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Calculating Jacobian coefficients of primitive constraints with respect to Euler parameters

Abstract : It is a fundamental problem to calculate Jacobiancoefficients of constraint equations in assembly constraintsolving because most approaches to solving an assemblyconstraint system will finally resort to a numerical iterativemethod that requires the first-order derivatives of theconstraint equations. The most-used method of derivingthe Jacobian coefficients is to use virtual rotation whichis originally presented to derive the equations of motionof constrained mechanical systems. However, when Eulerparameters are adopted as the state variables to represent thetransformation matrix, using the virtual rotation will yielderroneous formulae of Jacobian coefficients. The reason isthat Euler parameters are incompatible with virtual rotation.In this paper, correct formulae of Jacobian coefficients ofgeometric constraints with respect to Euler parameters arepresented in both Cartesian coordinates and relative generalizedcoordinates. Experimental results show that ourproposed formulae make Newton-Raphson iterative methodconverge faster and more stable.
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  • HAL Id : hal-00920668, version 1

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Yong Liu, Hai-Chuan Song, Jun-Hai Yong. Calculating Jacobian coefficients of primitive constraints with respect to Euler parameters. International Journal of Advanced Manufacturing Technology, Springer Verlag, 2013. ⟨hal-00920668⟩

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