Algorithm for the Inverse Kinematics Calculation of Cross Rods Parallel Machine Tools Based on Lie-Algebras
In order to solve the problems that traditional kinematics model built by the method of D-H parameters can only reflect relative movements between adjacent components and can't express directly the spatial poses of every component relative to static platform, Lie-algebras is used this paper to establish the product of exponential formula of forward direct kinematics of every branch chains. The elimination method and Paden - kahan sub-problems are used to calculate joint variables. Then the quick and intuitive inverse algorithm of cross rods parallel machine tools is acquired. The algorithm provides reliable proofs for the analysis of error compensation, kinematics interference and singularity. Finally we prove our theory with an example of an actual parallel machine tool.
Tian Huang, Dawei Zhang, Bin Lin, Anping Xu, Yanling Tian and Weiguo Gao
X.F. Fang et al., "Algorithm for the Inverse Kinematics Calculation of Cross Rods Parallel Machine Tools Based on Lie-Algebras", Materials Science Forum, Vols. 697-698, pp. 282-287, 2012