Analysis, optimization and synthesis of compliant linkage mechanisms for ultra-precision applications (2nd project phase)

Prof. L. Zentner
S. Henning, M. Sc.

State of the art

Flexure hinges are used as material coherent revolute joints in compliant linkage mechanisms for ultra-precision applications. In this case, the requirements for the precision are in the range of nanometers or angular subseconds. Compliant mechanisms are often synthetized by the substitution of rigid-body mechanisms. There is a need for research, because the influence of the concrete constructional design on the kinematic behavior has not been investigated in literature so far with the required resolution. Mostly flexure hinges with basic cut-out geometries are used. Therefore, compliant mechanisms based on these flexure hinges show a limited motion range and path accuracy. To overcome these limitations, in existing approaches the number of joints is increased in the kinematic chain of the mechanism, while there are no studies on the optimization of the flexure hinge contour with respect to the design of monolithic mechanisms. Thus, the inadequate knowledge of the kinematic properties limits advances in modern ultra-precise applications claiming for both highest precision and significantly increased motion ranges.

Aim and approach

The goal of this project is the development of fundamentals for the synthesis of compliant mechanisms with optimized flexure hinges. As the focal point of the first project phase, specifically the influence of the hinge contour on the mechanism properties has been investigated in comparison to the rigid-body counterpart. The investigations have shown that polynomial flexure hinges, which are directly optimized in the mechanism, are advantageous. Compared to conventional hinge contours polynomial flexure hinges allow a simultaneous increase of the range of motion and the precision. An additional improvement can be achieved by the application of different flexure hinges in one mechanism and by an appropriate design of the hinge orientation and of the coupler geometry as well. Based on the results of the first project phase, additional research is needed regarding the geometric design of monolithic micro and nanopositioning systems with macro dimensions. Here, the focus is on the further development of a novel synthesis method based on the rotation angles of each hinge, which is more precise compared to rigid-body model. It allows the goal-oriented design of the compliant mechanism with consideration of the influence of the scaling of spatial positioning systems.

TU Ilmenau

Contribution

Compared to the current state of research, particularly the aim to increase both, the precision and the stroke of compliant mechanisms is a new approach. Thus, the project contributes to the development of a multi-scale synthesis method for spatial compliant linkage mechanisms, which considers the degree of freedom of the mechanism and the integration of the drive into the position system. The results will be verified at two prototypes with different scaling. Finally, design guidelines for the further use in the ultra-precision technology will be formulated.

Publications (since 2018)

