1. Vehicle Dynamics & Safety: Multibody System Simulation tools based on MultiBody approach are widespread in vehicle design and testing

2. F M What is a Multibody System? System consisting of rigid or flexible parts connected by joints and undergoing large displacement: mechanisms, vehicles, trains …. Vehicle Dynamics & Safety: Multibody System

3. Multibody Approach What is the MB approach? The MultiBody approach consists in the automatic writing of the equation of motion of a MB system, starting from a description of the system itself. Different systems can be analyzed by the same software, as opposed to a dedicated approach.

4. MB System of different topologies must be analyzed Constraints must be reproduced System Forces must be modelled Rigid as well as deformable bodies must be available Multibody System

5. Topology of MB System A MB system can have an open chain (left, robot) or a closed chain (right, slider-crank mechanism) structure

6. Constraint must be modelled Constraints reduce the system d.o.f: Gruebler Formula: dof=6*n_body-n_constr Constraints

7. System forces Bodies exchange forces also through springs, dampers or more sophisticated elements (like tyres….)

8. Deformable bodies FEM discretization, followed by modal analysis and choice of relevant modes

9. MultiBody System coordinates To define the position of a MB system a reduced set of indipendent coordinates (joint) can be used or an extended/full set (body coordinates) of dependent coordinates

10. Joint coordinates Four bar linkage: 3 coordinates and 1 dof Two scalar constraint equations

11. Body coordinates Four bar linkage: 9 coordinates and 1 dof Eight scalar constraint equations

12. Body coordinates Body position in 3D is described by position of one point ( 3 dof, centre of mass) and by orientation (3 angles). Euler or Cardan conventions are used. In vehicle dynamics Roll(x)-Pitch(y)-Yaw(z)

13. Body orientation

14. Multibody simulation: classes of problems Kinematic analysis: position, velocity acceleration when no dof exists (forces have no influence on motion….) Dynamic analysis: nonlinear, linear (small oscillations, frequency response) Sensitivity/parametric analysis Optimization

15. Multibody simulation: kinematic analysis of a suspension

16. Geometric modelling

17. Constraints, Loads, Forces

18. Assembly

19. Kinematic analysis Position, velocity and acc. analysis. Range of motion, workspace, collisions …

20. Dynamic analysis and Post- processing

22. Modellistica e Simulazione dei Sistemi Meccanici Testi di consultazione: A. Shabana, Dynamics of Multibody Systems, Wiley. G. Legnani, Robotica industriale, Casa Editrice Ambrosiana. Esercitazioni Le esercitazioni consistono nella risoluzione numerica di problemi tramite Matlab e ADAMS. Modalità desame Lesame consiste in un colloquio orale