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Research Papers

Building Block-Based Spatial Topology Synthesis Method for Large-Stroke Flexure Hinges

[+] Author and Article Information
M. Naves

Chair of Precision Engineering,
University of Twente,
P.O. Box 217,
AE Enschede 7500, The Netherlands
e-mail: m.naves@utwente.nl

D. M. Brouwer

Chair of Precision Engineering,
University of Twente,
P.O. Box 217,
AE Enschede 7500, The Netherlands
e-mail: d.m.brouwer@utwente.nl

R. G. K. M. Aarts

Chair of Structural Dynamics,
Acoustics and Control,
University of Twente,
P.O. Box 217,
AE Enschede 7500, The Netherlands
e-mail: r.g.k.m.aarts@utwente.nl

1Corresponding author.

Manuscript received November 1, 2016; final manuscript received March 4, 2017; published online May 2, 2017. Assoc. Editor: Guimin Chen.

J. Mechanisms Robotics 9(4), 041006 (May 02, 2017) (9 pages) Paper No: JMR-16-1338; doi: 10.1115/1.4036223 History: Received November 01, 2016; Revised March 04, 2017

Large-stroke flexure mechanisms inherently lose stiffness in supporting directions when deflected. A systematic approach to synthesize such hinges is currently lacking. In this paper, a new building block-based spatial topology synthesis method is presented for optimizing large-stroke flexure hinges. This method consists of a layout variation strategy based on a building block approach combined with a shape optimization to obtain the optimal design tuned for a specific application. A derivative-free shape optimization method is adapted to include multiple system boundaries and constraints to optimize high complexity flexure mechanisms in a broad solution space. To obtain the optimal layout, three predefined three-dimensional (3D) “building blocks” are proposed, which are consecutively combined to find the best layout with respect to specific design criteria. More specifically, this new method is used to optimize a flexure hinge aimed at maximizing the frequency of the first unwanted vibration mode. The optimized topology shows an increase in frequency of a factor ten with respect to the customary three flexure cross hinge (TFCH), which represents a huge improvement in performance. The numerically predicted natural frequencies and mode shapes have been verified experimentally.

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Figures

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Fig. 1

Schematic representation of a topology optimization based on a combined shape optimization and layout synthesis

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Fig. 2

Parameterized model of a TFCH with design parameters p=[h,w,t,d] [12]

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Fig. 3

Visualization of the planes spanned by the degrees of constraint of the outer and inner building blocks of a TFCH

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Fig. 4

Calculated instant center of rotation of a cross hinge consisting of two and three flexures

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Fig. 5

Flexural building blocks used to “synthesize” flexure layout: (a) LS, (b) TRLS, and (c) TFCH

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Fig. 6

Pseudo rigid body representation of a double TFCH in series

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Fig. 7

Topology optimization based on a combined shape optimization and layout synthesis

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Fig. 8

Optimized shape for each intermediate layout. The inner building blocks are represented in red, the outer building blocks in blue. The natural frequency of the first unwanted vibration mode and the maximum stress is given in the top left corner. The optimal parameter set which describes the shape is given in the bottom left corner. Note: the rigid body of the load/end-effector and the base is not shown: (a) iteration 1 including description, (b) iteration 2, (c) iteration 3, (d) iteration 4, and (e) iteration 2 (see figure online for color).

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Fig. 9

Natural frequencies of the first unwanted vibration mode of intermediate shape optimized layouts

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Fig. 10

CAD rendering of the manufactured flexure mechanism existing of a TRLS(3x) supported by two double TFCH's: (a) section view and (b) complete view

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Fig. 11

Measurement setup for testing rot-x vibration modes at −20 deg deflection

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Fig. 12

Frequency response from impact to x-, y-, and z-accelerations at accelerometer location 2 and 0 deg deflection

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Fig. 13

Experimental validation of the natural frequencies of the first four vibration modes in the directions in which the motion is constrained. Markers indicate the experimental results.

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