Technical Brief

Kinematic Analysis of Foldable Plate Structures With Rolling Joints

[+] Author and Article Information
Cai Jianguo

Key Laboratory of C & PC Structures
of Ministry of Education,
National Prestress Engineering Research Center,
Southeast University,
Si Pai Lou 2#,
Nanjing 210096, China
e-mails: j.cai@seu.edu.cn; caijg_ren@hotmail.com

1Corresponding author.

Manuscript received June 17, 2015; final manuscript received December 2, 2015; published online March 7, 2016. Assoc. Editor: Mary Frecker.

J. Mechanisms Robotics 8(3), 034502 (Mar 07, 2016) (6 pages) Paper No: JMR-15-1145; doi: 10.1115/1.4032269 History: Received June 17, 2015; Revised December 02, 2015

Rolling joints, which are created by attaching two cylindrical surfaces of equal radius using two or more thin tapes or cable, are used for rigid origami considering the panel thickness. First, the concept and two implementation methods of this joint are given. Then planar linkages are chosen to study the mobility and kinematics of foldable plate structures with rolling joints. It can be found that the rolling joints preserve the full-cycle-motion of foldable plate structures. From the closure equations of linkages, the results show that the outputs of linkages with rolling joints are the same as that with traditional revolute joints if the lengths of links are equal. However, the results are different when the lengths of links are unequal. Moreover, the difference between linkages with rolling joints and revolute joints increases with an increase of the size of rolling joints.

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Fig. 1

Two methods for enabling rigid origami with thickness from Tachi

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Fig. 2

Rolling joints: (a) concept of rolling joints, (b) rolling joints connected with tapes, and (c) joints connected with cables

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Fig. 3

A series of panels with rolling joints

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Fig. 4

Foldable plate structures with rolling joints

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Fig. 5

Basic elements of foldable plate structures

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Fig. 6

Planar four-bar linkages: (a) plane four-bar linkage with traditional revolute joints, (b) plane four-bar linkage with rolling joints, and (c) schematic diagram of four-bar linkage with rolling joints

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Fig. 7

Vector loop for a linkage

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Fig. 8

Results of closure equations (r1 = r2 = r3 = r4 = 1.0) (a) θ3 versus θ1 and (b) θ4 versus θ1

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Fig. 9

Results of closure equations (r1 = 0.5, r2 = 1.0, r3 = 1.5, r4 = 2.0) (a) θ3 versus θ1 and (b) θ4 versus θ1

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Fig. 10

Results of closure equations (r1 = 1.0, r2 = 1.0, r3 = 2.5, r4 = 2.0) (a) θ3 versus θ1 and (b) θ4 versus θ1

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Fig. 11

Four-bar linkages with unequal lengths



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