### 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

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.

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