The relations among the associated linkages (ALs), the redundant constraints, the passive degree of freedom (DoF), and the degree of freedom are studied systematically for the type synthesis of the closed mechanisms in this paper. First, the kinematic pairs with multidegree of freedoms are formed by combination of the basic joints with single degree of freedom in series, and the formulae are derived for the calculation of the degree of freedoms of the associated linkages, the number of the basic joints, and the valid numbers of the basic links in the associated linkages. Second, many different associated linkages and the number of basic links are derived, and the relations among the associated linkages, the redundant constraints, the passive degree of freedom, and the degree of freedoms of the closed mechanisms are analyzed. Third, some topology graphs are derived and the relative closed mechanisms with the redundant constraints and the passive degree of freedom are synthesized. Finally, the redundant constraints and the degree of freedoms of the closed mechanisms are determined.
Issue Section:
Research Papers
References
1.
Gogu
, G.
, 2008, Structural Synthesis of Parallel Robots: Part 1: Methodology
, Springer
, New York
.2.
Huang
, Z.
, Zhao
, Y. S.
, and Zhao
, T. S.
, 2006, Advanced Spatial Mechanism
, High Education Press
, Beijing, China
.3.
Huang
, Z.
, Liu
, J.
, and Zeng
, D.
, 2009, “A General Methodology for Mobility Analysis of Mechanisms Based on Constraint Screw Theory
,” Sci. China, Ser. E: Technol. Sci.
, 52
(5
), pp. 1337
–1347
.4.
Kim
, J. G.
, and Yoon
, Y. S.
, 2005, “Systematic Development of Vehicle Suspensions Having Passive DOF and/or Redundant Constraint
,” Int. J. Veh. Des.
, 38
(4
), pp. 275
–289
.5.
Zhao
, J. S.
, Zhou
, K.
, and Feng
, Z. J.
, 2004, “A Theory of Degrees of Freedom for Mechanisms
,” Mech. Mach. Theory
, 39
(6
), pp. 621
–643
.6.
Gan
, D.
, Dai
, J. S.
, and Liao
, Q.
, 2009, “Mobility Change in Two Types of Metamorphic Parallel Mechanisms
,” Trans. ASME, J. Mech. Rob.
, 1
(4
), p. 041007
.7.
Gao
, F.
, Zhang
, Y.
, and Li
, W. M.
, 2005, “Type Synthesis of 3-DOF Reducible Translational Mechanisms
,” Robotica
, 23
(2
), pp. 239
–245
.8.
Li
, W. M.
, Gao
, F.
, and Zhang
, J. J.
, 2005, “R-CUBE, A Decoupled Parallel Manipulator Only With Revolute Joints
,” Mech. Mach. Theory
, 40
(4
), pp. 467
–473
.9.
Kong
, X. W.
, and Gosselin
, C. M.
, 2007, Type Synthesis of Parallel Mechanisms
(Springer Tracts in Advanced Robotics
), Springer-Verlag, Berlin, Heidelberg.10.
Dai
, J. S.
, Huang
, Z.
, and Lipkin
, H.
, 2006, “Mobility of Over Constrained Parallel Mechanisms
,” ASME J. Mech. Des.
, 128
(1
), pp. 220
–229
.11.
Vucina
, D.
, and Freudenstein
, F.
, 1991, “Application of Graph Theory and Nonlinear Programming to the Kinematic Synthesis of Mechanisms
,” Mech. Mach. Theory
, 26
(6
), pp. 553
–563
.12.
Tsai
, L. W.
, 2001, Mechanism Design: Enumeration of Kinematic Structures According to Function
, CRC Press
, Boca Raton, Florida, pp. 102
–328
.13.
Yan
, H. S.
, and Hsu
, C. H.
, 1988, “Contracted Graphs of Kinematic Chains With Multiple Joints
,” Math. Comput. Modell.
, 10
(9
), pp. 681
–695
.14.
Yang
, T. L.
, 2003, Topology Structure Design of Robot Mechanisms
, China Machine Press
, Beijing
.15.
Johnson
, R. C.
, 1987, Mechanical Design Synthesis: Creative Design and Optimization
, 2nd ed., Huntington
, New York
.16.
Lu
, Y.
, and Leinonen
, T.
, 2005, “Type Synthesis of Unified Planar-Spatial Mechanisms by Systematic Linkage and Topology Matrix-Graph Technique
,” Mech. Mach. Theory
, 40
(10
), pp. 1145
–1163
.17.
Tuttle
, E. R.
, Peterson
, S. W.
, and Titus
, J. E.
, 1989, “Further Applications of Group Theory to the Enumeration and Structural Analysis of Basic Kinematic Chains
,” ASME J. Mech., Transm., Autom. Des.
, 111
, pp. 494
–497
.18.
Hess-Coelho
, T. A.
, 2006, “Topological Synthesis of a Parallel Wrist Mechanism
,” ASME J. Mech. Des.
, 128
(1
), pp. 230
–235
.19.
Pucheta
, M.
, and Cardona
, A.
, 2007, “An Automated Method for Type Synthesis of Planar Linkages Based on a Constrained Subgraph Isomorphism Detection
,” Multibody Syst. Dyn.
, 18
(2
), pp. 233
–258
.20.
Hervé
, J. H.
, 1999, “The Lie Group of Rigid Displacements, a Fundamental Tool for Mechanical Design
,” Mech. Mach. Theory
, 34
(5
), pp. 719
–730
.21.
Wang
, X. Y.
, Baron
, L.
, and Cloutier
, G.
, 2008, “Topological and Geometrical Synthesis of Three-Degree-of-Freedom Fully Parallel Manipulators by Instantaneous Kinematics
,” ASME J. Mech. Des.
, 130
(3
), p. 032301
.22.
Lu
, Y.
, Mao
, B. Y.
, and Yu
, J. P.
, 2011, “Derivation of Valid Contracted Graphs With Pentagonal Links Plus Quaternary Links or Ternary Links for Closed Mechanisms by Arrays
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 225
(4
), pp. 1001
–1013
.23.
Lu
, Y.
, Ding
, L.
, and Yu
, J. P.
, 2010, “Autoderivation of Topological Graphs for Type Synthesis of Planar 3DOF Parallel Mechanisms
,” ASME J. Mech. Rob.
, 2
(1
), p. 011002
.24.
Lu
, Y.
, Ding
, L.
, Li
, S. Y.
, and Yu
, J. P.
, 2010, “Derivation of Topological Graphs of Some Planar 4-DOF Redundant Closed Mechanisms by Contracted Graphs and Arrays
,” ASME J. Mech. Rob.
, 2
(3
), p. 031011
.25.
Hu
, B.
, Lu
, Y.
, Zhang
, X. L.
, and Yu
, J. P.
, 2012, “Unified Analysis of Statics of Some Limited-DOF Parallel Manipulators
,” Robotica
30
(4
), pp. 333
–342
.26.
Li
, Y. M.
, and Xu
, Q. S.
, 2008, “Stiffness Analysis for a 3-PUU Parallel Kinematic Machine
,” Mech. Mach. Theory
, 43
(2
), pp. 186
–200
.27.
Stock
, M.
, and Miller
, K.
, 2003, “Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot
,” ASME J. Mech. Des.
, 125
(2
), pp. 292
–301
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
