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Research Papers: Design of Mechanisms and Robotic Systems

Exploration of Translational Joint Design Using Corrugated Flexure Units With Bézier Curve Segments

[+] Author and Article Information
Nianfeng Wang

Guangdong Key Laboratory of Precision
Equipment and Manufacturing Technology,
School of Mechanical and
Automotive Engineering,
South China University of Technology,
Guangzhou, 510640, China
e-mail: menfwang@scut.edu.cn

Zhiyuan Zhang, Fan Yue

Guangdong Key Laboratory of Precision
Equipment and Manufacturing Technology,
School of Mechanical and
Automotive Engineering,
South China University of Technology,
Guangzhou, 510640, China

Xianmin Zhang

Guangdong Key Laboratory of Precision
Equipment and Manufacturing Technology,
School of Mechanical and
Automotive Engineering,
South China University of Technology,
Guangzhou, 510640, China
e-mail: zhangxm@scut.edu.cn

1Corresponding authors.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 3, 2018; final manuscript received November 19, 2018; published online January 11, 2019. Assoc. Editor: Massimo Callegari.

J. Mech. Des 141(5), 052301 (Jan 11, 2019) (9 pages) Paper No: MD-18-1670; doi: 10.1115/1.4042366 History: Received September 03, 2018; Revised November 19, 2018

In order to satisfy particular design specifications, shape variation for limited geometric envelopes is often employed to alter the elastic properties of flexure joints. This paper introduces an analytical stiffness matrix method to model a new type of corrugated flexure (CF) beam with cubic Bézier curve segments. The cubic Bézier curves are used to depict the segments combined to form CF beam and translational joint. Mohr's integral is applied to derive the local-frame compliance matrix of the cubic Bézier curve segment. The global-frame compliance matrices of the CF unit and the CF beam with cubic Bézier curve segments are further formed by stiffness matrix method, which are confirmed by finite element analysis (FEA). The control points of Bézier curve are chosen as optimization parameters to identify the optimal segment shape, which maximizes both high off-axis/axial stiffness ratio and large axial displacements of translational joint. The results of experimental study on the optimum translational joint design validate the proposed modeling and optimization method.

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Figures

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Fig. 1

The translational joint structured with four identical CF beams

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Fig. 2

The cubic Bézier curve: (a) t = 0.54 and (b) t = 1.00

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Fig. 3

The CF beam with cubic Bézier curve segments

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Fig. 4

Local reference frame of the CF unit with cubic Bézier curve segment

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Fig. 5

In-plane loads Fx, Fy, and Mz for the cubic Bézier curve segment

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Fig. 6

The translational joint constructed with four CF beams with cubic Bézier curve segments

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Fig. 7

Finite element analysis results of the translational joint with cubic Bézier curve segments

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Fig. 8

The design domain has been divided into the grid

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Fig. 9

Relationship between the off-axis/axial stiffness ratio and coordinates of P1 with given position of P2: (a) P2 (0.476, 0.238), (b) P2 (0.476, 0.476), (c) P2 (0.476, 0.714), (d) P2 (0.476, 0.952), (e) P2 (0.476, 1.190), and (f) P2 (0.476, 1.428)

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Fig. 10

The model of the translational joint with control points as P1 (0.000, 0.952) and P2 (0.476, 0.952)

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Fig. 11

The prototype of the translational joint with cubic Bézier curve segments (a) and semi-circle segments (b) manufactured by WEDM

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Fig. 12

Experimental system. Numbered components are: (1) controller of laser displacement sensor; (2) sensor head; (3) translational joint; (4) VCM; (5) switching power supply (24 V); (6) driver of VCM.

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Fig. 13

Relationship between output displacement and input force

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