Evolution of the DeNOC-based dynamic modelling for multibody systems

Abstract. Dynamic modelling of a multibody system plays very essential role in its analyses. As a result, several methods for dynamic modelling have evolved over the years that allow one to analyse multibody systems in a very efficient manner. One such method of dynamic modelling is based on the concept of the Decoupled Natural Orthogonal Complement (DeNOC) matrices. The DeNOC-based methodology for dynamics modelling, since its introduction in 1995, has been applied to a variety of multibody systems such as serial, parallel, general closed-loop, flexible, legged, cam-follower, and space robots. The methodology has also proven useful for modelling of proteins and hyper-degree-of-freedom systems like ropes, chains, etc. This paper captures the evolution of the DeNOC-based dynamic modelling applied to different type of systems, and its benefits over other existing methodologies. It is shown that the DeNOC-based modelling provides deeper understanding of the dynamics of a multibody system. The power of the DeNOC-based modelling has been illustrated using several numerical examples.

[1]  Subir Kumar Saha,et al.  Denavit-Hartenberg Parameterization of Euler Angles , 2012 .

[2]  Peter Eberhard,et al.  Computational Dynamics of Multibody Systems: History, Formalisms, and Applications , 2006 .

[3]  Subir Kumar Saha,et al.  Simulation of Industrial Manipulators Based on the UDUT Decomposition of Inertia Matrix , 2003 .

[4]  Sandipan Bandyopadhyay,et al.  Dynamics of serial kinematic chains with large number of degrees-of-freedom , 2014 .

[5]  Oussama Khatib,et al.  A unified approach for motion and force control of robot manipulators: The operational space formulation , 1987, IEEE J. Robotics Autom..

[6]  S. S. Kim,et al.  A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations , 1986 .

[7]  Thomas R. Kane,et al.  The Use of Kane's Dynamical Equations in Robotics , 1983 .

[8]  J. K. Dutt,et al.  Dynamics of Tree-Type Robotic Systems , 2012 .

[9]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .

[10]  N. K. Mani,et al.  Application of Singular Value Decomposition for Analysis of Mechanical System Dynamics , 1985 .

[11]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[12]  Subir Kumar Saha,et al.  A decomposition of the manipulator inertia matrix , 1997, IEEE Trans. Robotics Autom..

[13]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

[14]  Ronald L. Huston,et al.  On Constraint Equations—A New Approach , 1974 .

[15]  Arend L. Schwab,et al.  Dynamics of Multibody Systems , 2007 .

[16]  Hooshang Hemami,et al.  Modeling of Nonholonomic Dynamic Systems With Applications , 1981 .

[17]  Abhinandan Jain,et al.  Spatial Operator Algebra for multibody system dynamics , 1992 .

[18]  Rajeevlochana G. Chittawadigi,et al.  Recursive Robot Dynamics in RoboAnalyzer , 2011 .

[19]  Subir Kumar Saha,et al.  The UDU/sup T/ decomposition of manipulator inertia matrix , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[20]  Wayne J. Book,et al.  Modeling Mechanisms with Nonholonomic Joints Using the Boltzmann-Hamel Equations , 1997, Int. J. Robotics Res..

[21]  J. Denavit,et al.  A kinematic notation for lower pair mechanisms based on matrices , 1955 .

[22]  Jorge Angeles,et al.  Dynamic Simulation of n-Axis Serial Robotic Manipulators Using a Natural Orthogonal Complement , 1988, Int. J. Robotics Res..

[23]  J. Angeles,et al.  Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator , 2005 .

[24]  Subir Kumar Saha,et al.  Dynamics and Balancing of Multibody Systems , 2008 .

[25]  Werner Schiehlen,et al.  Multibody Systems Handbook , 2012 .

[26]  John McPhee,et al.  On the use of linear graph theory in multibody system dynamics , 1996 .

[27]  Werner Schiehlen,et al.  Multibody System Dynamics: Roots and Perspectives , 1997 .

[28]  J. Angeles,et al.  Dynamics of Nonholonomic Mechanical Systems Using a Natural Orthogonal Complement , 1991 .

[29]  P. Sundarraman,et al.  Modeling and analysis of a fuel-injection pump used in diesel engines , 2012 .

[30]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[31]  J. Angeles,et al.  An algorithm for the inverse dynamics of n-axis general manipulators using Kane's equations , 1989 .

[32]  Hauz Khas,et al.  Dynamic model simplification of serial manipulators , 2006 .

[33]  Subir Kumar Saha,et al.  Analytical Expression for the Inverted Inertia Matrix of Serial Robots , 1999, Int. J. Robotics Res..

[34]  Subir Kumar Saha.  Introduction to Robotics , 2008 .

[35]  S. Saha,et al.  An improved dynamic modeling of a multibody system with spherical joints , 2009 .

[36]  Subir Kumar Saha,et al.  Recursive dynamics simulator (ReDySim): A multibody dynamics solver , 2012 .

[37]  J. G. Jalón,et al.  A Fast and Simple Semi-Recursive Formulation for Multi-Rigid-Body Systems , 2005 .

[38]  Wisama Khalil,et al.  A new geometric notation for open and closed-loop robots , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[39]  Subir Kumar Saha,et al.  Constraint Wrench Formulation for Closed-Loop Systems Using Two-Level Recursions , 2007 .

[40]  S. Saha.  Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices , 1999 .

[41]  Frank Chongwoo Park,et al.  A Lie Group Formulation of Robot Dynamics , 1995, Int. J. Robotics Res..

[42]  Dieter Bestle,et al.  An Orthogonal Complement Matrix Formulation for Constrained Multibody Systems , 1994 .

[43]  Ronald L. Huston,et al.  Dynamics of Multibody Systems , 1988 .

[44]  Roger W. Brockett,et al.  Dynamics of Kinematic Chains , 1996, Int. J. Robotics Res..

[45]  J. Angeles,et al.  The Formulation of Dynamical Equations of Holonomic Mechanical Systems Using a Natural Orthogonal Complement , 1988 .

[46]  Werner Schiehlen,et al.  RECURSIVE KINEMATICS AND DYNAMICS FOR PARALLEL STRUCTURED CLOSED-LOOP MULTIBODY SYSTEMS* , 2001 .

[47]  R. Pappu,et al.  Analysis of the conformational dependence of mass-metric tensor determinants in serial polymers with constraints. , 2004, The Journal of chemical physics.

[48]  S. Saha,et al.  Modular framework for dynamic modeling and analyses of legged robots , 2012 .

[49]  Dynamics and control of space manipulators during a satellite capturing operation , 2005 .

[50]  J. W. Kamman,et al.  Constrained multibody system dynamics: An automated approach , 1984 .

[51]  Subir Kumar Saha,et al.  A recursive, numerically stable, and efficient simulation algorithm for serial robots , 2007 .

[52]  D. T. Greenwood.  Principles of dynamics , 1965 .

[53]  C. G. Rajeevlochana,et al.  RoboAnalyzer: 3D Model Based Robotic Learning Software , 2011 .