Mechanical Engineering

About this course

The course deals with dynamics of mechanical and robotic systems under constraints, and specifically kinematic constraints of contact with friction. Motion of such systems is typically described by a hybrid dynamical system with non-smooth solutions due to transitions between different contact states and impact at the contacts. These systems are useful for motion analysis and control design of robotic systems for object grasping and manipulation, as well as legged mobile robots and wheeled or tracked vehicles. The class discusses basic topics in addition to phenomena which are unique to hybrid systems, as well as advanced research problems. The course involves four homework assignments and a final project, all involving analysis and numerical computation in Matlab

Topics: Lagrange’s equations, formulating the dynamics of mechanical systems with holonomic and non-holonomic constraints, with mechanical and/or kinematic inputs. Contact kinematics and contact forces. Friction, Coulomb’s model, planar multi-contact statics – graphical and computational analysis. Dynamics under different contact states, Painlevé paradox and dynamic jamming. Impact models with and without friction, Zeno phenomenon, simple models of dynamic walking, Poincaré map, stability of periodic orbits in hybrid systems.

Text Books: (some are available in electronic format online or via Technion’s library)

  1. M. T. Mason, "Mechanics of robotic manipulation", MIT Press 2001 LINK to Mason’s class lecture notes at CMU
  2. R. M. Murray, Z. Li, S. Sastry, "Mathematical Introduction to Robotic manipulation", CRC press 1994. LINK to author’s online printout.
  3. B. Brogliato, “Nonsmooth Mechanics: models, dynamics, and control”, Springer 1999
  4. E. R. Westervelt, J. W. Grizzle, C. Chevallereau, J. H. Choi, and B. Morris, "Feedback Control of Dynamic Bipedal Robot Locomotion", CRC Press 2007

Learning outcomes

The class discusses basic topics in addition to phenomena which are unique to hybrid systems, as well as advanced research problems.

Semester Start Date: November 30, 2024

Contact Hours: 3

Day & Time: TBD


Hybrid lectures, both in class at Technion, with live broadcast and/or recordings for remote participants. The lectures will be given in English, jointly for the Technion’s International Program in Mechanical Engineering with Israeli students in both undergraduate and graduate studies. Open for EuroTeQ students from undergraduate (senior year) and graduate studies.

Grading policy: Mandatory homework assignment – 60%, final project assignment – 25%. Submission in pairs is done electronically via the course’s MOODLE webpage. Personal meeting for oral defense on homework assignments and first part of final project - 15% Focused personal meetings for oral defense on submitted assignments may be applied upon lecturer’s considerations, and weighted in grades

Start Date: November 30, 2024 (semester start) Day & Time: TBD Hours: 3

Course requirements

Dynamics, Linear Systems, Introduction to Control or Mechanics of vibrations



Lectures, Homework & Final Project Assignment

Additional information

  • Credits
    ECTS 2
  • Level
  • Contact hours per week
  • Instructors
    Professor Yizhar Or
  • Mode of instruction
If anything remains unclear, please check the FAQ of Technion (Israel).


  • Start date

    3 November 2024

    • Ends
      2 March 2025
    • Term *
      Winter Semester 2024/25
    • Location
    • Instruction language
    • Register between
      14 May - 29 Jul 2024
    Only 5 days to enrol
    Apply now
These offerings are valid for students of EPFL (Switzerland)