- 1. Simulation Software: Performances and Examples Dr. Mario
Acevedo Multibody Systems and Mechatronics Laboratory Engineering
School, UNIVERSIDAD PANAMERICANA (Mexico City)
2. Agenda
- Simulation software: overview
- Simulation using web technology
3. Objective and Scope 4. About this Presentation
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- Introduce the topic of simulation software for robotic
multibody systems
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- Explain the problems that can be solved
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- Show an idea of the implementation
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- Motivate collaboration in the study of problems,
prototypes:
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- The development ofa common language to describe systems
(XML)
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- Use of WEB technologies for publications and collaboration
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- All theory and examples will be treated in 2D.
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- 3D systems are treated in similar way
5. Simulation Software: Overview 6. Simulation of MBS
- Many computer codes have been developed but they differ
in:
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- Choice of basic principles of mechanics
7. MBS Simulation Options Modeling Cartesian coordinates
Relative coordinates Fully Cartesian coordinates Graph theory
Spatial algebra Principles of Mechanics Virtual Power Newton-Euler
Hamiltons Principle Lagranges 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. Software
for Multibody Systems Simulation 1
- ADAMSby Mechanical Dynamics Inc., United States
- alaska, by Technical University of Chemnitz, Germany
- AUTOLEV, by OnLine Dynamics Inc., United States
- AutoSimby Mechanical Simulation Corp., United States
- DADSby CADSI, United States
- Dynawizby Concurrent Dynamics International
- DynaFlexby University of Waterloo, Canada
- HyperviewandMotionviewby Altair Engineering, United States
- MECANOby Samtech, Belgium
9. Software for Multibody Systems Simulation 1
- MBDynby Politecnico di Milano, Italy
- MBSoftby Universite Catholique de Louvain, Belgium
- NEWEULby University of Stuttgart, Germany
- RecurDynby Function Bay Inc., Korea
- Robotranby Universite Catholique de Louvain, Belgium
- SAMby Artas Engineering Software, The Netherlands
- SD/FASTby PTC, United States
- SIMPACKby INTEC GmbH, Germany
- Universal Mechanismby Bryansk State Technical University,
Russia
- Working Modelby Knowledge Revolution, United States
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. 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.
Kinematics Simulation
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- Coordinates, Constraints and Joints library
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- Positions, Velocities and Accelerations
13. Coordinates for Modeling
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- Minimum set of coordinates
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- Also known as Reference Point coordinates
- Fully Cartesian coordinates
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- Also known as Natural Coordinates
14. Constraints Equations
- If the selected set of coordinates is dependent, a set of
constraint equations can be found
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- Constraint equations relate the dependent coordinates and
define the movement geometry
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- NoC: Number of Constraints
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- NoDC: Number of Dependent Coordinates
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- NoDOF: Number of Degrees of Freedom
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- Constraint equations generally are not linear
15. Relative Coordinates
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- No constraint equations since it is an open kinematic
chain
1 2 X Y 16. Relative Coordinates
1 X Y 2 O D 3 17. Cartesian Coordinates
1 2 X Y y ( x y ( x y 18. Cartesian Coordinates
2 O D 1 X Y ( x y ( x y ( x y 3 19. Fully Cartesian
Coordinates
1 X Y y ( x y ( x y 2 ( x y 20. Fully Cartesian Coordinates
2 O D 1 X Y ( x y ( x y 3 21. Constraints Origin
- Constraint equations generally are obtained from:
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- The rigid body condition of the elements
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- Fully Cartesian coordinates
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- Cartesian and Fully Cartesian coordinates
- Joints definition can be part of a joints library
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- Treat the multibody system as a LEGO
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- Use computational tools in multibody systems
22. Kinematics of MBS
- Set of dependent coordinates:q
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- Set of constraint equations:
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- Solution using iterative procedures (Newton Raphson)
( 3 ) ( 2 ) ( 1 ) 23. Joints Definition
- Limited to systems in plane (2D)
- Lower-pairs :revoluteandprismatic
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- Show the general modeling for the joint
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- Identify the corresponding elements inand
- Higher-pairs : gears, cams, etc.
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- Require some information on the shape of the connected
bodies
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- Require to know the shape or curvature of a slot in one of the
bodies
24. Modeling of the Revolute Joint X Y i j r i r j P 25.
Modeling of the Prismatic Joint 1 X Y i j r i r j P i Q i P j 26.
Modeling of the Prismatic Joint 2 27. Kinematics Simulation
Computer Implementation Examples 28. Dynamics Simulation
29. Lagrange Multipliers
- The general form of equations of motion using Lagrange
multipliers is
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- This equation representsmequations innunknowns, it is necessary
to givenmore equations, a possibility are acceleration
equations
( 4 ) ( 5 ) 30. Velocity Transformations
- 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)
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- Second velocity transformation
( 7 ) ( 6 ) ( 8 ) ( 9 ) ( 10 ) 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. Dynamics Simulation
33. Dynamics Simulation
34. Simulation using WEB WEB Server Active Pages Java/JavaScript
35. References 1
- Cuadrado, J. et.al. Modeling and Solution Methods for Efficient
Real-Time Simulation of Multibody Dynamics , Multibody Systems
Dynamics, Vol. 1, No. 3, 1997.
- Garca de Jaln, J. and Bayo E.,Kinematic and Dynamic Simulation
of Multibody Systems, The Real-Time Challenge , Springer-Verlag,
1993.
- Schiehlen, S., Multibody Systems Dynamics: Roots and
Perspectives , Multibody Systems Dynamics, Vol. 1, No. 2,
1997.
- Shabana, A.,Computational Dynamics , Wiley, 1994.