Hooke and Coulomn Energy of Tripod Spiders

Tripod spiders are the simplest examples of arachnoid mechanisms. Their workspaces and configuration spaces are well known. For Hooke potential, we give a complete description of the Morse theory and treat the robust control of the spider. For the Coulomb energy, we use stationary charges and the trapping domain to study the robust control of spiders. We show that, for a regular triangle and positive charges, the domain of robust control is non-void. This relates to questions about the Maxwell conjecture about point charges. We end with several natural problems and research perspectives suggested by our results.