fulltext - Multibody Syst Dyn (2010) 23: 7797 DOI...

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Multibody Syst Dyn (2010) 23: 77–97 DOI 10.1007/s11044-009-9172-4 Analytical and experimental investigation of a parallel leaf spring guidance J.P. Meijaard · D.M. Brouwer · J.B. Jonker Received: 19 December 2008 / Accepted: 13 August 2009 / Published online: 23 September 2009 © Springer Science+Business Media B.V. 2009 Abstract The consequences for the static and dynamic system behaviour of misalign- ment in an overconstrained direction are analysed. Therefore, a relatively simple parallel leaf spring guidance, which is overdetermined only once, serves as a case to gain insight. A multibody program using Fexible beam theory is used to determine the change in vibra- tion mode frequencies and stiffnesses due to misalignment. A previously developed beam element for modelling the leaf springs is shown to be able to describe these phenomena with a limited number of elements. Buckling loads and associated buckling modes are also de- termined analytically. An instrument has been fabricated to measure the change of vibration mode frequencies due to a rotational misalignment in the overconstrained direction. Exper- iments using wire spark eroded leaf springs are in good agreement with the calculations. Differences between the experimental and calculated results are attributed to the imperfec- tions in the hardware model, in particular residual stresses, and the assumptions used for the beam element in the numerical model. A small misalignment, in this case 0.8–5.8 mrad, causes strong change of static and dynamic system behaviour. The decreased stiffnesses perpendicular to the compliant direction are disturbing, because these are designed to be large to enhance precision manipulation. The negative effects of overconstrained design are largest if relatively thin and wide leaf springs are used. If the misalignment is kept below 50% of the angle of which a bifurcation occurs, the overconstrained design of the parallel leaf spring mechanism does not signi±cantly inFuence the system natural frequencies and stiffness. Keywords Leaf spring · Parallel guidance · Misalignment · Buckling · Experiments J.P. Meijaard ( B ) Laboratory of Mechanical Automation and Mechatronics, ²aculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands e-mail: J.P.Meijaard@utwente.nl D.M. Brouwer · J.B. Jonker Laboratory of Mechanical Automation and Mechatronics, ²aculty of Engineering Technology, University of Twente, Enschede, The Netherlands D.M. Brouwer Demcon, Oldenzaal, The Netherlands
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78 J.P. Meijaard et al. 1 Introduction For the precision manipulation of objects, compliant mechanisms are often used [ 1 12 ]. These mechanisms do not suffer from friction, backlash, high hysteresis, stick–slip, or wear. Their behaviour is predictable and deterministic, which makes them useful if high repeata- bility is required. Industrial examples of precision manipulation are wafer positioning in a lithography machine and sample manipulation in scanning and transmission electron micro- scopes. To obtain a deterministic behaviour [ 1 6
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fulltext - Multibody Syst Dyn (2010) 23: 7797 DOI...

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