We compute the Lusternik-Schnirelmann category (LS-cat) and higher topological complexity ($TC_s$, $s\geq2$) of "no-$k$-equal" configuration space Conf$_k(\mathbb{R},n)$. This yields (with $k=3$) LS-cat Khovanov's group PP$_n$ pure planar braids on $n$ strands, which is an $\mathbb{R}$-analogue Artin's classical braid strands. Our methods can be used to describe optimal motion planners for prov...

This article presents the concept of a new class of mechanical devices for multi-phase motion generation tasks. Recon gurable Motion Generators are a new class of mechanical devices that are designed for a speci c part family and their associated motion generation tasks. The research endeavors to realize a novel concept for Recon gurable Motion Generators (RMGs) for multiphase planar motion gen...