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On flexes associated with higher-order flexible bar-joint frameworks
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The famous example of the double-Watt mechanism given by Connelly and Servatius raises some problems concerning the classical definitions of higher-order flexibility and rigidity, respectively. Recently, the author was able to give a proper redefinition of the flexion/rigidity order for bar-joint frameworks, but the question for the flexes associated with higher-order flexible structures remained open. In this paper we properly define these flexes based on the theory of algebraic curves and demonstrate their computation by means of Puiseux series. The presented algebraic approach also allows to take reality issues into account.
Forward citations
Cited by 2 Pith papers
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Higher Order Rigidity and Energy
A framework's rigidity order, defined by energy growth, is energy-independent and equals a maximum over higher-order flexes, yielding new proofs of second-order and dim-one higher-order rigidity.
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Second-order prestress stability and third-order rigidity of polyhedral surfaces
No fractional rigidity orders occur before third order, and second-order prestress stability can be checked by explicit linear-algebra criteria, but a general third-order test exists only when the rigidity matrix has ...
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