  • Henning, S.; Zentner, L.: Analysis of planar compliant mechanisms based on non-linear analytical modeling including shear and lateral contraction. In: Mechanism and Machine Theory 164, 104397, 2021 – DOI: 10.1016/j.mechmachtheory.2021.104397
  • Gräser, P.; Linß, S.; Harfensteller, F.; Torres, M.; Zentner, L.; Theska, R.: High-precision and large-stroke XY micropositioning stage based on serially arranged compliant mechanisms with flexure hinges, Precision Engineering, 2021. – DOI: 10.1016/j.precisioneng.2021.02.001
  • Henning, S.; Linß, S.; Zentner, L.: Synthesemethode zur Bestimmung geeigneter Geometrieparameter von Festkörpergelenken. In: Tagungsband Siebte IFToMM D-A-CH Konferenz 2021, 18.-19. Februar, 2021 – DOI: 10.17185/duepublico/74040
  • Henning, S.; Linß, S.; Gräser, P.; Schneider, J.D.; Theska, R.; Zentner, L.: Optimization of Compliant Path-Generating Mechanisms Based on Non-linear Analytical Modeling. In: Microactuators, Microsensors and Micromechanisms. MAMM 2020., Mechanisms and Machine Science, vol 96., Ilmenau; Zentner, L., Strehle, S., Eds.; Springer: Cham, 2021; pp 25–35. – DOI: 10.1007/978-3-030-61652-6_3
  • Darnieder, M.; Harfensteller, F.; Schorr, P.; Scharff, M.; Linß, S.; Theska, R.: Characterization of Thin Flexure Hinges for Precision Applications Based on First Eigenfrequency. In Microactuators, Microsensors and Micromechanisms. MAMM 2020., Mechanisms and Machine Science, vol 96., Ilmenau; Zentner, L., Strehle, S., Eds.; Springer: Cham, 2021; pp 15–24. – DOI: 10.1007/978-3-030-61652-6_2
  • Linß, S.; Gräser, P.; Torres, M.; Kaletsch, T.; Theska, R.; Zentner, L. A Novel Planar Two-Axis Leaf-Type Notch Flexure Hinge with Coincident Rotation Axes and Its Application to Micropositioning Stages. In: Microactuators, Microsensors and Micromechanisms. MAMM 2020., Mechanisms and Machine Science, vol 96., Ilmenau; Zentner, L., Strehle, S., Eds.; Springer: Cham, 2021; pp 1–14. – DOI: 10.1007/978-3-030-61652-6_1
  • Henning, S.; Linß, S.; Gräser, P.; Theska, R.; Zentner, L.: Non-linear analytical modeling of planar compliant mechanisms, Mechanism and Machine Theory, 155, 104067, 2021 – DOI: 10.1016/j.mechmachtheory.2020.104067
  • Henning. S.; Zentner, L.: Entwicklung eines PC-Programms zur Analyse von nachgiebigen Mechanismen für beliebige Bewegungsaufgaben. In: Tagungsband Sechste IFToMM D-A-CH Konferenz 2020, Lienz, Österreich, 27.-28. Februar, 2020 – DOI:10.17185/duepublico/71185
  • Henning. S.; Zentner, L.: Nichtlinear-analytische Modellbildung nachgiebiger Mechanismen unter Berücksichtigung des Querkraftschubs. In: Tagungsband 13. Kolloquium Getriebetechnik, Dortmund (Germany), Berlin: Logos Verlag, S. 31–40, 2019
  • Goncalves Junior, L.A.; Theska, R.; Lepsikon, H.A.; Ribeiro Junior, A.S.; Linß, S.; Gräser, P.: Theoretical and experimental investigation of performance characteristics and design aspects of cross-spring pivots. International Journal of Solids and Structures, In Press, Corrected Proof, 2019 – doi:10.1016/j.ijsolstr.2019.08.023
  • Linß, S.; Gräser, P.; Henning, S.; Harfensteller, F.; Theska, R.; Zentner, L.: Synthesis Method for Compliant Mechanisms of High-Precision and Large-Stroke by Use of Individually Shaped Power Function Flexure Hinges. In: Uhl, T. (Hg.): Mechanisms and Machine Science 73. Advances in Mechanism and Machine Science. Proceedings of the 15th IFToMM World Congress on Mechanism and Machine Science 2019, Cham: Springer International Publishing (Mechanisms and Machine Science, 73), S. 1569–1578, 2019 – doi:10.1007/978-3-030-20131-9_155
  • Henning, S.; Linß, S.; Vollrath, T.; Zentner, L.: Elasto-Kinematic Modeling of Planar Flexure Hinge-Based Compliant Mechanisms Incorporating Branched Links. In: Uhl, T. (Hg.): Mechanisms and Machine Science 73. Advances in Mechanism and Machine Science. Proceedings of the 15th IFToMM World Congress on Mechanism and Machine Science 2019, Cham: Springer International Publishing (Mechanisms and Machine Science, 73), S. 1599–1608, 2019 – doi:10.1007/978-3-030-20131-9_158
