Wohlhart's Three-Loop Mechanism: An Overconstrained and Shaky Linkage
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911161187827712 |
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| author | Mueller, Andreas |
| author_facet | Mueller, Andreas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wohlhart's Three-Loop Mechanism: An Overconstrained and Shaky Linkage Mueller, Andreas Robotics Numerical Analysis Differential Geometry Group Theory 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. |
| title | Wohlhart's Three-Loop Mechanism: An Overconstrained and Shaky Linkage |
| topic | Robotics Numerical Analysis Differential Geometry Group Theory |
| url | https://arxiv.org/abs/2509.14698 |