5 problems

Students' conjecture. The linkage produces a circular arc and a straight line segment if two bars of it are crossing.

Complementarity conditions conjecture. There always exist an $(I,t)$-linkage $\mathcal{P}$ and a vertex set $X\ni t$ such that $\mathcal{P}$ and $X$ satisfy the complementarity con…

Four-bar linkage pop-reachability conjecture. For almost every four-bar linkage, the neighborhood of any configuration that can be reached by smooth motion can also be reached by a…

Critical-point conjecture. For a generic $4$-bar linkage, the Coulomb potential can have no more than four critical points, and their types are the same as in Example 1.

Let $P$ be a planar polygonal linkage, and let $M(P)$ be its configuration space modulo congruences, including configurations with self-intersections. Let $M^o(P)\subset M(P)$ be t…