Kinematic analysis of geared robotic mechanism using matroid and T-T graph methods

In this paper, the kinematic structure of the geared robotic mechanism (GRM) is investigated with the aid of two different methods which are based on directed graphs and the methods are compared. One of the methods is Matroid Method developed by Talpasanu and the other method is Tsai-Tokad (T-T) Graph method developed by Uyguroğlu and Demirel. It is shown that the kinematic structure of the geared robotic mechanism can be represented by directed graphs and angular velocity equations of the mechanisms can be systematically obtained from the graphs. The advantages and disadvantages of both methods are demonstrated relative to each other.

[1]  A. C. Rao.  A Genetic Algorithm for Topological Characteristics of Kinematic Chains , 2000 .

[2]  Ferdinand Freudenstein,et al.  Kinematics and statics of a coupled epicyclic spur-gear train , 1972 .

[3]  L. W. Tsai.  An Application of Graph Theory to the Detection of Fundamental Circuits in Epicyclic Gear Trains , 1995 .

[4]  Miao Zhang,et al.  A modified Hopfield neural networks model for graphs-based kinematic structure design , 2009, Engineering with Computers.

[5]  M. Uyguroğlu,et al.  Kinematic analysis of tendon-driven robotic mechanisms using oriented graphs , 2006 .

[6]  Ferdinand Freudenstein,et al.  Mechanics of Epicyclic Bevel-Gear Trains , 1973 .

[7]  P. H. Roe.  Networks and systems , 1966 .

[8]  T. Davies.  Kirchhoff's circulation law applied to multi-loop kinematic chains , 1981 .

[9]  Stillman W Robinson.  The Principles of Mechanism , 1904, Nature.

[10]  Parviz E. Nikravesh,et al.  Euler Parameters in Computational Kinematics and Dynamics. Part 1 , 1985 .

[11]  Lung-Wen Tsai,et al.  The kinematics of spatial robotic bevel-gear trains , 1988, IEEE J. Robotics Autom..

[12]  George Henry Martin,et al.  Kinematics and Dynamics of Machines , 1969 .

[13]  A. Hedman.  Transmission Analysis—Automatic Derivation of Relationships , 1993 .

[14]  Sun-Lai Chang.  Redundant-Drive Backlash-Free Robotic Mechanisms: Mechanisms Creation, Analysis, and Control , 1991 .

[15]  Hasan Demirel,et al.  TSAI–TOKAD (T–T) Graph: The Combination of Non-oriented and Oriented Graphs for the Kinematics of Articulated Gear Mechanisms , 2005 .

[16]  Ettore Pennestrì,et al.  Kinematic and Power-Flow Analysis of Bevel Gears Planetary Gear Trains with Gyroscopic Complexity , 2013 .

[17]  D. Gibson,et al.  Symbolic Notation and Kinematic Equations of Motion of the Twenty-Two Basic Spur Planetary Gear Trains , 1984 .

[18]  Kishore Singhal,et al.  A Systems Approach to Three-Dimensional Multibody Systems Using Graph-Theoretic Models , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  B. Anderson,et al.  Analysis of discrete physical systems , 1967, IEEE Transactions on Automatic Control.

[20]  Franziska Frankfurter,et al.  Theory Of Machines And Mechanisms , 2016 .

[21]  R. J. Willis,et al.  On the Kinematics of the Closed Epicyclic Differential Gears , 1982 .

[22]  J. W. Polder.  A network theory for variable epicyclic gear trains , 1969 .

[23]  E. R. Maki,et al.  The Categorization Of Planetary Gear Trains For Automatic Transmissions According To Kinematic Topology , 1988 .

[24]  T. S. Mruthyunjaya,et al.  Structural Analysis of Kinematic Chains and Mechanisms Based on Matrix Representation , 1979 .

[25]  Ferdinand Freudenstein,et al.  Synthesis of kinematic structure of geared kinematic chains and other mechanisms , 1970 .

[26]  Cheng-Ho Hsu,et al.  Automatic Analysis of Kinematic Structure of Planetary Gear Trains , 1993 .

