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Research Papers

# Design and Performance Optimization of Large Stroke Spatial Flexures

[+] Author and Article Information
R. G. K. M. Aarts

e-mail: r.g.k.m.aarts@utwente.nl
Faculty of Engineering Technology,
University of Twente,
P.O. Box 217 Enschede,
AE 7500, The Netherlands

D. M. Brouwer

Faculty of Engineering Technology,
University of Twente,
P.O. Box 217 Enschede,
AE 7500, The Netherlands
PH 7521, The Netherlands

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 29, 2012; final manuscript received October 9, 2013; published online November 7, 2013. Assoc. Editor: Johannes Gerstmayr.

J. Comput. Nonlinear Dynam 9(1), 011016 (Nov 07, 2013) (10 pages) Paper No: CND-12-1212; doi: 10.1115/1.4025669 History: Received November 29, 2012; Revised October 09, 2013

## Abstract

Flexure hinges inherently lose stiffness in supporting directions when deflected. In this paper a method is presented for optimizing the geometry of flexure hinges, which aims at maximizing supporting stiffnesses. In addition, the new $∞$-flexure hinge design is presented. The considered hinges are subjected to a load and deflected an angle of up to ±20 deg. The measure of performance is defined by the first unwanted natural frequency, which is closely related to the supporting stiffnesses. During the optimization, constraints are applied to the actuation moment and the maximum occurring stress. Evaluations of a curved hinge flexure, cross revolute hinge, butterfly flexure hinge, two cross flexure hinge types, and the new $∞$-flexure hinge are presented. Each of these hinge types is described by a parameterized geometric model. A flexible multibody modeling approach is used for efficient modeling while it accounts for the nonlinear geometric behavior of the stiffnesses. The numerical efficiency of this model is very beneficial for the design optimization. The obtained optimal hinge designs are validated with a finite element model and show good agreement. The optimizations show that a significant increase in supporting stiffness, with respect to the conventional cross flexure hinge, can be achieved with the $∞$-flexure hinge.

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## Figures

Fig. 1

Leaf-spring flexure (figure based on Ref. [16])

Fig. 2

Loadcase defined in the load coordinate system Oxlylzl, with principal axis of inertia x'y'z', where φ is the angle between the projection of y'-axis on the xl-yl plane and yl-axis

Fig. 3

Hinge coordinate system Oxyz, actuation moment M and angle of deflection θ of the hinge

Fig. 4

Double clamped flexure with parameterized finite element beam model

Fig. 5

Constrained warping stiffening factor γ as a function of the aspect ratio i (for ν=0.3)

Fig. 6

The geometric interpretation of the loadcase, which is based on the mechanism of Ref. [4]

Fig. 7

Parameterization of the SFCH and illustration of the angle of deflection θ

Fig. 8

Optimal geometry of the SFCH with the principal axes of inertia x' and y', dimensions in mm

Fig. 9

Second eigenfrequency as a function of the angle of deflection for the optimal solutions, determined with the FE method

Fig. 10

Parameterization of the TFCH

Fig. 11

Optimal geometry of the TFCH, with the principal axes given in the pivot of the hinge, dimensions in mm

Fig. 12

Second eigenfrequency as a function of the angle of deflection for the optimal solution of the TFCH. Determined by SPACAR, with (SPACAR CW) and without (SPACAR) the inclusion of constrained warping, and the FE method.

Fig. 13

Parameterization of the BFH

Fig. 14

Optimal geometry of the BFH, with the principal axes given in the pivot of the hinge, dimensions in mm

Fig. 15

Isometric and front view of the parameterized CHF

Fig. 16

Optimal geometry of the CHF, dimensions in mm

Fig. 17

Isometric view and parameterization of the CRH

Fig. 18

Top view of the optimized CRH geometry, dimensions in mm

Fig. 19

Isometric and front view of the parameterized ∞-FH (part 1)

Fig. 20

Isometric and front view of the parameterized ∞-FH (part 2)

Fig. 21

Optimal geometry of the ∞-FH, with the principal axes of inertia, dimensions in mm

Fig. 22

Variation of the ∞-FH as a function of parameter d

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