Abstract Grashof linkage was well studied in planar and spherical 4R linkage. In this paper, this characteristic is associated with a spatial linkage evolved from an kirigami loop. Both the overconstrained geometric conditions and the explicit closure equations are derived with the D-H method. It is found out that the 6R overconstrained linkage can work as a crank-rocker or a double crank linkage. Its bifurcation behaviours under two motion modes are analysed. We further transfer this 6R linkage back into the kirigami form and discuss its kinematic behaviours such as spatial 8-shaped trajectories. This work sets up the bridge between the spatial linkages and rigid kirigami forms to develop emerging kinematic behaviours.

中文翻译：

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受剪纸启发的具有空间曲柄摇杆特性的双球形 6R 连杆

摘要 Grashof 连杆在平面和球形4R 连杆中得到了很好的研究。在本文中，这一特征与从剪纸循环演变而来的空间联系有关。过约束几何条件和显式闭合方程都是用 DH 方法导出的。发现6R过约束连杆可以作为曲柄摇杆或双曲柄连杆工作。分析了其在两种运动模式下的分叉行为。我们进一步将这个 6R 连接转换回剪纸形式并讨论其运动学行为，例如空间 8 形轨迹。这项工作在空间联系和刚性剪纸形式之间架起了桥梁，以发展新兴的运动学行为。