An implicit formulation for cylindrical joints (pivots) connecting slender rods in large deformations is presented exploiting the G1 map at the beam's end. The rotation at the end of the rod is decomposed in the rotation of the pivot axis and a rotation around this axis. A mixed variational formulation that uses the spherical linear interpolation for the rotations is implemented. It allows to effectively model both rigid and elastic mechanisms. The proposed formulation is applied to several examples ranging from spherical scissor mechanism to elastic deployable structures that exploit the onset of instability for achieving the target shape.

中文翻译：

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用于分析弹性铰接结构的目标最小约束公式


利用梁端部的 G1 映射，提出了一个连接大变形细长杆的圆柱形接头（枢轴）的隐式公式。杆末端的旋转在枢轴的旋转和围绕该轴的旋转中分解。实现了一个混合变分公式，该公式使用球面线性插值进行旋转。它允许有效地模拟刚性和弹性机构。所提出的公式应用于几个示例，从球形剪刀机构到弹性可展开结构，这些结构利用不稳定性的开始来实现目标形状。