{"ID":2869194,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.14698","arxiv_id":"2509.14698","title":"Wohlhart's Three-Loop Mechanism: An Overconstrained and Shaky Linkage","abstract":"This paper revisits a three-loop spatial linkage that was proposed in an ARK 2004 paper by Karl Wohlhart (as extension of a two-loop linkage proposed by Eddie Baker in 1980) and later analyzed in an ARK 2006 paper by Diez-Martinez et. al. A local analysis shows that this linkage has a finite degree of freedom (DOF) 3 (and is thus overconstrained) while in its reference configuration the differential DOF is 5. It is shown that its configuration space is locally a smooth manifold so that the reference configuration is not a c-space singularity. It is shown that the differential DOF is locally constant, which makes this linkage shaky (so that the reference configuration is not a singularity). The higher-order local analysis is facilitated by the computation of the kinematic tangent cone as well as a local approximation of the c-space.","short_abstract":"This paper revisits a three-loop spatial linkage that was proposed in an ARK 2004 paper by Karl Wohlhart (as extension of a two-loop linkage proposed by Eddie Baker in 1980) and later analyzed in an ARK 2006 paper by Diez-Martinez et. al. A local analysis shows that this linkage has a finite degree of freedom (DOF) 3 (...","url_abs":"https://arxiv.org/abs/2509.14698","url_pdf":"https://arxiv.org/pdf/2509.14698v1","authors":"[\"Andreas Mueller\"]","published":"2025-09-18T07:41:00Z","proceeding":"cs.RO","tasks":"[\"cs.RO\",\"math.DG\",\"math.GR\",\"math.NA\"]","methods":"[]","has_code":false}