Lecture, SS 2012

Lecturer: Josef Schicho

Time: Monday, 10:00-11:45.

Place: SP2 416/1

In kinematics, the motions of rigid bodies are described by concepts like position, orientation, velocity etc. . These concepts are related to the group of Euclidean displacements. This group and the class of functions into it describing motions can be described efficiently and investigated by means of quaternions, Lie groups, or algebraic geometry. These descriptions will be explained and applied to typical problems in kinematics, such as the construction of linkages generating a prescribed motion, or the classification of overconstrained linkages.

We start by introducing some basic concepts from the mathematical areas mentioned above: projective spaces, quadric hypersurfaces, basic intersection theory, dual quaternions. Then we formulate the kinematic problems mentioned above in terms of these concepts. Some of these problems can then be solved by general theorems, some others lead to algebraic constructions of concrete linkages.

Reading:This article relates the synthesis of linkages with rotational or tranlational joints to factorisation of certain polynomials over the algebra of dual quaternions.

This wiki page contains examples of linkages.