  • Gräser, P.; Linß, S.; Zentner, L.; Theska, R.: Investigations of different compliant manipulator concepts for a high-precise rotational motion. In: 19th International Conference of the European Society for Precision Engineering and Nanotechnology (euspen), June 3rd – June 7th 2019. Bilbao, Spain, S. 64– 67, 2019 – ISBN 978-0-9957751-4-5
  • Gräser, P.; Linß, S.; Zentner, L.; Theska, R.: Optimization of Compliant Mechanisms by Use of Different Polynomial Flexure Hinge Contours. In: Kecskeméthy, A. et al. (Hg.): Interdisciplinary Applications of Kinematics. Proceedings of the Third International Conference (IAK) 2018, Cham: Springer Nature (Mechanisms and Machine Science, 71), S. 265–274, 2019 – doi:10.1007/978-3-030-16423-2_25
  • Theska, R.; Zentner, L.; Fröhlich, T.; Weber, C.; Manske, E.; Linß, S.; Gräser, P.; Harfensteller, F.; Darnieder, M.; Kühnel, M.: Compliant Mechanisms for Ultra-Precise Applications. In: Kecskeméthy, A. et al. (Hg.): Interdisciplinary Applications of Kinematics. Proceedings of the Third International Conference (IAK) 2018, Cham: Springer Nature (Mechanisms and Machine Science, 71), S. 249–256, 2019 – doi:10.1007/978-3-030-16423-2_23
  • Linß, S.; Henning, S.; Zentner, L.: Modeling and Design of Flexure Hinge-Based Compliant Mechanisms. In: Mizrahi, J. (Hg.): Kinematics. Rijeka, Croatia: IntechOpen, 2019 – doi:10.5772/intechopen.85224
  • Torres Melgarejo, M. A.; Darnieder, M.; Linß, S.; Zentner, L.; Fröhlich, T.; Theska, R.: On Modeling the Bending Stiffness of Thin Semi-Circular Flexure Hinges for Precision Applications. In: Actuators 7 (4), 2018, p. 86 – DOI:10.3390/act7040086
  • Henning, S., Linß, S., Zentner, L.: detasFLEX – A computational design tool for the analysis of various notch flexure hinges based on non-linear modeling. In: Mechanical Sciences 9., 2018, S. 389-404 – DOI: 10.5194/ms-9-389-2018
  • Gräser, P.; Linß, S.; Räder, T.; Zentner, L.; Theska, R.: Investigations of the geometrical scaling in the systematic synthesis of compliant mechanisms. In: 18th International Conference of the European Society for Precision Engineering and Nanotechnology (euspen), June 4th – June 8th 2018. Venice, Italy, 2018, S. 67-68 – ISBN 978-0-9957751-2-1
  • Linß, S., Gräser, P., Räder, T., Henning, S., Theska, R., Zentner, L.: Influence of geometric scaling on the elasto-kinematic properties of flexure hinges and compliant mechanisms, Mechanism and Machine Theory, 125C, 220–239, 2018 – DOI: 10.1016/j.mechmachtheory.2018.03.008
  • Henning, S., Linß, S., Zentner, L.: Numerical Calculation of Compliant Four-bar Mechanisms with Flexure Hinges, In: Proceedings of the 4th International Conference Mechanical Engineering in XXI Century, Niš, Serbia, April 19-20, S. 267–279, 2018 – ISBN 978-86-6055-103-2
  • Theska, R., Zentner, L., Fröhlich, T., Weber, C., Manske, E., Linß, S., Gräser, P., Harfensteller, F., Darnieder, M., Kühnel, M.: State of the Art Precision Motion Systems Based on Compliant Mechanisms, In: Proceedings of the 4th International Conference Mechanical Engineering in XXI Century, Niš, Serbia, April 19-20, S. 3–8, 2018 – ISBN 978-86-6055-103-2
  • Henning, S.; Linß, S.; Schorr, P.; Zentner, L.: PC-Programm zur Analyse und Synthese von Festkörpergelenken mit unterschiedlichen Aussparungsgeometrien, In: Tagungsband Vierte IFToMM D-A-CH Konferenz 2018, Lausanne, Schweiz, 15.-16. Februar, 2018 – DOI: 10.17185/duepublico/45331
  • Schorr, P.; Linß, S.; Zentner, L.; Zimmermann, K.: Einfluss der Orientierung von Festkörpergelenken auf die elasto-kinematischen Eigenschaften, In: Tagungsband Vierte IFToMM D-A-CH Konferenz 2018, Lausanne, Schweiz, 15.-16. Februar, 2018 – DOI: 10.17185/duepublico/45330

