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Simulation Software Performances And Examples

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Simulation Software Performances And Examples

  1. 1. Simulation Software: Performances and Examples Dr. Mario Acevedo Multibody Systems and Mechatronics Laboratory Engineering School, UNIVERSIDAD PANAMERICANA (Mexico City)
  2. 2. Agenda <ul><li>Objective and scope </li></ul><ul><li>Simulation software: overview </li></ul><ul><li>Kinematics simulation </li></ul><ul><li>Dynamics simulation </li></ul><ul><li>Simulation using web technology </li></ul><ul><li>Final remarks </li></ul>
  3. 3. Objective and Scope
  4. 4. About this Presentation <ul><li>Objectives: </li></ul><ul><ul><li>Introduce the topic of simulation software for robotic multibody systems </li></ul></ul><ul><ul><ul><li>Explain the problems that can be solved </li></ul></ul></ul><ul><ul><ul><li>Show an idea of the implementation </li></ul></ul></ul><ul><ul><ul><li>Motivate collaboration in the study of problems, prototypes: </li></ul></ul></ul><ul><ul><ul><ul><li>The development of a common language to describe systems (XML) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Use of WEB technologies for publications and collaboration </li></ul></ul></ul></ul><ul><li>Scope </li></ul><ul><ul><li>All theory and examples will be treated in 2D. </li></ul></ul><ul><ul><ul><li>3D systems are treated in similar way </li></ul></ul></ul>
  5. 5. Simulation Software: Overview
  6. 6. Simulation of MBS <ul><li>Many computer codes have been developed but they differ in: </li></ul><ul><ul><li>Model description </li></ul></ul><ul><ul><li>Choice of basic principles of mechanics </li></ul></ul><ul><ul><li>Topological structure </li></ul></ul><ul><ul><li>Numeric vs. Symbolic </li></ul></ul><ul><ul><li>Formulations </li></ul></ul>
  7. 7. MBS Simulation Options Modeling Cartesian coordinates Relative coordinates Fully Cartesian coordinates Graph theory Spatial algebra Principles of Mechanics Virtual Power Newton-Euler Hamilton’s Principle Lagrange’s Equations Gibbs-Apell Equations Formulations Spatial Algebra Velocity Transformations Recursive Methods Baumgarte Stabilization Penalty Methods Augmented Lagrangian Numerical Integration ODE Methods Implicit Integrators Explicit Integrators Single step vs Multistep DAE Methods Backward Difference Implicit Runge-Kutta Intelligent Simulator
  8. 8. Software for Multibody Systems Simulation 1 <ul><li>ADAMS by Mechanical Dynamics Inc., United States </li></ul><ul><li>alaska , by Technical University of Chemnitz, Germany </li></ul><ul><li>AUTOLEV , by OnLine Dynamics Inc., United States </li></ul><ul><li>AutoSim by Mechanical Simulation Corp., United States </li></ul><ul><li>COMPAMM by CEIT, Spain </li></ul><ul><li>DADS by CADSI, United States </li></ul><ul><li>Dynawiz by Concurrent Dynamics International </li></ul><ul><li>DynaFlex by University of Waterloo, Canada </li></ul><ul><li>Hyperview and Motionview by Altair Engineering, United States </li></ul><ul><li>MECANO by Samtech, Belgium </li></ul>
  9. 9. Software for Multibody Systems Simulation 1 <ul><li>MBDyn by Politecnico di Milano, Italy </li></ul><ul><li>MBSoft by Universite Catholique de Louvain, Belgium </li></ul><ul><li>NEWEUL by University of Stuttgart, Germany </li></ul><ul><li>RecurDyn by Function Bay Inc., Korea </li></ul><ul><li>Robotran by Universite Catholique de Louvain, Belgium </li></ul><ul><li>SAM by Artas Engineering Software, The Netherlands </li></ul><ul><li>SD/FAST by PTC, United States </li></ul><ul><li>SIMPACK by INTEC GmbH, Germany </li></ul><ul><li>Universal Mechanism by Bryansk State Technical University, Russia </li></ul><ul><li>Working Model by Knowledge Revolution, United States </li></ul>
  10. 10. Actual State of MBS Simulators Model Description User Interface SOLVER Post-processor 1 Model Description User Interface SOLVER Post-processor 2 Model Description User Interface SOLVER Post-processor n … … … …
