Simulation Software Performances And Examples

Robotic

1. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ1
Simulation Software: Simulation Software:
Performances and Performances and
ExamplesExamples
Dr. Mario Acevedo
Multibody Systems and Mechatronics Laboratory
Engineering School,
UNIVERSIDAD PANAMERICANA
(Mexico City)

2. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ2
AgendaAgenda
Objective and scope
Simulation software: overview
Kinematics simulation
Dynamics simulation
Simulation using web technology
Final remarks

3. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ3
Objective and ScopeObjective and Scope

4. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ4
About this PresentationAbout this Presentation
Objectives:
Introduce the topic of simulation software for robotic
multibody systems
Explain the problems that can be solved
Show an idea of the implementation
Motivate collaboration in the study of problems, prototypes:
oThe development of a common language to describe systems
(XML)
oUse of WEB technologies for publications and collaboration
Scope
All theory and examples will be treated in 2D.
3D systems are treated in similar way

5. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ5
Simulation Software: Simulation Software:
OverviewOverview

6. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ6
Simulation of MBSSimulation of MBS
Many computer codes have been
developed but they differ in:
Model description
Choice of basic principles of mechanics
Topological structure
Numeric vs. Symbolic
Formulations

7. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ7
MBS Simulation OptionsMBS 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. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ8
Software for Multibody Systems Software for Multibody Systems
Simulation 1Simulation 1
ADAMS by Mechanical Dynamics Inc., United States
alaska , by Technical University of Chemnitz, Germany
AUTOLEV , by OnLine Dynamics Inc., United States
AutoSim by Mechanical Simulation Corp., United States
COMPAMM by CEIT, Spain
DADS by CADSI, United States
Dynawiz by Concurrent Dynamics International
DynaFlex by University of Waterloo, Canada
Hyperview and Motionview by Altair Engineering, United States
MECANO by Samtech, Belgium

9. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ9
Software for Multibody Systems Software for Multibody Systems
Simulation 1Simulation 1
MBDyn by Politecnico di Milano, Italy
MBSoft by Universite Catholique de Louvain, Belgium
NEWEUL by University of Stuttgart, Germany
RecurDyn by Function Bay Inc., Korea
Robotran by Universite Catholique de Louvain, Belgium
SAM by Artas Engineering Software, The Netherlands
SD/FAST by PTC, United States
SIMPACK by INTEC GmbH, Germany
Universal Mechanism by Bryansk State Technical University,
Russia
Working Model by Knowledge Revolution, United States

10. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ10
Actual State of MBS SimulatorsActual 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. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ11
Desired Goal of MBSDesired 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. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ12
Kinematics SimulationKinematics Simulation
Modeling:
 Coordinates, Constraints and Joints library
Analysis:
 Positions, Velocities and Accelerations

13. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ13
Coordinates for ModelingCoordinates for Modeling
Relative coordinates
Minimum set of coordinates
Cartesian coordinates
Also known as Reference Point
coordinates
Fully Cartesian coordinates
Also known as Natural Coordinates
Mixed coordinates

14. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ14
Constraints EquationsConstraints Equations
If the selected set of coordinates is
dependent, a set of constraint equations can
be found
Constraint equations relate the dependent
coordinates and define the movement geometry
NoC = NoDC – NoDOF
NoC: Number of Constraints
NoDC: Number of Dependent Coordinates
NoDOF: Number of Degrees of Freedom
Constraint equations generally are not linear

15. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ15
Relative CoordinatesRelative Coordinates
Open kinematic chain
Model
Close loop
Constraints
No constraint
equations since it is
an open kinematic
chain




1
2
X
Y

16. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ16
Relative CoordinatesRelative Coordinates
Close kinematic chain
Model
Constraints
NoDC = 3
NoDOF = 1
NoC = 3 - 1 = 2
Non linear
Transcendental
functions


1
X
Y


2


O D
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    0sinsinsin
0coscoscos
321321211
321321211
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LLL
ODLLL
3

17. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ17
Cartesian CoordinatesCartesian Coordinates
Open kinematic chain
Model
Constraints
NoDC = 6
NoDOF = 2
NoC = 6 - 2 = 4
Non linear




1
2
X
Y
y

(x

y

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(x

y

 

  
   0sin
2
sin
0cos
2
cos
0sin
2
0cos
2
22
2
11
22
2
11
11
1
11
1
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
y
L
L
x
L
L
y
L
x
L

18. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ18
Cartesian CoordinatesCartesian Coordinates
Close kinematic chain
Model
Constraints
NoDC = 9
NoDOF = 1
NoC = 9 - 1 = 8
Non linear


2


O D
1
X
Y
(x

y




(x
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y


(x

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

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  
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 
    