[27]  P. Murty,et al.  Open Chain Systems Based on Oriented Graph - Matroid Theory , 2008 .

[28]  Yi-Chang Wu,et al.  Automatic Detection of Embedded Structure in Planetary Gear Trains , 1997 .

[29]  N. White.  Theory of Matroids , 2008 .

[30]  Sherman Y.T. Lang,et al.  Graph-theoretic modelling of epicyclic gear systems , 2005 .

[31]  K. C. Gupta,et al.  On the motion of oblique bevel geared robot wrists , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[32]  Ferdinand Freudenstein,et al.  Kinematic Analysis of Robotic Bevel-Gear Trains , 1984 .

[33]  Ferdinand Freudenstein,et al.  An Application of Boolean Algebra to the Motion of Epicyclic Drives , 1971 .

[34]  J. D. Everett.  A Treatise on the Theory of Screws , 1901, Nature.

[35]  Lung-Wen Tsai,et al.  Kinematic Analysis of Epicyclic-Type Transmission Mechanisms Using the Concept of Fundamental Geared Entities , 1996 .

[36]  M. Uyguroĝlu,et al.  A dynamic model for the Bendix wrist , 1999 .

[37]  Cheng-Ho Hsu.  A graph representation for the structural synthesis of geared kinematic chains , 1993 .

[38]  Herman E. Koenig,et al.  Electromechanical system theory , 1961 .

[39]  C. T.R.N..  Kinematic analysis of bevel-gear trains using graphs , 2005 .

[40]  Y. Tokad,et al.  A network model for rigid-body motion , 1992 .

[41]  P. A. Simionescu,et al.  Kinematic Analysis of Epicyclic Bevel Gear Trains With Matroid Method , 2012 .

[42]  C. P. Day,et al.  Kinematic Design and Analysis of Coupled Planetary Bevel-Gear Trains , 1983 .

[43]  B. Paul.  A Unified Criterion for the Degree of Constraint of Plane Kinematic Chains , 1960 .

[44]  F.L. Litvin,et al.  Robotic Bevel-gear Differential Train , 1986 .

[45]  Robert L. Norton,et al.  Design of Machinery , 1991 .

[46]  R. Rosenberg,et al.  System Dynamics: Modeling and Simulation of Mechatronic Systems , 2006 .

[47]  C. Barus.  A treatise on the theory of screws , 1998 .

[48]  H. Whitney.  On the Abstract Properties of Linear Dependence , 1935 .

[49]  Cheng-Ho Hsu.  A graph notation for the kinematic analysis of differential gear trains , 1992 .

[50]  Józef Wojnarowski,et al.  The application of signal flow graphs—the kinematic analysis of planetary gear trains , 1975 .

[51]  Y. Tokad,et al.  Kinematic Analysis of Robotic Bevel-Gear Trains: An Application of Network Model Approach , 1998 .

[52]  P. A. Simionescu,et al.  Application of matroid method in kinematic analysis of parallel axes epicyclic gear trains , 2006 .

[53]  Ferdinand Freudenstein,et al.  Kinematic Synthesis of Linkages , 1965 .

[54]  Ferdinand Freudenstein,et al.  An Application of Dual Graphs to the Automatic Generation of the Kinematic Structures of Mechanisms , 1986 .

[55]  Lung-Wen Tsai,et al.  Mechanism Design: Enumeration of Kinematic Structures According to Function , 2001 .

[56]  Stefan Staicu.  Inverse dynamics of a planetary gear train for robotics , 2008 .

[57]  Offer Shai,et al.  The multidisciplinary combinatorial approach (MCA) and its applications in engineering , 2001, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[58]  S. Staicu,et al.  Inverse dynamics of a 3-PRC parallel kinematic machine , 2012 .

[59]  Lung-Wen Tsai,et al.  Computer-Aided Sketching of Epicyclic-Type Automatic Transmission Gear Trains , 1996 .

[60]  Donald R. Riley,et al.  Topological Analysis of Single-Degree-of-Freedom Planetary Gear Trains , 1991 .

[61]  J. Kopeć,et al.  Gears and graphs , 2006 .