  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.

Robotics