Abstract
The structural synthesis of planar kinematic chains (KCs) with prismatic pairs (P-pairs) is the basis of innovating mechanisms containing P-pairs. In the literature, only a little research has been carried out to synthesize planar KCs with P-pairs. Moreover, these synthesis methods for KCs with P-pairs involve all possible combinations of edges, resulting in a large number of isomorphic KCs and a low synthesis efficiency. In this study, our previous similarity recognition algorithm is improved and applied to synthesize planar KCs with P-pairs. Only a small number of isomorphic KCs are generated in the synthesis process and the synthesis efficiency is greatly enhanced. Our method is applied to synthesize 9-link 2-DOF, 10-link 1-DOF, and 11-link 2-DOF KCs with one and two P-pairs. Our synthesis results are consistent with those of the existing literature. The present work is helpful to design mechanisms with P-pairs and can be extended to mechanisms with other types of kinematic pairs.
Issue Section:
Research Papers
References
1.
Tsai
, L. W.
, 2000
, Mechanism Design: Enumeration of Kinematic Structures According to Function
, CRC Press
, Boca Raton, FL
.2.
Yan
, H. S.
, 1992
, “A Methodology for Creative Mechanism Design
,” Mech. Mach. Theory
, 27
(3
), pp. 235
–242
. 3.
Yang
, W.
, and Ding
, H.
, 2019
, “The Complete set of one-Degree-of-Freedom Planetary Gear Trains With up to Nine Links
,” ASME J. Mech. Des.
, 141
(4
), p. 043301
. 4.
Gilmartin
, M. J.
, and Duffy
, J.
, 1969
, “Limit Positions of Four-Link Spatial Mechanisms—2. Mechanisms Having Revolute, Cylindric and Prismatic Pairs
,” J. Mech.
, 4
(3
), pp. 273
–281
. 5.
Freudenstein
, F.
, and Maki
, E. R.
, 1979
, “The Creation of Mechanisms According to Kinematic Structure and Function
,” Environ. Plan B Plann Des.
, 6
(4
), pp. 375
–391
. 6.
Yan
, H. S.
, and Hwang
, Y. W.
, 1991
, “The Specialization of Mechanisms
,” Mech. Mach. Theory
, 26
(6
), pp. 541
–551
. 7.
Chen
, D. Z.
, and Pai
, W. M.
, 2005
, “A Methodology for Conceptual Design of Mechanisms by Parsing Design Specifications
,” ASME J. Mech. Des.
, 127
(6
), pp. 1039
–1044
. 8.
Pucheta
, M.
, and Cardona
, A.
, 2007
, “An Automated Method for Type Synthesis of Planar Linkages Based on a Constrained Subgraph Isomorphism Detection
,” Multibody Sys. Dyn.
, 18
(2
), pp. 233
–258
. 9.
Popescu
, I.
, and Marghitu
, D. B.
, 2008
, “Structural Design of Planar Mechanisms With Dyads
,” Multibody Sys. Dyn.
, 19
(4
), pp. 407
–425
. 10.
Ding
, W.
, and Yao
, Y. A.
, 2013
, “A Novel Deployable Hexahedron Mobile Mechanism Constructed by Only Prismatic Joints
,” ASME J. Mech. Rob.
, 5
(4
), p. 041016
. 11.
Li
, S. J.
, Wang
, H. G.
, and Dai
, J. S.
, 2015
, “Assur-Group Inferred Structural Synthesis for Planar Mechanisms
,” ASME J. Mech. Rob.
, 7
(4
), p. 041001
. 12.
Kang
, S. W.
, Kim
, S. I.
, and Kim
, Y. Y.
, 2016
, “Topology Optimization of Planar Linkage Systems Involving General Joint Types
,” Mech. Mach. Theory
, 104
, pp. 130
–160
. 13.
Olson
, D. G.
, Erdman
, A. G.
, and Riley
, D. R.
, 1985
, “A Systematic Procedure for Type Synthesis of Mechanisms With Literature Review
,” Mech. Mach. Theory
, 20
(4
), pp. 285
–295
. 14.
Hung
, C. C.
, Yan
, H. S.
, and Pennock
, G. R.
, 2008
, “A Procedure to Count the Number of Planar Mechanisms Subject to Design Constraints From Kinematic Chains
,” Mech. Mach. Theory
, 43
(6
), pp. 676
–694
. 15.
Mruthyunjaya
, T.
, 1984
, “A Computerized Methodology for Structural Synthesis of Kinematic Chains: Part 1—Formulation
,” Mech. Mach. Theory
, 19
(6
), pp. 487
–495
. 16.
Rao
, A.