Publications (2014-2017)

  • Linß, S.; Schorr, P.; Henning, S.; Zentner, L.: Contour-independent design equations for the calculation of the rotational properties of commonly used and polynomial flexure hinges. In: Proceedings of the 59th IWK, September 11th – 15th, Ilmenau Scientific Colloquium, Ilmenau, Germany, 2017URN: urn:nbn:de:gbv:ilm1-2017iwk-001:5
  • Gräser, P.; Linß, S.; Zentner, L.; Theska, R.: On the influence of the flexure hinge orientation in planar compliant mechanisms for ultra-precision applications. In: Proceedings of the 59th IWK, September 11th – 15th, Ilmenau Scientific Colloquium, Ilmenau, Germany, 2017URN: urn:nbn:de:gbv:ilm1-2017iwk-090:9
  • Linß, S., Schorr, P., Zentner, L.: General design equations for the rotational stiffness, maximal angular deflection and rotational precision of various notch flexure hinges. Mechanical Sciences. 8, 2017, S. 29–49 – DOI: 10.5194/ms-8-29-2017
  • Gräser, P; Linß, S; Harfensteller, F.; Zentner, L; Theska, R: Large stroke ultra-precision planar stage based on compliant mechanisms with polynomial flexure hinge design. In: 17th International Conference of the European Society for Precision Engineering and Nanotechnology (euspen), May 29th - June 2nd 2017. Hannover, Germany, 2017, S. 107-108 – ISBN 978-0-9957751-0-7
  • Gräser, P.; Linß, S.; Zentner, L.; Theska, R.: Design and Experimental Characterization of a Flexure Hinge-Based Parallel Four-Bar Mechanism for Precision Guides. In: Microactuators and Micromechanisms. Mechanisms and Machine Science 45, Springer International Publishing, Cham, 2017, S. 139-152 – DOI: 10.1007/978-3-319-45387-3_13
  • Gräser, P; Linß, S; Zentner, L; Theska, R: Increasing the stroke of an ultra-precise compliant mechanism with optimised flexure hinge contours. In: 16th International Conference of the European Society for Precision Engineering and Nanotechnology (euspen), May 30th - June 3rd 2016. Nottingham, UK, 2016, S. 487-488 – ISBN 978-0-9566790-8-6
  • Gräser, P.; Linß, S.; Zentner, L.; Theska, R.: Synthese und Untersuchung eines nachgiebigen Koppelmechanismus für Präzisionsführungen. In: Tagungsband Zweite IFToMM D-A-CH Conference 2016, 25. - 26. Februar 2016, Innsbruck. Universität Innsbruck, 2016, insges. 8 S.
  • Linß, S.; Milojević, A.; Pavlović, N. D.; Zentner, L.: Synthesis of Compliant Mechanisms based on Goal-Oriented Design Guidelines for Prismatic Flexure Hinges with Polynomial Contours. In: The 14th IFToMM World Congress: Taipei, Taiwan, October 25-30, 2015, 6 S. – DOI: 10.6567/IFToMM.14TH.WC.PS10.008
  • Linß, S.; Zentner, L.: FEM-Based Analysis of the Influence of Notch Contour and Scale on Flexure Hinge Design Goals. In: The 3rd International Conference Mechanical Engineering in XXI Century: Proceedings: 17. - 18. September 2015. Niš, Serbia, 2015, S. 283-286 – ISBN 978-86-6055-072-1
  • Linß, S.: Ein Beitrag zur geometrischen Gestaltung und Optimierung prismatischer Festkörpergelenke in nachgiebigen Koppelmechanismen, Ilmenau : Univ.-Verl. Ilmenau, zugl. Diss., Ilmenau, Techn. Univ., 2015 – URN: urn:nbn:de:gbv:ilm1-2015000283
  • Gräser, P.; Linß, S.; Zentner, L.; Theska, R.: Ultra-precise linear motion generated by means of compliant mechanisms. In: 15th International Conference of the European Society for Precision Engineering and Nanotechnology (euspen), 1 - 5 June 2015. Leuven, Belgium, 2015, S. 241-242 – ISBN 978-0-9566790-7-9
  • Linß, S.; Opfermann, R.; Gräser, P.; Theska, R.; Zentner, L.: Nachgiebige Koppelmechanismen mit optimierten Festkörpergelenken für Präzisionsanwendungen. In: Tagungsband First IFToMM D-A-CH Conference 2015, 11. März 2015, Dortmund. Universität Duisburg-Essen, 2015, S. 79-85 – DOI: 10.17185/duepublico/37267
  • Linß, S.; Milojević, A.; Zentner, L.: Considering the Design of the Flexure Hinge Contour for the Synthesis of Compliant Linkage Mechanisms. In: Shaping the future by engineering: 58th IWK, 8 - 12 September 2014; Proceedings. Ilmenau: Univ.-Bibliothek, ilmedia, 2014 – URN: urn:nbn:de:gbv:ilm1-2014iwk-033:4

Project duration

01/2018 - 03/2021

1st project phase (2014-2017)

  • Analysis, optimization and synthesis of compliant linkage mechanisms for ultra-precision applications

Acknowledgment