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Analyzing Overconstrained Design of Compliant Mechanisms

Authors: Aarts, R.G.K.M.; Boer, S.E.; Meijaard, J.P.; Brouwer, D.M.; Jonker, J.B.;

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 carefully. In an overconstrained design the actual natural frequencies and stiffnesses can differ considerably from their intended values. For this reason the awareness and possibly the avoidance of an overconstrained condition is important. We have developed a kinematic analysis with which under-constraints and overconstraints can be detected. A finite element based multibody approach is applied which offers a flexible beam element that is particularly suited to model the wire and sheet flexures frequently encountered in compliant mechanisms. For each element a fixed number of independent discrete deformations are defined that are invariant under arbitrary rigid body motions of the element. In the kinematic analysis only deformations associated with low stiffnesses are allowed, whereas the remaining deformations are prescribed zero. A singular value decomposition is used to determine the rank of the Jacobian matrix associated with the dependent nodal coordinates. Column and row rank deficiency indicate an underconstrained and overconstrained system, respectively. For an overconstrained system a statically indeterminate stress distribution can be derived from the left singular matrix. In this way the overconstraints can be visualized clearly as is illustrated with examples of compliant straight guidance mechanisms. The possible solutions to eliminate the overconstraints are found easily from the visualization.

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Netherlands
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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