Open AccessUse of dual numbers in kinematical analysis of spatial mechanisms. Part I: principle of the method
Author(s) -
Florina-Carmen Ciornei,
Stelian Alaci,
Radu Dumitru Pentiuc,
Ioan Doroftei
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/568/1/012033
Subject(s) - closure (psychology) , matrix (chemical analysis) , dual (grammatical number) , mathematics , notation , simple (philosophy) , calculus (dental) , computer science , mathematical analysis , arithmetic , law , medicine , art , materials science , literature , dentistry , composite material , philosophy , epistemology , political science
The general methodology of solving a problem of kinematical analysis of a spatial mechanism is presented. The method is based on the system proposed by Hartenberg and Denavit, concerning the notations of the coordinate frames attached to the elements of the mechanism and on the closure matrix equation of a kinematical chain. Carrying out the closure equation for the case of spherical mechanisms and then applying the transfer principle of Kotelnikov, the equations which allow for finding the unknown parameters of the kinematical chain are obtained. Starting from the typical form of closure equation based on homogenous operators Hartenberg-Denavit, the closure matrix equation is obtained in dual format. By identifying two special matrices it is shown that the coefficient of the dual part from the closure equation is in fact a sum in which each term is attained from the real part of the closure equation by performing simple operations involving the special matrices, that reduce the calculus volume.