**Fundamental Mechanism Theory and Machine Dynamics for Robotics**

**Content**

- Mathematics
- Trigonometry
- Properties of the trigonometric functions
- Identities and inverse functions
- Half-angle-method

- Applied linear algebra
- Basic concepts of vectors and matrices
- Vector products and geometrical applications
- Vector spaces
- Systems of linear equations

- Mathematical representations of rotations and homogenous transformations
- Euler-angles
- Roll-pitch-yaw convention
- Angle-axis-convention
- Rotation matrices
- Quaternions
- Homogenous transformations

- Mechanism Theory
- Classification of mechanisms according to dimension, application, main-link features
- Joint variants and mobility of mechanisms
- Mechanism analysis
- Velocities and accelerations in mechanisms

- Machine Dynamics
- Modelling of dynamic systems
- Discrete single-degree-of-freedom systems
- Discrete multiple-degree-of-freedom systems

- Trigonometry

**Learning Objectives**

- The students can apply trigonometric functions for the solution of common tasks from machine dynamics, mechanism theory and robotics.
- The students can perform basic operations of vectors and matrices quickly and understand the geometrical meaning of these operations.
- The students can apply methods from linear algebra for the solution of linear equation systems from machine dynamics, mechanism theory and robotics.
- The students understand the concept of Eigenvalues and Eigenvectors.
- The students understand the different meanings of rotations.
- The students know different possibilities to represent rotations mathematically and their respective advantages and disadvantages.
- The students can use the mathematical representations of rotations for the solution of common tasks from machine dynamics, mechanism theory and robotics.
- The students understand the difference between rotations and homogenous transformations and their mathematical description.
- The students can use the mathematical representations of homogenous transformations for the solution of common tasks from machine dynamics, mechanism theory and robotics.
- The students can distinguish between different kinds of mechanisms.
- The students know the general elements of mechanisms and their relationship to the motion of the mechanism.
- The students understand the relationship between mechanisms theory and the kinematics of robots.
- The students know the basic procedures of mechanism analysis and the relationship to the design of robots.
- The students can apply methods from mechanism theory to common tasks from robotics.
- The students know how to model dynamic systems based on given technical system such as robots.
- The students have a basic understanding of oscillations and stability for single and multiple-degree-of-freedom systems.
- The students can apply their knowledge from machine dynamics to common tasks from robotics.