Robot Mechanics

Lecture Notes — Jun.-Prof. Dr. Edoardo Milana

Universität Freiburg – IMTEKLaboratory for Soft Machines

1 Course information

Lecturer Jun.-Prof. Dr. Edoardo Milana (Laboratory for Soft Machines, IMTEK)
Tutors Xin Li, Johannes Frey
Semester Sommersemester 2026 (Apr 20 – Jul 25, 2025)
Room G.-Köhler-Allee 101, SR 00-017/19
Course number 11LE50V-5727

Schedule. Monday and Friday, 14:00–16:00, same room. There is no distinction between lecture and exercise sessions: each slot begins with 30–45 minutes of lecture followed by work on the weekly problem set.

Attendance is not mandatory but highly recommended.

Final exam: written, 120 minutes. Students who have solved the weekly problem sets throughout the course are very well prepared.

2 Course objectives

Understanding Robotic Architecture. By the end of the course, students should have a comprehensive understanding of how classical robots are built and what are their main components: mechanisms, sensors, actuators, and control architecture.

Robot Mechanical Analysis. Students will be able to analyse and model robotic manipulators using direct, inverse, and differential kinematics, concluding with the statics of a robotic manipulator.

3 Lecture notes

Download lecture notes (PDF)

These notes develop the geometry and mechanics of robotic manipulators, from rigid-body pose to differential kinematics, statics, and actuator modelling. They follow the structure of the lecture course and are intended as a concise reference and complement to the lecture slides.

Chapter Topic
1. Introduction Scope, manipulator families, course roadmap
2. Robot Components Mobility (Grübler), actuators, gears, strain sensing
3. Rigid Body Pose Rotation matrices, Euler angles, quaternions, homogeneous transforms
4. Direct and Inverse Kinematics DH convention, worked examples, inverse kinematics
5. Differential Kinematics and Statics Jacobian, singularities, virtual work, statics

4 References

Main textbook (selected chapters)

  • Siciliano, Bruno et al. Foundations of Robotics. Springer, 2025.

Extra reading

  • Tsai, Lung-Wen. Robot Analysis: The Mechanics of Serial and Parallel Manipulators. John Wiley & Sons, 1999.
  • Lynch, Kevin M., and Frank C. Park. Modern Robotics. Cambridge University Press, 2017.

Online resources