Journal of Jilin University(Engineering and Technology Edition) ›› 2020, Vol. 50 ›› Issue (1): 66-76.doi: 10.13229/j.cnki.jdxbgxb20180835

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Kinematic analysis and simulation of folding process for rigid origami mechanisms

Zhen GUO(),Hong-ying YU(),Zhong-xin HUA,Di ZHAO   

  1. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China
  • Received:2018-08-13 Online:2020-01-01 Published:2020-02-06
  • Contact: Hong-ying YU E-mail:guozhen.vip@foxmail.com;mcadyhy@hit.edu.cn

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Abstract:

In order to analyze the kinematic characteristics of rigid origami mechanism and study the folding process of different patterns, the kinematic model of rigid origami mechanisms is established and the folding state of typical pattern is analyzed. Firstly, the relation equation between the rotation angle of creases at a single vertex is established, the explicit expression of the unknown angle of creases is derived, and the interference solution is eliminated through the mutual test of equation solutions to obtain the actual rotation angle of the arbitrary folding state. Secondly, using the rotation transformation matrix, the real time coordinates of the vertex are calculated. Thirdly, the intersection test algorithm of triangular facets is applied to judge interference of rigid origami mechanism, and the interference in the folding process is detected. Finally, the folding process simulation platform is established, and the folding process of typical rigid origami mechanism is analyzed. The simulation results coincide with the actual folding process, which verifies the correctness of the kinematic analysis method of rigid origami mechanisms and the applicability of the simulation platform.

Key words: mechanical design and theory, rigid origami mechanism, kinematic analysis, interference judgment, simulation of folding process

CLC Number: 

  • TH112

Fig.1

Single vertex configuration and its folded state"

Fig.2

Process of coordinate transformation"

Fig.3

Two folded states"

Fig.4

Solving process of relation equations between rotation angle of creases"

Fig.5

Rotation transformation process"

Fig.6

Point p0 rotate around multiple axes and change to point p0'"

Fig.7

Positional relationship between points and triangular facets"

Fig.8

Four-sided flasher model"

Fig.9

Relationship between rotation angles of creases"

Fig.10

Whole process of simulation analysis"

Fig.11

Configurations and their folding states"

Table 1

Running time of simulation analysis of each configuration"

构型交点数自由度60个中间构态运行时间/s45个中间构态运行时间/s
flasher(中心为等边三角形)331.418 2601.122 093
flasher(中心为正方形)442.366 6391.899 969
三浦折叠412.527 5171.962 476
waterbomb181722.896 67917.315 526
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