多顶点三角形刚性折纸自由度分析

Analysis of Freedom Degree of Multi-vertex Triangle Rigid Origami

针对多顶点折纸机构自由度分析困难问题,提出了在多顶点折纸机构的自由度分析中,利用邻接矩阵分析刚性折纸自由度的方法;用邻接矩阵表示顶点之间的连接关系,通过引入消元矩阵,用矩阵乘法描述了确定运动状态的过程;通过计算顶点对应的行元素之和来确定约束的个数,避免了交叉折痕顶点自由度的计算误差;以分析单顶点4折痕折纸图案自由度为基础,拓扑到分析多顶点三角形刚性折纸图案自由度;最后,通过软件仿真验算刚性折纸图案自由度计算结果的正确性。

Rigid foldability is an important feature of the paper folding mechanism,allowing continuous movement along a predetermined crease between the folded and unfolded state without stretching or bending the surface.It has great potential in engineering applications.In view of the difficulty in the analysis of the freedom degree of multi-vertex origami mechanism,a method using adjacency matrix to analyze the freedom degree of rigid origami is proposed.The adjacency matrix is used to represent the connection relationship between vertices,then,by introducing an elimination matrix,the process of determining the motion state is described by matrix multiplication.The number of constraints is determined by calculating the sum of the row elements corresponding to the vertices,which avoid the calculation error of the freedom degree of the vertices of the cross crease.Based on the analysis of the freedom degree of the single-vertex 4-fold origami pattern,the topology is used to analyze the freedom degree of multi-vertex triangular rigid origami pattern.Finally,the correctness of the calculation results of the freedom degree of the rigid origami pattern is checked by software simulation.