Fundamental Mechanism Theory and Machine Dynamics for Robotics

 

Learning Objectives

Copyright: © IGMR

• 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.

 

Course 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