Analyzing Overconstrained Design of Compliant Mechanisms

Aarts, RM Ronald; Boer, Steven; Meijaard, J. P.; Brouwer, Dannis Michel; Jonker, Jan B.

doi:10.1115/detc2011-48548

Cited by 2 publications

(7 citation statements)

References 7 publications

(15 reference statements)

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“…In this paper, the approach is demonstrated with straight guiding mechanisms. It paves the path toward a systematic approach to realise systems satisfying exact constraint design [6].…”

Section: Discussionmentioning

confidence: 99%

“…This is also true for a wire flexure, which is thin in two directions. It will deform easily in torsion and all bending directions (ε [2][3][4][5][6] ), while only the stiffness for the elongation (ε 1 ) is high.…”

Section: Spatial Finite Elementsmentioning

confidence: 99%

“…1, the constrained deformations are the elongation ε 1 and the bending deformations ε 3,4 in the in-plane z-direction. The torsion ε 2 and bending deformations ε 5,6 in the out-of-plane y-direction are the other three deformations that are allowed to vary. Combining two sheets, there are six deformations in the folded sheet flexure that are not suppressed.…”

Section: Kinematic Analysis Of Wire Flexures and Folded Sheet Flexuresmentioning

confidence: 99%

“…When used in a compliant mechanism, the sheet flexure is meant to deform relatively easily by out-ofplane bending and torsion, i.e. the deformations ε 5,6 and ε 2 for this beam element. It should provide support in other directions as the stiffnesses for in-plane bending and elongations are much higher, i.e.…”

Section: Spatial Finite Elementsmentioning

confidence: 99%

“…Then there are twelve independent nodal coordinates and six rigid body degrees of freedom, so that six independent deformation modes can be defined. For the spatial flexible beam, one deformation mode ε 1 is taken to describe the elongation, ε 2 for torsion, and four modes ε [3][4][5][6] for the bending deformations of the element. For readability, the superscripts (k) indicating the element number are omitted.…”

Section: Spatial Finite Elementsmentioning

confidence: 99%

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Flexible multibody modelling for exact constraint design of compliant mechanisms

2011

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In high precision equipment, the use of compliant mechanisms is favourable as elastic joints offer the advantages of low friction and no backlash. If the constraints in a compliant mechanism are not carefully dealt with, even small misalignments can lead to changes in natural frequencies and stiffnesses. Such unwanted behaviour can be avoided by applying exact constraint design, which implies that the mechanism should have exactly the required degrees of freedom and non-redundant constraints so that the system is kinematically and statically determinate. For this purpose, we propose a kinematic analysis using a finite element based multibody modelling approach. In compliant mechanisms, the system's degrees of freedom are presented clearly from the analysis of a system in which the deformation modes with a low stiffness are free to deform while the deformation modes with a high stiffness are considered rigid. If the Jacobian matrix associated with the dependent coordinates is not full column or row rank, the system is under-constrained or over-constrained. The rank of this matrix is calculated from a singular value decomposition. For an under-constrained system, any motion in the mechanism that is not accounted for by the current set of degrees of freedom is visualised using data from the right singular matrix. For an over-constrained system, a statically indeterminate stress distribution is derived from the left singular matrix and is used to visualise the over-constraints. The analysis is exemplified for the design of a straight guiding mechanism, where under-constrained and over-constrained conditions are visualised clearly.

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“…In this paper, the approach is demonstrated with straight guiding mechanisms. It paves the path toward a systematic approach to realise systems satisfying exact constraint design [6].…”

Section: Discussionmentioning

confidence: 99%

Section: Spatial Finite Elementsmentioning

confidence: 99%

Section: Kinematic Analysis Of Wire Flexures and Folded Sheet Flexuresmentioning

confidence: 99%

Section: Spatial Finite Elementsmentioning

confidence: 99%

Section: Spatial Finite Elementsmentioning

confidence: 99%

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Flexible multibody modelling for exact constraint design of compliant mechanisms

2011

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Constraint and Dynamic Analysis of Compliant Mechanisms with a Flexible Multibody Modelling Approach

Aarts

2012

Multibody System Dynamics, Robotics and Control

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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.

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Analyzing Overconstrained Design of Compliant Mechanisms

Abstract: Whereas the use of compliant mechanisms is favorable for high precision applications, the constraints must be dealt with

Cited by 2 publications

References 7 publications

Flexible multibody modelling for exact constraint design of compliant mechanisms

Flexible multibody modelling for exact constraint design of compliant mechanisms

Constraint and Dynamic Analysis of Compliant Mechanisms with a Flexible Multibody Modelling Approach

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