Wohlhart 三环机构：一种过约束且颤动的连杆机构
Wohlhart's Three-Loop Mechanism: An Overconstrained and Shaky Linkage
AI总结：
本文重新分析Wohlhart三环空间连杆机构，证明其有限自由度为3且过约束，微分自由度为5并局部恒定，位形空间局部光滑，从而揭示该机构具有颤动特性而非奇点。
摘要：
本文重新审视了一种三环空间连杆机构，该机构由 Karl Wohlhart 在 2004 年 ARK 论文中提出（作为 Eddie Baker 于 1980 年提出的双环连杆机构的扩展），随后由 Diez-Martinez 等人在 2006 年 ARK 论文中进行了分析。局部分析表明，该连杆机构具有有限的自由度（DOF）3（因此是过约束的），而在其参考位形下微分自由度为 5。研究证明其位形空间局部是一个光滑流形，因此参考位形不是位形空间奇点。进一步证明微分自由度是局部恒定的，这使得该连杆机构具有颤动特性（因此参考位形不是奇点）。通过计算运动学切锥以及位形空间的局部近似，促进了高阶局部分析。
英文摘要：
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.
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