Robotic

1. Simulation Software: Performances and Examples Dr. Mario Acevedo Multibody Systems and Mechatronics Laboratory Engineering School, UNIVERSIDAD PANAMERICANA (Mexico City)

3. Objective and Scope

5. Simulation Software: Overview

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

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

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

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

34. Simulation using WEB WEB Server Active Pages Java/JavaScript