A closed linkage mechanism having the shape of a discrete M\"obius strip.
A closed linkage mechanism having the shape of a discrete M\"obius strip.
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具有离散Mobius带形状的闭合连杆机构。
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
S. Kaji
中科院分区：
文献类型：
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作者：
S. Kaji
三维空间中的闭合连杆机构是一种包括以类似念珠的圆形形式用铰链连接的刚性体的物体。这种连接包括Bricard 6 R和Bennett 4 R。设计这样的封闭连杆机构，需要求解一个高次代数方程，这一般是困难的。在这个演讲中，作者提出了一个新的家庭封闭连杆机构与任意数量的铰链作为一个特定的Bricard 6 R的扩展。它们具有奇异的性质，例如一维自由度（1-DOF），并且无论状态如何，某些能量都取恒定值。这些连杆机构可以被视为离散的莫比乌斯带，并可能在纯数学的背景下，以及感兴趣的。然而，这里描述的许多性质仅在数值上得到了证实，没有严格的数学证明，应该谨慎解释。
A closed linkage mechanism in three-dimensional space is an object comprising rigid bodies connected with hinges in a circular form like a rosary. Such linkages include Bricard6R and Bennett4R. To design such a closed linkage, it is necessary to solve a high-degree algebraic equation, which is generally difficult. In this lecture, the author proposes a new family of closed linkage mechanisms with an arbitrary number of hinges as an extension of a certain Bricard6R. They have singular properties, such as one-dimensional degree of freedom (1-DOF), and certain energies taking a constant value regardless of the state. These linkage mechanisms can be regarded as discrete Mobius strips and may be of interest in the context of pure mathematics as well. However, many of the properties described here have been confirmed only numerically, with no rigorous mathematical proof, and should be interpreted with caution.