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Kinematical and dynamical analysis of closed kinematic chains using graphs and contour equations
Author(s) -
Drewniak J.,
Zawiślak S.
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910246
Subject(s) - kinematics , graph , position (finance) , representation (politics) , dynamical systems theory , kinematic chain , enumeration , relation (database) , mechanical system , mathematics , computer science , classical mechanics , combinatorics , physics , artificial intelligence , finance , quantum mechanics , database , politics , political science , law , economics
The classical method of determination of velocities and accelerations of the closed kinematical chains consists in calculation of derivatives of the position vector in relation to time. In the paper, the methods of kinematical and dynamical analysis of the closed kinematical systems based upon the graph representation are presented. Planetary gears are the exemplary mechanical systems which have been considered. Two types of graphs are assigned to the gears. Both graphs allow for derivation of systems of equations which constitute the kinematical analysis. The results of classical and graph‐based methods were compared. The graph based methods allow for further considerations like e.g. synthesis, enumeration of design solutions and even evolutionary design of mechanisms. Dynamical analysis is shown in graphical form, only. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)