The vector algebra approach to the kinematic analysis of the structural groups of the 2nd class by Artobolevsky

Abstract

The methodology for analyzing velocities and accelerations of characteristic points, as well as angular velocities and angular accelerations of links, of the structural groups of the 2nd class according to Artobolevsky is developed using exclusively the tools of vector algebra. There are exist five forms of the structural groups of the 2nd class by Artobolevsky, each form has been considered. The position analyses of the structural groups, which are described by the links’ direction vectors and the radius-vectors of points of external kinematic pairs, and in addition, if necessary, the position analysis of external links are assumed to have been carried out by the vector algebra or some other approach. Provided for all forms of the structural groups formulas for calculations are prepared for creating a software product that automatizes the kinematic analysis of planar linkages of the 2nd class according to Artobolevsky. Also, they can be used for the kinetostatic and dynamic analyses of the mentioned linkages. The specified limits of application of the presented approach are pointed out.