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DISCONTINUOUS MOBILITY OF A FOLDING SQUARE-BLOCK TOY - A CLASS OF SINGLE LOOP SPATIAL 8-BAR MECHANISM

机译:方形方块玩具的不连续运动-一类单环空间8杆机构

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摘要

Based on the group theory and group algebraic structure of the displacement set, an interesting playing toy of the magic folding square block belonging to one class of single-loop spatial eight-revolute mechanism is offered to illustrate the discontinuous mobility of mechanism. This folding toy's mobility generally has two finite global dofs as a whole kinematic chain. Nevertheless, during the movement, the permanent finite mobility of mechanism depends on the various positions of joints. When the block profile-shape constraints are taken into account, one bifurcation between one 2-dimensional manifold and one 1-dimensional manifold occurs at an initial transition position and the other bifurcation between two 1-dimensional manifolds exists in another specified configuration. In addition, any motion of one working mode destroys the geometrical condition that is required for the other modes but a bifurcation toward a spatial mode with two finite dofs remains possible by ingoring the profile shape constraints. In fact, there is a discontinuous mobility with a trifurcation among three subsets. It is composed of a general spatial mode with 2-dimensional manifold, one part mobility chain of 2-dimensional manifoid and another part mobility chain of 1-dimensional manifold.
机译:基于位移集的群论和群代数结构,提供了一种有趣的,属于一类单环空间八转机构的魔术折叠方块玩具,以说明机构的不连续运动性。这种折叠玩具的移动性通常在整个运动学链中具有两个有限的全局自由度。然而,在运动过程中,机构的永久有限移动性取决于关节的各个位置。当考虑到块轮廓形状约束时,一个二维歧管和一个一维歧管之间的一个分叉发生在初始过渡位置处,而另一个一维歧管之间的另一个分叉以另一种指定配置存在。另外,一种工作模式的任何运动都会破坏其他模式所需的几何条件,但是通过使轮廓形状约束复杂化,仍然可以分叉到具有两个有限自由度的空间模式。实际上,在三个子集之间存在不连续的移动,具有三叉关系。它由具有二维流形的一般空间模式,一个二维流形的一部分迁移链和另一维一维流形的迁移链组成。

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