    0sinsinsin
0coscoscos
0sin
2
0cos
2
0sin
2
sin
0cos
2
cos
0sin
2
0cos
2
332211
332211
33
3
33
3
22
2
11
22
2
11
11
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11
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
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y
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x
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y
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x
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3

19. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ19
Fully Cartesian CoordinatesFully Cartesian Coordinates
Open kinematic chain
Model
Constraints
NoDC = 4
NoDOF = 2
NoC = 4 - 2 = 2
Non linear
1
X
Y
y

(x

y


(x

y


2
(x

y


   
    0
0
2
2
2
12
2
12
2
1
2
1
2
1


Lyyxx
Lyyxx
OO

20. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ20
Fully Cartesian CoordinatesFully Cartesian Coordinates
Close kinematic chain
Model
Constraints
NoDC = 4
NoDOF = 1
NoC = 4 - 1 = 3
Non linear
2
O D
1
X
Y
(x

y


(x

y


3    
   
    0
0
0
2
3
2
2
2
2
2
2
2
12
2
12
2
1
2
1
2
1
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
Lyyxx
Lyyxx
Lyyxx
DD
OO

21. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ21
Constraints OriginConstraints Origin
Constraint equations generally are obtained
from:
Close loop equations
Relative coordinates
The rigid body condition of the elements
Fully Cartesian coordinates
Joints definition
Cartesian and Fully Cartesian coordinates
Joints definition can be part of a joints library
Treat the multibody system as a LEGO
Use computational tools in multibody systems

22. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ22
Kinematics of MBSKinematics of MBS
Set of dependent coordinates: q
Positions analysis.
Set of constraint equations:
Solution using iterative procedures (Newton
Raphson)
Velocity analysis:
Acceleration analysis:
 t,qΦ
 
tt ΦqqΦ
q ,
( 3 )
( 2 )
( 1 )
  cqΦΦqqΦ
qq  
tt,

23. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ23
Joints DefinitionJoints Definition
Limited to systems in plane (2D)
Cartesian coordinates
Lower-pairs: revolute and prismatic
Show the general modeling for the joint
Identify the corresponding elements in
and
Higher-pairs: gears, cams, etc.
Require some information on the shape of the connected
bodies
Require to know the shape or curvature of a slot in one of
the bodies
 
t
t ΦqqΦ
q
,
  cqΦΦqqΦ
qq  
tt,

24. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ24
Modeling of the Revolute JointModeling of the Revolute Joint
X
Y
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r
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j
P
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


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cossin01cossin01
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25. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ25
Modeling of the Prismatic Joint 1Modeling of the Prismatic Joint 1
X
Y
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r
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P
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in
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ji
T
it dn
Φ

26. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ26
Modeling of the Prismatic Joint 2Modeling of the Prismatic Joint 2
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27. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ27
Kinematics SimulationKinematics Simulation
Computer Implementation
Examples

28. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ28
Dynamics SimulationDynamics Simulation
Constraint Dynamics
 Lagrange multipliers
 Velocity transformations
 Numerical integration

29. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ29
Lagrange MultipliersLagrange Multipliers
The general form of equations of motion
using Lagrange multipliers is
This equation represents m equations in n unknowns, it is
necessary to give n more equations, a possibility are
acceleration equations
Equations to solve
QλΦqM
q
T



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



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
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




c
Q
λ
q
0Φ
ΦM
q
q

T
( 4 )
( 5 )

30. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ30
Velocity TransformationsVelocity 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)
Open loop systems
Close loop systems
Lagrange multipliers
Second velocity transformation
pRq pRpRq  
 pRMQRpMRR
TT
 
 pRMQRμΦpMRR
T
p
T
 
T
  zSMRRzSRMQRSzMRSRS
TTTTT
 
( 7 )( 6 )
( 8 )
( 9 )
( 10 )

31. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ31
Numerical vs SymbolicalNumerical vs Symbolical
Model description
Data input
Formalism
Numerical equations
Simulation
Local output
Global result
N
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Model description
Data input
Formalism
Symbolical equations
Simulation
Local output
Global result
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n

32. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ32
Dynamics SimulationDynamics Simulation
Lagrange Multipliers
Computer Implementation
Examples
Inverse dynamics
Direct dynamics

33. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ33
Dynamics SimulationDynamics Simulation
Velocity transformations
Computer Implementation
Examples
Inverse dynamics
Direct dynamics

34. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ34
Simulation using WEBSimulation using WEB
WEB Server
Active Pages
Java/JavaScript

35. Nobember 4th to 7th, 20031st International Course on Robotics, UNIVERSIDAD NACIONAL DE INGENIERÍA, Lima PERÚ35
References 1References 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.
García de Jalón, 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.