  11. 11. Desired Goal of MBS Model Description ( Neutral Data Format ) User Interface SOLVER Signal Analysis 1 User Interface SOLVER Animation 2 User Interface SOLVER Strength Analysis n … … Standardized Result Description Visualization
  12. 12. Kinematics Simulation <ul><ul><li>Modeling: </li></ul></ul><ul><ul><ul><li>Coordinates, Constraints and Joints library </li></ul></ul></ul><ul><ul><li>Analysis: </li></ul></ul><ul><ul><ul><li>Positions, Velocities and Accelerations </li></ul></ul></ul>
  13. 13. Coordinates for Modeling <ul><li>Relative coordinates </li></ul><ul><ul><li>Minimum set of coordinates </li></ul></ul><ul><li>Cartesian coordinates </li></ul><ul><ul><li>Also known as Reference Point coordinates </li></ul></ul><ul><li>Fully Cartesian coordinates </li></ul><ul><ul><li>Also known as Natural Coordinates </li></ul></ul><ul><li>Mixed coordinates </li></ul>
  14. 14. Constraints Equations <ul><li>If the selected set of coordinates is dependent, a set of constraint equations can be found </li></ul><ul><ul><li>Constraint equations relate the dependent coordinates and define the movement geometry </li></ul></ul><ul><ul><li>NoC = NoDC – NoDOF </li></ul></ul><ul><ul><ul><li>NoC: Number of Constraints </li></ul></ul></ul><ul><ul><ul><li>NoDC: Number of Dependent Coordinates </li></ul></ul></ul><ul><ul><ul><li>NoDOF: Number of Degrees of Freedom </li></ul></ul></ul><ul><ul><li>Constraint equations generally are not linear </li></ul></ul>
  15. 15. Relative Coordinates <ul><li>Open kinematic chain </li></ul><ul><ul><li>Model </li></ul></ul><ul><li>Close loop </li></ul><ul><ul><li>Constraints </li></ul></ul><ul><ul><ul><li>No constraint equations since it is an open kinematic chain </li></ul></ul></ul>    1 2 X Y
  16. 16. Relative Coordinates <ul><li>Close kinematic chain </li></ul><ul><ul><li>Model </li></ul></ul><ul><li>Constraints </li></ul><ul><ul><li>NoDC = 3 </li></ul></ul><ul><ul><li>NoDOF = 1 </li></ul></ul><ul><ul><li>NoC = 3 - 1 = 2 </li></ul></ul><ul><ul><li>Non linear </li></ul></ul><ul><ul><li>Transcendental functions </li></ul></ul>  1 X Y   2   O D 3
  17. 17. Cartesian Coordinates <ul><li>Open kinematic chain </li></ul><ul><ul><li>Model </li></ul></ul><ul><li>Constraints </li></ul><ul><ul><li>NoDC = 6 </li></ul></ul><ul><ul><li>NoDOF = 2 </li></ul></ul><ul><ul><li>NoC = 6 - 2 = 4 </li></ul></ul><ul><ul><li>Non linear </li></ul></ul>    1 2 X Y y  ( x  y   ( x  y  
  18. 18. Cartesian Coordinates <ul><li>Close kinematic chain </li></ul><ul><ul><li>Model </li></ul></ul><ul><li>Constraints </li></ul><ul><ul><li>NoDC = 9 </li></ul></ul><ul><ul><li>NoDOF = 1 </li></ul></ul><ul><ul><li>NoC = 9 - 1 = 8 </li></ul></ul><ul><ul><li>Non linear </li></ul></ul>  2   O D 1 X Y ( x  y     ( x  y   ( x  y   3
  19. 19. Fully Cartesian Coordinates <ul><li>Open kinematic chain </li></ul><ul><ul><li>Model </li></ul></ul><ul><li>Constraints </li></ul><ul><ul><li>NoDC = 4 </li></ul></ul><ul><ul><li>NoDOF = 2 </li></ul></ul><ul><ul><li>NoC = 4 - 2 = 2 </li></ul></ul><ul><ul><li>Non linear </li></ul></ul>1 X Y y  ( x  y   ( x  y   2 ( x  y  
  20. 20. Fully Cartesian Coordinates <ul><li>Close kinematic chain </li></ul><ul><ul><li>Model </li></ul></ul><ul><li>Constraints </li></ul><ul><ul><li>NoDC = 4 </li></ul></ul><ul><ul><li>NoDOF = 1 </li></ul></ul><ul><ul><li>NoC = 4 - 1 = 3 </li></ul></ul><ul><ul><li>Non linear </li></ul></ul>2 O D 1 X Y ( x  y   ( x  y   3
  21. 21. Constraints Origin <ul><li>Constraint equations generally are obtained from: </li></ul><ul><ul><li>Close loop equations </li></ul></ul><ul><ul><ul><li>Relative coordinates </li></ul></ul></ul><ul><ul><li>The rigid body condition of the elements </li></ul></ul><ul><ul><ul><li>Fully Cartesian coordinates </li></ul></ul></ul><ul><ul><li>Joints definition </li></ul></ul><ul><ul><ul><li>Cartesian and Fully Cartesian coordinates </li></ul></ul></ul><ul><li>Joints definition can be part of a joints library </li></ul><ul><ul><li>Treat the multibody system as a LEGO </li></ul></ul><ul><ul><li>Use computational tools in multibody systems </li></ul></ul>
