Mech Mach Theory 2013; 61: 184–190.

Hariharan

Kaup

Babu

A new computational methodology for the synthesis of simple jointed kinematic chains. AIP Conf Proc. 2019; 2134: 070003.

Ying

Ruiqin

Limin

Automatic identification and elimination of rigid sub-chains in kinematic chains. J Mech Transm 2018; 42(07): 19–24.

Ding

Huang

Computer-aided structure decomposition theory of kinematic chains and its applications. Mech Mach Theory 2008; 43(12): 1596–1609.

Ding

Huang

A new theory for the topological structure analysis of kinematic chains and its applications. Mech Mach Theory 2007; 42(10): 1264–1279.

Martins

Simoni

Carboni

AP.

Fractionation in planar kinematic chains: reconciling enumeration contradictions. Mech Mach Theory 2010; 45(11): 1628–1641.

Nie

Liu

Qiu

. A maximal loop approach to automatic sketching of mechanisms. In: ASME international mechanical engineering congress and exposition, 2007, pp.501–509.

Yang

Ding

Kecskeméthy

A new method for the automatic sketching of planar kinematic chains. Mech Mach Theory 2018; 121: 755–768.

10.

Sun

Kong

Sun

A novel graphical joint-joint adjacent matrix method for the automatic sketching of kinematic chains with multiple joints. Mech Mach Theory 2020; 150: 103847.

11.

Huang

Ding

Yang

, et al. An automatic method for the connectivity calculation in planar closed kinematic chains. Mech Mach Theory 2017; 109: 195–219.

12.

Sunkari

Schmidt

LC.

Structural synthesis of planar kinematic chains by adapting a Mckay-type algorithm. Mech Mach Theory 2006; 41(9): 1021–1030.

13.

Mruthyunjaya

TS.

Kinematic structure of mechanisms revisited. Mech Mach Theory 2003; 38(4): 279–320.

14.

Crossley

. A contribution to Gruebler’s theory in the number synthesis of plane mechanisms. 1964; 86(1): 1–5.

15.

Freudenstein

Dobrjanskyj

On a theory for the type synthesis of mechanisms, applied mechanics. Springer, 1966, pp.420–428.

16.

Kaicheng

Graph theory and its applications. Tsinghua University Press, 1984.

17.

Tingli

Basic theories of mechanical systems - structural mechanics, kinematics, and dynamics. China Machine Press, 1995.

18.

Weiqing

Analysis and synthesis of linkage mechanisms. 2nd ed. Science Press, 2002.

19.

Ding

Loop theory, isomorphism discrimination of kinematic chains and establishment of Atlas Library. Yanshan University, 2007.

20.

Ding

Zhao

Huang

. Unified topological representation models of planar kinematic chains. 2009; 131: 114503.

21.

Olson

Thompson

Riley

, et al. An algorithm for automatic sketching of planar kinematic chains. 1985, pp. 106–111.

22.

Chieng

Hoeltzel

. A combinatorial approach for the automatic sketching of planar kinematic chains and epicyclic gear trains. 1990; 112(1): 6–15.

23.

Liu

Renbin

XIAO

. A new method for drawing planar mechanism kinematic chains based on loop configuration and its computer implementation. Journal of Mechanical Engineering 2002; 38(06): 21–25.

24.

Xiao

Liu

Wang

An improved approach to automatic sketching of mechanism based on loop configuration and its implementation. In: International design engineering technical conferences and computers and information in engineering conference, 2002, vol. 36533, pp.655–660. American Society of Mechanical Engineers.

25.

Ding

Huang

. A new topological description method of kinematic chain. In: 14th national conference on mechanisms in Chongqing, 2004, pp.161–164.

26.

Ding

Zhen

Automatic generation of topological graphs of kinematic chains and establishment of Atlas Library. J Mech Eng 2006; 42(04): 32–36.

27.

Nie

Liu

Qiu

A maximal loop approach to automatic sketching of mechanisms. In: ASME international mechanical engineering congress and exposition, 2007, vol. 43033, pp.501–509.

28.

Nie

Hongzhao

Maximal loop method of automatic sketching of planar closed kinematic chains. J Mech Eng 2009; 45(11): 30–37.

29.

Pucheta

Ulrich

Cardona

Combined graph layout algorithms for automated sketching of kinematic chains. In: International design engineering technical conferences and computers and information in engineering conference, 2012, vol. 45035, pp.513–523. American Society of Mechanical Engineers.

30.

Pucheta

Ulrich

Cardona

Automated sketching of non-fractionated kinematic chains. Mech Mach Theory 2013; 68: 67–82.

31.

Yang

Ding

, et al. Studying the optimal layout of topological graphs to facilitate the automatic sketching of kinematic chains. J Mech Des 2017; 139(8): 082301.

32.

Chai

. Automatic sketching of planar kinematic chains based on the optimal layout algorithm. In: Proceedings of the 2024 3rd international symposium on control engineering and robotics, 2024, pp.216–222.

33.

Zhang

Quan

Large graph layout optimization based on vision and computational efficiency: a survey. Vis Intell 2023; 1(1): 14.

34.

Yang

Ding

Kecskeméthy

Structural synthesis towards intelligent design of plane mechanisms: current status and future research trend. Mech Mach Theory 2022; 171: 104715.

35.

Lohumi

Mohammad

Khan

IA.

Hierarchical clustering approach for determination of isomorphism among planar kinematic chains and their derived mechanisms. J Mech Sci Technol 2012; 26(12): 4041–4046.

36.

Zou

Pei

Automatic topological structural synthesis algorithm of planar simple joint kinematic chains. Adv Mech Eng 2016; 8(3): 1687814016638055.