, 1997
, “Hamming Number Technique—II. Generation of Planar Kinematic Chains
,” Mech. Mach. Theory
, 32
(4
), pp. 489
–499
. 17.
Tuttle
, E. R.
, 1996
, “Generation of Planar Kinematic Chains
,” Mech. Mach. Theory
, 31
(6
), pp. 729
–748
. 18.
Sunkari
, R. P.
, and Schmidt
, L. C.
, 2006
, “Structural Synthesis of Planar Kinematic Chains by Adapting a Mckay-Type Algorithm
,” Mech. Mach. Theory
, 41
(9
), pp. 1021
–1030
. 19.
Ding
, H.
, Cao
, W.
, Kecskeméthy
, A.
, and Huang
, Z.
, 2012
, “Complete Atlas Database of 2-DOF Kinematic Chains and Creative Design of Mechanisms
,” ASME J. Mech. Des.
, 134
(3
), p. 031006
. 20.
Ding
, H.
, Hou
, F.
, Kecskeméthy
, A.
, and Huang
, Z.
, 2012
, “Synthesis of the Whole Family of Planar 1-DOF Kinematic Chains and Creation of Their Atlas Database
,” Mech. Mach. Theory
, 47
, pp. 1
–15
. 21.
Yan
, H. S.
, and Chiu
, Y. T.
, 2015
, “On the Number Synthesis of Kinematic Chains
,” Mech. Mach. Theory
, 89
, pp. 128
–144
. 22.
Ding
, H.
, Huang
, P.
, Yang
, W.
, and Kecskeméthy
, A.
, 2016
, “Automatic Generation of the Complete Set of Planar Kinematic Chains With up to six Independent Loops and up to 19 Links
,” Mech. Mach. Theory
, 96
, pp. 75
–93
. 23.
Dharanipragada
, V.
, and Chintada
, M.
, 2016
, “Split Hamming String as an Isomorphism Test for One Degree-of-Freedom Planar Simple-Jointed Kinematic Chains Containing Sliders
,” ASME J. Mech. Des.
, 138
(8
), p. 082301
. 24.
Eleashy
, H.
, 2018
, “A New Atlas for 8-Bar Kinematic Chains With up to 3 Prismatic Pairs Using Joint Sorting Code
,” Mech. Mach. Theory
, 124
, pp. 118
–132
. 25.
Yang
, W.
, Ding
, H.
, and Kecskeméthy
, A.
, 2018
, “Automatic Synthesis of Plane Kinematic Chains with Prismatic Pairs and up to 14 Links
,” Mech. Mach. Theory
, 132
, pp. 236
–247
. 26.
Harary
, F.
, and Palmer
, E. M.
, 1966
, “On Similar Points of a Graph
,” J. Math. Mech.
, 15
, pp. 623
–630
.27.
Freudenstein
, F.
, 1967
, “The Basic Concepts of Polya's Theory of Enumeration, With Application to the Structural Classification of Mechanisms
,” J. Mech.
, 2
(3
), pp. 275
–290
. 28.
Lv
, T.
, 1989
, “Sufficient and Necessary Conditions for Similarity
,” J. Beijing Univ. Technol.
, 15
(4
), pp. 63
–66
.29.
Wang
, Y. X.
, and Yan
, H. S.
, 2002
, “Computerized Rules-Based Regeneration Method for Conceptual Design of Mechanisms
,” Mech. Mach. Theory
, 37
(9
), pp. 833
–849
. 30.
Rao
, A. C.
, 2000
, “A Genetic Algorithm for Topological Characteristics of Kinematic Chains
,” ASME J. Mech. Des.
, 122
(2
), pp. 228
–231
. 31.
Kuo
, C.
, and Shih
, K.
, 2008
, “Computational Identification of Link Adjacency and Joint Incidence in Kinematic Chains and Mechanisms
,” ASME J. Mech. Des.
, 130
(8
), p. 084501
. 32.
Sun
, L.
, Cui
, R.
, Ye
, Z.
, Zhou
, Y.
, Xu
, Y.
, and Wu
, C.
, 2020
, “Similarity Recognition and Isomorphism Identification of Planar Kinematic Chains
,” Mech. Mach. Theory
, 145
, p. 103678
. 33.
Sun
, L.
, Ye
, Z.
, Cui
, R.
, Yang
, W.
, and Wu
, C.
, 2020
, “Compound Topological Invariant Based Method for Detecting Isomorphism in Planar Kinematic Chains
,” ASME J. Mech. Rob.
, 12
(5
), p. 054504
. 34.
Lu
, K.
, and Lu
, H.
, 1995
, Graph Theory and Application
, Tsinghua University Press
, Beijing
.Copyright © 2021 by ASME
You do not currently have access to this content.
