揭示一种新型过约束三环空间连杆机构的运动特性。
Wohlhart's Three-Loop Mechanism: An Overconstrained and Shaky Linkage
- 通过局部分析发现该机构自由度为3，属过约束结构。
- 参考构型下微分自由度为5，但整体配置空间光滑无奇点。
- 首次用运动学切锥与局部近似验证其动态稳定性，适合机构设计研究者。
本文重新研究了卡尔·沃尔哈特于2004年提出的一种三环空间连杆机构（基于1980年埃迪·贝克尔的双环机构扩展），并结合2006年迪埃兹-马丁内斯等人的分析。局部分析表明，该机构具有有限的自由度3（即过约束），而在参考构型下微分自由度为5。研究表明，其配置空间在局部为光滑流形，因此参考构型并非配置空间奇点。进一步证明微分自由度在局部恒定，表明该机构为“摇晃型”（shaky），参考构型非奇点。高阶局部分析借助运动学切锥计算及配置空间的局部逼近得以实现。
原文摘要 · Abstract (English)
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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