Accurate low DOF modeling of a planar compliant mechanism with flexure hinges: the equivalent beam methodology

Zettl, B.; Szyszkowski, W.; Zhang, W.J.

doi:10.1016/j.precisioneng.2004.09.001

Cited by 39 publications

(14 citation statements)

References 6 publications

(11 reference statements)

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“…This finding is different from the result in Refs. [10,11] and betrays our expectation. The influence from beam length of the CBPM is stronger than that of the CDPM, due to the fact that the CBPM exhibits loadstiffening behavior.…”

Section: Fea Simulation Results and Analysismentioning

confidence: 65%

“…Since the required actuation force is proportional to the used modulus under the same primary motion [10,11], the following two equations can be obtained:…”

Section: Study Descriptionmentioning

confidence: 99%

“…If an analytical model for this modulus ratio is hard to derive, an empirical equation based on finite element analysis (FEA) is desired. References [10,11] reported interesting work on equivalent modulus of right circular planar flexure hinges (short beams) using an FEA method, and proposed an empirical equation of the equivalent modulus (or modulus ratio as defined above). It is shown that the equivalent modulus of the right circular planar flexure hinges is larger than the Young's modulus but smaller than the plate modulus, and that it is reasonable to use planar stress (or strain) assumption if beam out-of-plane thickness compared to the in-plane thickness is small enough (or large enough).…”

Section: Introductionmentioning

confidence: 99%

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Understanding coupled factors that affect the modelling accuracy of typical planar compliant mechanisms

Hao

Kemalcan

et al. 2016

Front. Mech. Eng.

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In order to accurately model compliant mechanism utilizing plate flexures, qualitative planar stress (Young's modulus) and planar strain (plate modulus) assumptions are not feasible. This paper investigates a quantitative equivalent modulus using nonlinear finite element analysis (FEA) to reflect coupled factors in affecting the modelling accuracy of two typical distributed-compliance mechanisms. It has been shown that all parameters have influences on the equivalent modulus with different degrees; that the presence of large load-stiffening effect makes the equivalent modulus significantly deviate from the planar assumptions in two ideal scenarios; and that a plate modulus assumption is more reasonable for a very large out-of-plane thickness if the beam length is large.

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Section: Fea Simulation Results and Analysismentioning

confidence: 65%

“…Since the required actuation force is proportional to the used modulus under the same primary motion [10,11], the following two equations can be obtained:…”

Section: Study Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Understanding coupled factors that affect the modelling accuracy of typical planar compliant mechanisms

Hao

Kemalcan

et al. 2016

Front. Mech. Eng.

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“…The second issue is that the in-plane stiffness of the leaf beam in the plate plane is relatively small since the leaf's thickness in the DOC (degree of constraint) direction is limited by the dimension of the plate (Awtar and Slocum, 2005), and that this DOC stiffness can degrade significantly over the primary motion (Nijenhuis et al, 2015). The final issue is that modelling a leaf beam is extremely complex when considering warping effect and effective modulus to be used (Nijenhuis et al, 2015;Zettl et al, 2004). In order to address the above stiffness issues, References (Hao and Kong, 2014;Merriam and Howell, 2016) have used wire-beam based design to replace the leaf beam for the applications in an XY Z manipulator and in a cross-axis flexure pivot, respectively.…”

Section: Introductionmentioning

confidence: 99%

Design and analysis of symmetric and compact 2R1T (in-plane 3-DOC) flexure parallel mechanisms

Hao

2017

Mech. Sci.

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Abstract. Symmetry is very necessary in flexure mechanisms, which can eliminate parasitic motions, avoid buckling, and minimize thermal and manufacturing sensitivity. This paper proposes two symmetric and compact flexure designs, in-plane 3-DOC (degree of constraint) mechanisms, which are composed of 4 and 6 identical wire beams, respectively. Compared to traditional leaf-beam-based designs, the two present designs have lower stiffness in the primary motion directions, and have smaller stiffness reduction in the parasitic directions. Analytical modelling is conducted to derive the symbolic compliance equations, enabling quick analysis and comparisons of compliances of the two mechanisms. A prototype has been tested statically to compare with analytical models.

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“…In order to reduce nDOF, the machine has been divided into subcomponents or modules, and these modules have been coupled with boundary conditions [5][6][7][8]. Also in the simulations of positioning system with flexture hinges, hinges are modelled as a simple beam element to reduce nDOF [9].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of modelling approaches for machine tool design

Kono

Lorenzer

Weikert

et al. 2010

Precision Engineering

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a b s t r a c tIn order to evaluate the configuration of machine tools, the IWF Axis Construction Kit (ACK) has been developed. This paper describes the evaluation of this approach. The ACK supports rigid body simulations and simple elastic body simulations. The ACK is compared with commercial FEM software to investigate its usability and reliability. Required time was compared in modelling of a machine tool. The ACK needed 30% of the total required time for the FEM because of its modularity in machine modelling. Then, in order to investigate the reliability of the ACK, static and dynamic simulations of both approaches were compared with each other and with analytical calculations on basic beam models. The result showed that the ACK provided equivalent results to the FEM. Static and dynamic simulations were also compared with measurements on an actual machine tool. The ACK obtained almost equivalent results to the FEM. Almost all lower structural mode shapes and their natural frequencies could be reproduced with the ACK when crucial parts were modelled using elastic bodies.

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Accurate low DOF modeling of a planar compliant mechanism with flexure hinges: the equivalent beam methodology

Cited by 39 publications

References 6 publications

Understanding coupled factors that affect the modelling accuracy of typical planar compliant mechanisms

Understanding coupled factors that affect the modelling accuracy of typical planar compliant mechanisms

Design and analysis of symmetric and compact 2R1T (in-plane 3-DOC) flexure parallel mechanisms

Evaluation of modelling approaches for machine tool design

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