折纸结构折叠运动学分析的节点坐标法
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摘要
折纸结构在可展结构的工程实践中具有重要应用价值。为对折纸结构的折叠过程进行运动学数值模拟,文章基于广义逆矩阵理论,提出基于节点坐标的折纸结构折叠过程的运动学分析方法,以实现通过节点外力控制折纸结构的折叠运动;提出一种空间折纸基本单元,采用典型Miura-Ori数值模型的折叠计算验证此基本单元的可行性;通过完整折纸结构模型与含有开口的折纸模型,对动不定折纸体系的折叠过程进行分析与考察,阐明其折叠路径与结构刚体位移的联系。数值结果表明,文章提出的方法可行,分析准确。其研究能够以节点坐标为未知量,为折纸结构的研究人员及设计者从节点坐标控制角度提供一种可行的分析方法。
A nodal coordinate approach is proposed for the folding analysis method of origami structure based on the generalized inverse theory. Hence, the folding process of the origami structures can be controlled by the external forces. A novel origami unit is presented for the methodology. The numerical behavior is demonstrated though the folding analysis of typical Miura-Ori patterns. To investigate the folding performance of kinematic indeterminate origami structures, both the comprehensive model and the model with defect are discussed. The relationship of the folding paths and the rigid motion modes are elaborated.
A nodal coordinate approach is proposed for the folding analysis method of origami structure based on the generalized inverse theory. Hence, the folding process of the origami structures can be controlled by the external forces. A novel origami unit is presented for the methodology. The numerical behavior is demonstrated though the folding analysis of typical Miura-Ori patterns. To investigate the folding performance of kinematic indeterminate origami structures, both the comprehensive model and the model with defect are discussed. The relationship of the folding paths and the rigid motion modes are elaborated.
引文
[1] Miura K.Proposition of pseudo-cylindrical concave polyhedral shells[C].IASS Symposium on Folded Plates and Prismatic Structures,1970.
[2] Feng H,Chen Y,Dai J S,et al.Kinematic study of the general plane-symmetric Bricard linkage and its bifurcation variations[J].Mechanism and Machine Theory,2017,116:89-104.
[3] Dudte L H,Vouga E,Tachi T,et al.Programming curvature using origami tessellations[J].Nature Materials,2016,15(5):583-588.
[4] Cai J,Qian Z,Jiang C,et al.Mobility and kinematic analysis of foldable plate structures based on rigid origami[J].Journal of Mechanisms and Robotics,2016,8(6)064502.
[5] Watanabe N,Kawaguchi K.The method for judging rigid foldability[C].Origami 4,2009:165-174.
[6] 半谷裕彦,川口健一.形态解析:广义逆矩阵及应用[M].北京:知识产权出版社,2014.
[7] Tachi T.Geometric considerations for the design of rigid origami structures[C].Proceedings of the IASS Symposium,2010:458-460.
[2] Feng H,Chen Y,Dai J S,et al.Kinematic study of the general plane-symmetric Bricard linkage and its bifurcation variations[J].Mechanism and Machine Theory,2017,116:89-104.
[3] Dudte L H,Vouga E,Tachi T,et al.Programming curvature using origami tessellations[J].Nature Materials,2016,15(5):583-588.
[4] Cai J,Qian Z,Jiang C,et al.Mobility and kinematic analysis of foldable plate structures based on rigid origami[J].Journal of Mechanisms and Robotics,2016,8(6)064502.
[5] Watanabe N,Kawaguchi K.The method for judging rigid foldability[C].Origami 4,2009:165-174.
[6] 半谷裕彦,川口健一.形态解析:广义逆矩阵及应用[M].北京:知识产权出版社,2014.
[7] Tachi T.Geometric considerations for the design of rigid origami structures[C].Proceedings of the IASS Symposium,2010:458-460.