Tudor-Dan Rad

Tudor-Dan Rad, Hans-Peter Schröcker

The paper presents an optimal synthesis of overconstrained linkages, based on the factorization of rational curves (representing one parametric motions) contained in Study's quadric. The group of Euclidean displacements is embedded in a affine space where a metric between motions based on the homogeneous mass distribution of the end effector is used to evolve the curves such that they are fitted to a set of target poses. The metric will measure the distance (in Euclidean sense) between the two resulting vectors of the feature points displaced by the two motions. The evolution is driven by the normal velocity of the curve projected in the direction of the target points. In the end we present an example for the optimal synthesis of an overconstrained $6R$ linkage by choosing a set of target poses and explaining in steps how this approach is implemented.

Tudor-Dan Rad, Hans-Peter Schröcker

We characterise the kinematic image of the constraint variety of a 2R dyad as a regular ruled quadric in a 3-space that contains a "null quadrilateral". Three prescribed poses determine, in general, two such quadrics. This allows us to modify a recent algorithm for the synthesis of 6R linkages in such a way that two consecutive revolute axes coincide, thus producing a 5R linkage. Using the classical geometry of twisted cubics on a quadric, we explain some of the peculiar properties of the the resulting synthesis procedure for 5R linkages.

Zijia Li, Tudor-Dan Rad, Josef Schicho et al.

Since its introduction in 2012, the factorization theory for rational motions quickly evolved and found applications in theoretical and applied mechanism science. We provide an accessible introduction to motion factorization with many examples, summarize recent developments and hint at some new applications. In particular, we provide pseudo-code for the generic factorization algorithm, demonstrate how to find a replacement linkage for a special case in the synthesis of Bennett mechanisms and, as an example of non-generic factorization, synthesize open chains for circular and elliptic translations.