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Research Papers: Design of Mechanisms and Robotic Systems

Second-Order Cone Programming Approach to Design of Linkage Mechanisms With Arbitrarily Inclined Hinges

[+] Author and Article Information
Makoto Ohsaki

Department of Architecture and
Architectural Engineering,
Kyoto University,
Kyoto-Daigaku Katsura,
Nishikyo, Kyoto 615-8540, Japan
e-mail: ohsaki@archi.kyoto-u.ac.jp

Yoshihiro Kanno

Mathematics and Informatics Center,
The University of Tokyo,
Hongo 7-3-1,
Bunkyo, Tokyo 113-8656, Japan
e-mail: kanno@mist.i.u-tokyo.ac.jp

Yuki Yamaoka

Department of Architecture and
Architectural Engineering,
Kyoto University,
Kyoto-Daigaku Katsura,
Nishikyo, Kyoto 615-8540, Japan
e-mail: y.yamaoka28@gmail.com

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 3, 2017; final manuscript received July 8, 2018; published online July 30, 2018. Assoc. Editor: Nam H. Kim.

J. Mech. Des 140(10), 102301 (Jul 30, 2018) (9 pages) Paper No: MD-17-1667; doi: 10.1115/1.4040879 History: Received October 03, 2017; Revised July 08, 2018

An optimization approach is presented for generating linkage mechanisms consisting of frame members with arbitrarily inclined hinges. A second-order cone programming (SOCP) problem is solved to obtain the locations and directions of hinges of an infinitesimal mechanism. It is shown that the primal and dual SOCP problems correspond to the plastic limit analysis problems based on the lower-bound and upper-bound theorems, respectively, with quadratic yield functions. Constraints on displacement components are added to the dual problem, if a desirable deformation is not obtained. A finite mechanism is generated by carrying out geometrically nonlinear analysis and, if necessary, adding hinges and removing members. Effectiveness of the proposed method is demonstrated through examples of two- and three-dimensional mechanisms.

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Figures

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Fig. 1

Definition of member coordinates and independent member-end forces: (a) local and global coordinates and (b) six independent member-end forces

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Fig. 2

A plane grid model (Model 1)

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Fig. 3

Mechanisms of the plane grid model obtained by solving various types of optimization problem; filled circle indicates a hinge: (a) linear programming problem [16], (b) problem (12) without displacement constraints, (c) problem (12) with displacement constraints, and (d) finite mechanism obtained by removing four members of infinitesimal mechanism

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Fig. 4

A simple square-grid model (Model 2): (a) plan view and node/member indices and (b) diagonal view and input/output loads

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Fig. 5

Locations and directions of hinges of Model 2; an infinitesimal mechanism is obtained by solving problems (5) and (6)

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Fig. 6

Locations of hinges of Model 2; finite mechanism after adding eight torsional hinges

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Fig. 7

Deformation process of finite mechanism of Model 2

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Fig. 8

A plane grid consisting of two square grids (Model 3); (a) node and element indices and (b) input and output loads

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Fig. 9

Locations of hinges of Model 3; infinitesimal mechanism obtained by solving problem (12)

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Fig. 10

Deformation process of finite mechanism of Model 3: (a) diagonal view and (b) elevation

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Fig. 11

Relation between the path parameter and the displacements at nodes 6 and 14 of Model 3; solid line: node 6, dashed line: node 14

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