First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
INO2044864, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2016/17

Information on the course unit
Degree course Second cycle degree in
IN0518, Degree course structure A.Y. 2011/12, A.Y. 2017/18
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Website of the academic structure
Department of reference Department of Industrial Engineering
E-Learning website
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge MATTEO MASSARO ING-IND/13

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses ING-IND/13 Applied Mechanics for Machinery 6.0

Course unit organization
Period Second semester
Year 2nd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 26/02/2018
End of activities 01/06/2018

Examination board
Board From To Members of the board
5 A.A. 2017/18 01/10/2017 30/11/2018 MASSARO MATTEO (Presidente)
DORIA ALBERTO (Membro Effettivo)
4 A.A. 2016/17 01/10/2016 30/11/2017 MASSARO MATTEO (Presidente)
DORIA ALBERTO (Membro Effettivo)

Prerequisites: Applied mechanics
Mechanical vibrations
Mechanical and thermal measurement systems
Target skills and knowledge: The course aims to provide a comprehensive overview of the methods and tools for the modeling and simulation of mechanical systems using multibody techniques, including the theoretical and practical tools necessary to properly use multibody codes and guiding the student in the modeling activity.
Examination methods: The exam includes two mandatory activities: an individual assignment and a written exam. The assignment contributes 15/30 of the final grade while the written exam contributes 15/30. The assignment consists in carrying out a multibody modelling and simulation project and presenting such project. The written exam consists in answering three open questions in about 2 hours; the use of lecture notes and/or textbooks is not permitted. The exam may be carried out either in Italian or in English, according to the student’s preference.
Assessment criteria: ASSIGNMENT
• correctness of the final solution
• clarity and synthesis in the presentation of the results
• ability to illustrate the topics in a clear and concise way
• knowledge and understanding of the course contents
• ability to illustrate the topics in a clear and concise way
• appropriateness of use of technical terminology
Course unit contents: Kinematics of multibody systems: translation and rotation matrices for three-dimensional systems, Rodrigues formula, conventions for the orientation of bodies in space (with three and four parameters), singular points, angular velocities expressed in ground frame and moving frame, main constraints for multibody systems, Grubler equation for three-dimensional systems, problems related to redundant constraints, position and velocity initial analysis, examples in Maple and applications in Adams.

Dynamics of multibody systems: Lagrange's equations for systems with constraints and resulting DAE system, different conventions for the inertia tensor, first order reduction of the equations of motion, DAE index, stabilization of constraint equations using the Baumgarte method, from DAE to ODE using the coordinate partitioning method, automatic partitioning using the LU decomposition, different definitions of 'stiff' systems, 'Gear-Gupta-Leimkuhler' and 'Hiller-Anantharaman' formulations for the reduction of the DAE index, equilibria, examples in Maple and applications in Adams.

Linearization of multibody systems: computation of the state matrices A,B,C,D and matrices M,C,K, independent vs. dependent coordinates formulations, vibration modes for multibody systems with damping, linearization of rotating systems, examples in Maple and applications in Adams.

Multibody systems with flexible bodies: different formulations, component modes synthesis, fixed interface modes, free interface modes, normal modes, constraint modes, Craig-Bampton method, examples in Maple and applications in Adams.

Contacts in multibody systems: different formulations (continuous vs. instantaneous), modelling of normal forces, modelling of tangential forces, applications in Adams.

Tyre modelling in multibody systems: forces, torques, slip, magic formula, applications in Adams.
Planned learning activities and teaching methods: Lectures in class and in the computation lab using the math code Maple and the multibody code Adams.
Additional notes about suggested reading: Lecture notes and slides, maple scripts and adams files on moodle, reference books.
Textbooks (and optional supplementary readings)
  • JG de Jalón and E Bayo, Kinematic and Dynamic Simulation of Multibody Systems. --: Springer, 1994. Cerca nel catalogo
  • F. Cheli, E. Pennestrì, Cinematica e Dinamica dei Sistemi Multibody. --: CEA, 2006. Cerca nel catalogo
  • J. Wittenburg, Dynamics of Multibody Systems. --: Springer, 2007.
  • A.A. Shabana, Dynamics of Multibody Systems. --: Cambridge University Press, 2013. Cerca nel catalogo
  • P.E. Nikravesh, Computer-Aided Analysis of Mechanical Systems. --: Prentice-Hall, 1988.

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Adams