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

Marijn Nijenhuis; Jacob Philippus Meijaard; Justus Laurens Herder; Shorya Awtar; Dannis Michel Brouwer

doi:10.1115/DETC2015-46591

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

Marijn Nijenhuis, Jacob Philippus Meijaard, Justus Laurens Herder, Shorya Awtar, Dannis Michel Brouwer

Faculty of Engineering Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

3 Citations (Scopus)

Abstract

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.

Original language	English
Title of host publication	ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Subtitle of host publication	Volume 5A: 39th Mechanisms and Robotics Conference
Place of Publication	Boston, MA, USA
Publisher	American Society of Mechanical Engineers
Pages	-
Volume	5A
Edition	39
ISBN (Print)	978-0-7918-5712-0
DOIs	https://doi.org/10.1115/DETC2015-46591
Publication status	Published - 2 Aug 2015
Event	39th Mechanisms and Robotics Conference 2015 - Boston, United States Duration: 2 Aug 2015 → 5 Aug 2015 Conference number: 39

Conference

Conference	39th Mechanisms and Robotics Conference 2015
Country/Territory	United States
City	Boston
Period	2/08/15 → 5/08/15

Keywords

METIS-311301
IR-104850

Access to Document

10.1115/DETC2015-46591

Cite this

Nijenhuis, M., Meijaard, J. P., Herder, J. L., Awtar, S., & Brouwer, D. M. (2015). An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip. In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference : Volume 5A: 39th Mechanisms and Robotics Conference (39 ed., Vol. 5A, pp. -). Article DETC2015-46591 American Society of Mechanical Engineers. https://doi.org/10.1115/DETC2015-46591

Nijenhuis, Marijn ; Meijaard, Jacob Philippus ; Herder, Justus Laurens et al. / An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip. ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference : Volume 5A: 39th Mechanisms and Robotics Conference. Vol. 5A 39. ed. Boston, MA, USA : American Society of Mechanical Engineers, 2015. pp. -

@inproceedings{adba29007afe474c909c3bccf1db5240,

title = "An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip",

abstract = "A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.",

keywords = "METIS-311301, IR-104850",

author = "Marijn Nijenhuis and Meijaard, {Jacob Philippus} and Herder, {Justus Laurens} and Shorya Awtar and Brouwer, {Dannis Michel}",

year = "2015",

month = aug,

day = "2",

doi = "10.1115/DETC2015-46591",

language = "English",

isbn = "978-0-7918-5712-0",

volume = "5A",

pages = "--",

booktitle = "ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference",

publisher = "American Society of Mechanical Engineers",

address = "United States",

edition = "39",

note = "39th Mechanisms and Robotics Conference 2015 ; Conference date: 02-08-2015 Through 05-08-2015",

}

Nijenhuis, M , Meijaard, JP, Herder, JL, Awtar, S & Brouwer, DM 2015, An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip. in ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference : Volume 5A: 39th Mechanisms and Robotics Conference. 39 edn, vol. 5A, DETC2015-46591, American Society of Mechanical Engineers, Boston, MA, USA, pp. -, 39th Mechanisms and Robotics Conference 2015, Boston, Massachusetts, United States, 2/08/15. https://doi.org/10.1115/DETC2015-46591

An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip. / Nijenhuis, Marijn ; Meijaard, Jacob Philippus; Herder, Justus Laurens et al.
ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference : Volume 5A: 39th Mechanisms and Robotics Conference. Vol. 5A 39. ed. Boston, MA, USA: American Society of Mechanical Engineers, 2015. p. - DETC2015-46591.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

AU - Nijenhuis, Marijn

AU - Meijaard, Jacob Philippus

AU - Herder, Justus Laurens

AU - Awtar, Shorya

AU - Brouwer, Dannis Michel

N1 - Conference code: 39

PY - 2015/8/2

Y1 - 2015/8/2

N2 - A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.

AB - A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.

KW - METIS-311301

KW - IR-104850

U2 - 10.1115/DETC2015-46591

DO - 10.1115/DETC2015-46591

M3 - Conference contribution

SN - 978-0-7918-5712-0

VL - 5A

SP - -

BT - ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

PB - American Society of Mechanical Engineers

CY - Boston, MA, USA

T2 - 39th Mechanisms and Robotics Conference 2015

Y2 - 2 August 2015 through 5 August 2015

ER -

Nijenhuis M , Meijaard JP, Herder JL, Awtar S, Brouwer DM. An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip. In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference : Volume 5A: 39th Mechanisms and Robotics Conference. 39 ed. Vol. 5A. Boston, MA, USA: American Society of Mechanical Engineers. 2015. p. -. DETC2015-46591 doi: 10.1115/DETC2015-46591

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

Abstract

Conference

Keywords

Access to Document

Fingerprint

Cite this