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Research Papers

Kinematic Analysis and Stiffness Validation of Origami Cartons

[+] Author and Article Information
C. Qiu

e-mail: chen.qiu@kcl.ac.uk

Vahid Aminzadeh

Postdoctoral Research Associate
e-mail: vahid.aminzadeh@kcl.ac.uk
Centre for Robotic Research,
Kings's College London,
London WC2R 2LS, UK

Jian S. Dai

Chair of Mechanisms and Robotics,
MoE Key Laboratory for Mechanism Theory and Equipment Design,
Tianjin University,
Tianjin, China
Centre for Robotic Research,
Kings's College London,
London WC2R 2LS, UK
e-mail: jian.dai@kcl.ac.uk

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 7, 2013; final manuscript received August 28, 2013; published online September 27, 2013. Assoc. Editor: Larry L. Howell.

J. Mech. Des 135(11), 111004 (Sep 27, 2013) (13 pages) Paper No: MD-13-1072; doi: 10.1115/1.4025381 History: Received February 07, 2013; Revised August 28, 2013

Origami-type cartons have been widely used in packaging industry because of their versatility, but there is a lack of systematic approach to study their folding behavior, which is a key issue in designing packaging machines in packaging industry. This paper addresses the fundamental issue by taking the geometric design and material property into consideration, and develops mathematical models to predict the folding characteristics of origami cartons. Three representative types of cartons, including tray cartons, gable cartons, and crash-lock cartons were selected, and the static equilibrium of folding process was developed based on their kinematic models in the frame work of screw theory. Subsequently, folding experiments of both single crease and origami carton samples were conducted. Mathematical models of carton folding were obtained by aggregating single crease's folding characteristics into the static equilibrium, and they showed good agreements with experiment results. Furthermore, the mathematical models were validated with folding experiments of one complete food packaging carton, which shows the overall approach has potential value in predicting carton's folding behavior with different material properties and geometric designs.

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Figures

Grahic Jump Location
Fig. 4

Tray carton mechanism and its geometric relationship. (a) Tray carton mechanism and (b) geometry of a tray carton.

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Fig. 3

Carton corner linkage models in three origami-type cartons

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Fig. 2

Folding stages of different origami-type cartons

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Fig. 1

Origami-type cartons and tested carton samples. (a) A group of origami-type cartons, tray carton in the left, crash-lock carton in the middle, and gable carton in the right and (b) origami carton samples, and they correspond to the origami cartons used in food packaging industry.

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Fig. 8

Folding moment and stiffness comparisons of virgin and repeated folding process. (a) Folding moment comparison between virgin and repeated folding, solid and dashed lines represent experiment results, and dashed-dotted lines represent ±1 standard deviation. (b) Folding stiffness comparison, solid and dashed lines represent experiment results, error bars represent standard deviations within ±5 deg range of eight folding positions every 10 deg from 10 deg to 80 deg.

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Fig. 10

Folding moment and stiffness comparisons with different folding velocities. (a) Folding moment comparison, dashed line, dashed-dotted line, and solid line correspond to experiment results, and dotted lines represent ±1 standard deviation. (b) Folding stiffness comparison, dashed line, dashed-dotted line, and solid line correspond to experiment results, seven folding positions every 10 deg from 20 deg to 80 deg are selected to represent motion-stiffness curves.

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Fig. 11

Folding moment and stiffness comparisons of tray carton. (a) Folding moment comparison, dashed line represents mathematical model, solid line represents experiment result. (b) Folding stiffness comparison, dashed line represents mathematical model, solid line represents experiment result.

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Fig. 5

Gable carton mechanism and geometric relationship. (a) Gable carton mechanism and (b) geometry of a gable carton.

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Fig. 6

Crash-lock carton mechanism and geometric relationship. (a) Crash-lock carton mechanism and (b) geometry of a crash-lock carton.

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Fig. 9

Folding moment and stiffness comparisons with different crease lengths. (a) Folding moment comparison, dashed line, dashed-dotted line and solid line corresponds to experiment results, and dotted lines represent ±1 standard deviation. (b) Folding stiffness comparison, dashed line, dashed-dotted line and solid line correspond to experiment results, seven folding positions every 10 deg from 20 deg to 80 deg are selected to represent motion-stiffness curves.

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Fig. 13

Folding moment and stiffness comparisons of crash-lock carton. (a) Folding moment comparison, dashed line represents mathematical model, solid line represents experiment result. (b) Folding stiffness comparison, dashed line represents mathematical model, solid line represents experiment result.

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Fig. 12

Folding moment and stiffness comparisons of gable-style carton. (a) Folding moment comparison, dashed line represents mathematical model, solid line represents experiment result. (b) Folding stiffness comparison, dashed line represents mathematical model, solid line represents experiment result.

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Fig. 14

Carton equivalent mechanism and the carton corner linkages. (a) Manipulated carton and equivalent mechanism and (b) corner linkages A.

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Fig. 15

Folding moment and stiffness comparisons of single crease with various crease lengths. (a) Folding moment comparison, dashed line, dashed-dotted line, and solid line correspond to experiment results, and dotted lines represent ±1 standard deviation. (b) Folding stiffness comparison, dashed line, dashed-dotted line, and solid line correspond to experiment results, 12 folding positions every 6 deg from 10 deg to 76 deg are selected to represent motion-stiffness curves.

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Fig. 16

Folding moment and stiffness comparisons between mathematical model and experimental data. (a) Folding moment comparison, dashed line represents mathematical model, solid line represents experiment result. (b) Folding stiffness comparison, dashed line represents mathematical model, solid line represents experiment result.

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