Origami crease patterns are folding paths that transform flat sheets into spatial objects. Origami patterns with a single degree of freedom (DOF) have creases that fold simultaneously. More often, several substeps are required to sequentially fold origami of multiple DOFs, and at each substep some creases fold and the rest remain fixed. In this study, we combine the loop closure constraint with Lagrange multiplier method to account for the sequential folding of rigid origami of multiple DOFs, by controlling the rotation of different sets of creases during successive substeps. This strategy is also applicable to model origami-inspired devices, where creases may be equipped with rotational springs and the folding process involves elastic energy. Several examples are presented to verify the proposed algorithms in tracing the sequential folding process as well as searching the equilibrium configurations of origami with rotational springs.

中文翻译：

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用拉格朗日乘子法对刚性折纸进行折叠模拟

折纸折痕图案是将平板转换为空间对象的折叠路径。具有单自由度 (DOF) 的折纸图案具有同时折叠的折痕。更常见的是，需要几个子步骤来顺序折叠多个自由度的折纸，并且在每个子步骤中，一些折痕折叠而其余部分保持固定。在这项研究中，我们将闭环约束与拉格朗日乘子法相结合，通过控制连续子步骤中不同折痕组的旋转，来解释多个自由度刚性折纸的顺序折叠。这种策略也适用于模型折纸启发的设备，其中折痕可能配备旋转弹簧，折叠过程涉及弹性能量。