Modal Measurements and Model Corrections of A Large Stroke Compliant Mechanism

Wijma, W.; Boer, Steven; Aarts, RM Ronald; Brouwer, Dannis Michel; Hakvoort, Wouter

doi:10.2478/meceng-2014-0020

Cited by 4 publications

(3 citation statements)

References 17 publications

(16 reference statements)

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“…For example, we ran a model of a simplified four-bar mechanism with a rotational misalignment of one of the hinges in the actuation direction of 1 deg. The results show a decrease in the vertical support stiffness at the equilibrium position of about 20% [37]. The decrease in stiffness, with respect to perfectly aligned leaf-springs, become less moving away from the equilibrium position, which is also shown by the measurements.…”

Section: Measurementssupporting

confidence: 71%

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Exact Constraint Design of a Two-Degree of Freedom Flexure-Based Mechanism1

Brouwer¹,

Folkersma²,

Boer³

et al. 2013

Journal of Mechanisms and Robotics

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We present the exact constraint design of a two degrees of freedom cross-flexure-based stage that combines a large workspace to footprint ratio with high vibration mode frequencies. To maximize unwanted vibration mode frequencies the mechanism is an assembly of optimized parts. To ensure a deterministic behavior the assembled mechanism is made exactly constrained. We analyze the kinematics of the mechanism using three methods; Grüblers criterion, opening the kinematic loops, and with a multibody singular value decomposition method. Nine release-flexures are implemented to obtain an exact constraint design. Measurements of the actuation force and natural frequency show no bifurcation, and load stiffening is minimized, even though there are various errors causing nonlinearity. Misalignment of the exact constraint designs does not lead to large stress, it does however decrease the support stiffness significantly. We conclude that designing an assembled mechanism in an exactly constrained manner leads to predictable stiffnesses and modal frequencies.

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Section: Measurementssupporting

confidence: 71%

“…We measured the third and fourth natural frequency, which are the first and second unwanted frequency, of the two-DOF stage over the range of motion [37]. We used a shaker, compliantly suspended, and a laser vibrometer attached to an industrial robot to track several measurement positions.…”

Section: Measurementsmentioning

confidence: 99%

Exact Constraint Design of a Two-Degree of Freedom Flexure-Based Mechanism1

Brouwer¹,

Folkersma²,

Boer³

et al. 2013

Journal of Mechanisms and Robotics

View full text Add to dashboard Cite

show abstract

“…This difference in frequency is probably caused by hardware imperfections in the experimental setup that were not included in the numerical model. These factors can be the clamping effects of the hinges and errors in manufacturing and assembly [22].…”

Section: Resultsmentioning

confidence: 99%

Effects of misalignments on the static and dynamic behaviour of a multiple overconstrained compliant 4-bar mechanism

Sande

Aarts

Brouwer

2019

Precision Engineering

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The use of overconstrained mechanisms is often avoided in precision mechanics. Misalignments in the mechanism can cause deteriorated system behaviour, such as buckling. Overconstrained designs do have several advantages, such as higher load bearing capacity and higher natural frequencies. However, these advantages are only present if the mechanism is aligned within certain tolerances. In this paper a method is introduced to identify the limits of these alignment tolerances. The method allows the calculation of the forces in the mechanism due to misalignment. The internal forces are compared to the buckling loads of the mechanism yielding the critical misalignments; the method is corroborated using a multibody simulations. Subsequently, both analyses are compared to an experimental setup; this setup measures the first three modal frequencies and identifies the buckling modes. The proposed method and multibody simulation match with each other and the experiment. However, the critical misalignments are about 20% larger in the experiment; this is mainly attributed to hardware imperfections. Due to misalignment and flatness limitations of the flexures, the undeflected stiffness in the experiment is lower than modelled. The deterioration of the support stiffness is smaller in the experiment. In the most serious case, it retains 80% of the modal frequency in the support directions. The proposed method can be used as a guideline to estimate the manufacturing and assembly tolerances of an overconstrained flexure-based mechanism.

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An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

Nijenhuis

Meijaard

Mariappan

et al. 2017

Journal of Mechanical Design

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This paper presents a framework for modeling the deformation and stiffness characteristics of static 3-D flexure strips (leaf springs), based on a discrete beam model that is suited for analytical calculations. As a case study, a closed-form parametric expression is derived for the lateral support stiffness of a parallel flexure mechanism. Continuous modelA spatial Timoshenko beam with Reissner's finite strain measures -capturing shear, bending and torsion deformation -and linear elastic material behavior serves as a model for flexure strips. Discrete modelA discretized version of the continuous model has been implemented in numeric flexible multibody software as a two-node beam element [1]. It is observed that a single such element captures stiffness characteristics of spatially deforming flexure strips with reasonable accuracy, owing to the inclusion of finite strain measures. As the mathematics of a single element remain comprehensible, the discrete model is well-suited for closed-form analysis. The available software implementation then serves as a calculation aid that facilitates the analytical modeling process. Case study: parallel flexure mechanismWhen a parallel flexure mechanism (figure 1) moves in the degree of freedom, the stiffness characteristics deteriorate: the lateral support stiffness decreases (figure 2). By using four discrete beam elements, a case-specific improvement of the torsion interpolation, and an approximation of the equilibrium configuration, this behavior is captured by the simple closed-form expression

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Modal Measurements and Model Corrections of A Large Stroke Compliant Mechanism

Cited by 4 publications

References 17 publications

Exact Constraint Design of a Two-Degree of Freedom Flexure-Based Mechanism1

Exact Constraint Design of a Two-Degree of Freedom Flexure-Based Mechanism1

Effects of misalignments on the static and dynamic behaviour of a multiple overconstrained compliant 4-bar mechanism

An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

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