  22. 22. Kinematics of MBS <ul><li>Set of dependent coordinates: q </li></ul><ul><li>Positions analysis. </li></ul><ul><ul><li>Set of constraint equations: </li></ul></ul><ul><ul><ul><li>Solution using iterative procedures (Newton Raphson) </li></ul></ul></ul><ul><li>Velocity analysis: </li></ul><ul><li>Acceleration analysis: </li></ul>( 3 ) ( 2 ) ( 1 )
  23. 23. Joints Definition <ul><li>Limited to systems in plane (2D) </li></ul><ul><ul><li>Cartesian coordinates </li></ul></ul><ul><li>Lower-pairs : revolute and prismatic </li></ul><ul><ul><li>Show the general modeling for the joint </li></ul></ul><ul><ul><li>Identify the corresponding elements in and </li></ul></ul><ul><li>Higher-pairs : gears, cams, etc. </li></ul><ul><ul><li>Require some information on the shape of the connected bodies </li></ul></ul><ul><ul><li>Require to know the shape or curvature of a slot in one of the bodies </li></ul></ul>
  24. 24. Modeling of the Revolute Joint X Y i j r i r j P
  25. 25. Modeling of the Prismatic Joint 1 X Y i j r i r j P i Q i P j
  26. 26. Modeling of the Prismatic Joint 2
  27. 27. Kinematics Simulation Computer Implementation Examples
  28. 28. Dynamics Simulation <ul><ul><li>Constraint Dynamics </li></ul></ul><ul><ul><ul><li>Lagrange multipliers </li></ul></ul></ul><ul><ul><ul><li>Velocity transformations </li></ul></ul></ul><ul><ul><ul><li>Numerical integration </li></ul></ul></ul>
  29. 29. Lagrange Multipliers <ul><li>The general form of equations of motion using Lagrange multipliers is </li></ul><ul><ul><li>This equation represents m equations in n unknowns, it is necessary to give n more equations, a possibility are acceleration equations </li></ul></ul><ul><li>Equations to solve </li></ul>( 4 ) ( 5 )
  30. 30. Velocity Transformations <ul><li>Based on the fact that it is possible to express equations (5) in terms of a different set coordinates by a linear transformation (velocity transformation) </li></ul><ul><ul><li>Open loop systems </li></ul></ul><ul><ul><li>Close loop systems </li></ul></ul><ul><ul><ul><li>Lagrange multipliers </li></ul></ul></ul><ul><ul><ul><li>Second velocity transformation </li></ul></ul></ul>( 7 ) ( 6 ) ( 8 ) ( 9 ) ( 10 )
  31. 31. Numerical vs Symbolical Model description Data input Formalism Numerical equations Simulation Local output Global result Next time step Model variation Parameter variation Model description Data input Formalism Symbolical equations Simulation Local output Global result Next time step Model variation Parameter variation
  32. 32. Dynamics Simulation <ul><li>Lagrange Multipliers </li></ul><ul><ul><li>Computer Implementation </li></ul></ul><ul><ul><li>Examples </li></ul></ul><ul><ul><ul><li>Inverse dynamics </li></ul></ul></ul><ul><ul><ul><li>Direct dynamics </li></ul></ul></ul>
  33. 33. Dynamics Simulation <ul><li>Velocity transformations </li></ul><ul><ul><li>Computer Implementation </li></ul></ul><ul><ul><li>Examples </li></ul></ul><ul><ul><ul><li>Inverse dynamics </li></ul></ul></ul><ul><ul><ul><li>Direct dynamics </li></ul></ul></ul>
  34. 34. Simulation using WEB WEB Server Active Pages Java/JavaScript
  35. 35. References 1 <ul><li>Cuadrado, J. et.al. “ Modeling and Solution Methods for Efficient Real-Time Simulation of Multibody Dynamics ”, Multibody Systems Dynamics, Vol. 1, No. 3, 1997. </li></ul><ul><li>García de Jalón, J. and Bayo E., Kinematic and Dynamic Simulation of Multibody Systems, The Real-Time Challenge , Springer-Verlag, 1993. </li></ul><ul><li>Schiehlen, S., “ Multibody Systems Dynamics: Roots and Perspectives ”, Multibody Systems Dynamics, Vol. 1, No. 2, 1997. </li></ul><ul><li>Shabana, A., Computational Dynamics , Wiley, 1994. </li></ul>

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