Calculating Jacobian coefficients of primitive constraints with respect to Euler parameters - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles International Journal of Advanced Manufacturing Technology Year : 2013

Calculating Jacobian coefficients of primitive constraints with respect to Euler parameters

Yong Liu
  • Function : Author
Hai-Chuan Song
  • Function : Author
Jun-Hai Yong
  • Function : Author

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.
Fichier principal
Vignette du fichier
a_a_2013a_Jacobian.pdf (152.44 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00920668 , version 1 (19-12-2013)

Identifiers

  • HAL Id : hal-00920668 , version 1

Cite

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, 2013. ⟨hal-00920668⟩
68 View
1103 Download

Share

Gmail Facebook X LinkedIn More