Exceptional Stewart-Gough Platforms, Segre Embeddings, and the Special Euclidean Group
Exceptional Stewart-Gough Platforms, Segre Embeddings, and the Special Euclidean Group
复制标题
出色的 Stewart-Gough 平台、Segre 嵌入和特殊欧几里得群
DOI：
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发表时间：
2018
影响因子：
1.2
通讯作者：
C. Wampler
中科院分区：
文献类型：
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作者：
J. Hauenstein;Samantha N. Sherman;C. Wampler
Stewart-Gough平台是由基座和平台两个刚体通过球铰连接的六条腿组成的机构。对于固定的腿长，一个通用的Stewart-高夫平台是刚性的40个组件配置（在复数），而特殊的Stewart-高夫平台有无限多个组件配置，因此有自我运动。我们定义了一个家庭的特殊Stewart-高夫平台称为Segre依赖Stewart-高夫平台所产生的线性依赖的点对下的塞格雷嵌入和计算这个家庭的不可约分解。我们也考虑Stewart-高夫平台，移动两个自由度。由于塞格雷嵌入产生的特殊欧几里德集团在三维度为40的表示，我们认为在其他维度的特殊欧几里德集团和计算空间斯图尔特-高夫平台，在4维空间移动。
Stewart--Gough platforms are mechanisms which consist of two rigid objects, a base and a platform, connected by six legs via spherical joints. For fixed leg lengths, a generic Stewart--Gough platform is rigid with 40 assembly configurations (over the complex numbers), while exceptional Stewart--Gough platforms have infinitely many assembly configurations and thus have self-motion. We define a family of exceptional Stewart--Gough platforms called Segre-dependent Stewart--Gough platforms which arise from a linear dependency of point-pairs under the Segre embedding and compute an irreducible decomposition of this family. We also consider Stewart--Gough platforms which move with two degrees of freedom. Since the Segre embedding arises from a representation of the special Euclidean group in three dimensions which has degree 40, we consider the special Euclidean group in other dimensions and compute spatial Stewart--Gough platforms that move in 4-dimensional space.
DOI：
10.1007/978-3-319-72453-9_8
发表时间：
2017-11
期刊：
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影响因子：
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作者：
Daniel J. Bates;Daniel A. Brake;J. Hauenstein;A. Sommese;C. Wampler
通讯作者：
Daniel J. Bates;Daniel A. Brake;J. Hauenstein;A. Sommese;C. Wampler