Abstract
The models used in the conceptual phase of the mechatronic design should not be too complicated, yet they should capture the dominant system behaviour. Firstly, the awareness and possibly the avoidance of an overconstrained condition is important. Secondly, the models should reveal the system’s natural frequencies and mode shapes in a relevant frequency range. For the control system synthesis the low frequent behaviour up to the cross-over frequency needs to be known. Furthermore, the closed-loop system can be unstable due to parasitic modes at somewhat higher frequencies.
In this chapter the applicability of a multibody modelling approach based on non-linear finite elements is demonstrated for the mechatronic design of a compliant six DOF manipulator. A kinematic analysis is applied to investigate the exact constrained design of the system. From dynamic models the natural frequencies and mode shapes are predicted and a state-space model is derived that describes the system’s input-output relations. The models have been verified with experimental identification and closed-loop motion experiments. The predicted lowest natural frequencies and closed-loop performance agree sufficiently well with the experimental data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Blanding DL (1999) Exact constraint: machine design using kinematic principles. ASME Press, New York
Hale LC (1999) Principles and techniques for designing precision machines. Ph.D. thesis, University of California, Livermore
Soemers HMJR (2010) Design principles for precision mechanisms. T-point print, Enschede
van Dijk J, Aarts RGKM, Jonker JB (2012) Analytical one parameter method for PID motion controller settings. In: IFAC conference on advances in PID control – PID’12, Brescia, 28–30 Mar 2012
Xu JX (2008) New lead compensator designs for control education and engineering. In: Proceedings of 27th Chinese control conference, 16–18 July 2008
Aarts RGKM, van Dijk J, Jonker JB (2009). Efficient analyses for the mechatronic design of mechanisms with flexible joints undergoing large deformations. In: ECCOMAS thematic conference multibody dynamics 2009, Warsaw University of Technology, Warsaw, June 29–July 2
Aarts RGKM, van Dijk J, Jonker JB (2010) Flexible multibody modelling for the mechatronic design of compliant mechanisms. In: The 1st joint international conference on multibody system dynamics, Lappeenranta, 25–27 May 2010
Aarts RGKM, van Dijk J, Brouwer DM, Jonker JB (2011) Application of flexible multibody modelling for control synthesis in mechatronics. In: Multibody dynamics 2011, ECCOMAS thematic conference, Brussels, 4–7 July 2011
Aarts RGKM, Boer SE, Meijaard JP, Brouwer DM, Jonker JB (2011) Analyzing overconstrained design of compliant mechanisms. In: Proceedings of ASME 2011 international design engineering technical conference & computers and information in engineering conference – IDETC/CIE 2011, Washington, DC, 28–31 Aug 2011
Jonker JB, Meijaard JP (2009) Definition of deformation parameters for the beam element and their use in flexible multibody system analysis. In: ECCOMAS thematic conference multibody dynamics 2009, Warsaw University of Technology, Warsaw, June 29–July 2
Jonker JB, Aarts RGKM, van Dijk J (2009) A linearized input-output representation of flexible multibody systems for control synthesis. Multibody Syst Dyn 21(2):99–122
Brouwer DM, de Jong BR, Soemers HMJR (2010) Design and modeling of a six DOF’s MEMS-based precision manipulator. Precis Eng 34(2):307–319
Meijaard JP, Brouwer DM, Jonker JB (2010) Analytical and experimental investigation of a parallel leaf spring guidance. Multibody Syst Dyn 23(1):77–97
Boer SE, Aarts RGKM, Brouwer DM, Jonker JB (2010) Multibody modelling and optimization of a curved hinge flexure. In: The 1st joint international conference on multibody system dynamics, Lappeenranta, 25–27 May 2010
Spijksma SA (2010) Analysis and MIMO control of a 6 DOFs parallel kinematic precision manipulator. M.Sc. thesis, Report number Wa-1293, University of Twente, Enschede
Nijsse G (2006) A subspace based approach to the design, implementation and validation of algorithms for active vibration isolation control. PhD thesis, University of Twente, Enschede
van Overschee P, de Moor B (1994) N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems. Automatica 30(1):75–93
Acknowledgements
The author acknowledges the contributions from Steven Boer, Dannis Brouwer, Johannes van Dijk, Ben Jonker and Jaap Meijaard to the design, modelling and control as outlined in this chapter. Martijn Huijts and Sytze Spijksma are acknowledged for the design, analysis and testing of the manipulator.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Wien
About this paper
Cite this paper
Aarts, R.G.K.M. (2013). Constraint and Dynamic Analysis of Compliant Mechanisms with a Flexible Multibody Modelling Approach. In: Gattringer, H., Gerstmayr, J. (eds) Multibody System Dynamics, Robotics and Control. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1289-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-7091-1289-2_3
Published:
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-1288-5
Online ISBN: 978-3-7091-1289-2
eBook Packages: EngineeringEngineering (R0)