Abstract
Based on Groebner base method and computer symbolic manipulating technique, symbolic solutions for direct displacement analysis of a three-DOF spatial parallel machine tool are proposed in this paper. A set of nonlinear polynomial equations are transformed into a set of equivalent triangularization equations by using the following operations: ordering of variables, forming all pairs of polynomials, finding S-polynomial, and reduction etc. The analytical solutions in the closed form are obtained. The Jacobian matrix is derived and symbolic technique is introduced into the procedure of derivation of Jacobian matrix. The manipulability of the parallel machine tool is investigated. Two numerical examples are given for illustration.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Huang, L.B.: Research on kinematics of the robots’ mechanism-including discussion of solving method for nonlinear algebra equations. Southeast university (2001)
Li, L., Chen, G.: Symbolic Approach for the Problems of Mechanism Based on Groebner Base Method. Mechanical Science and Technology for Aerospace Engineering 17, 5–7 (1998)
Liu, M.L.: Theory and Application of Groebner Basis. Science press (2000)
Yoshikawa, T.: Manipulability of robotic mechanisms. International Journal of Robotics Research 4(2), 3–9 (1987)
Salisburg, J.K., Craig, J.: Articulated hands kinematic and force control issues. International Journal of Robotics Research 1(2), 12–15 (1982)
Rao, Q., Bai, S.X.: Manipulability analysis and definition of 6_6 Steward Robot. Robot 16, 345–349 (1994)
Huang, Z., Kong, J.F., Fang, Y.F.: Mechanism theory and controlling system of parallel robot. China machine press (1997)
Fan, S.W., Xu, L.J.: Forward solution of position and analysis of working space for a new typed hybrid virtual axle machine tool. Machine Design 8, 27–29 (2002)
Fan, S.W., Xu, L.J.: Close Form Solution to Singularity Configuration of a New Type Parallel Machine Tool. Journal of University of Electronic Science and Technology of China 4, 369–373 (2002)
Xu, L.J., Fan, S.W., Xu, X.M.: A New Type of Hybird Five Degrees of Freedom Vitual Axis Machine Tool. China Patent ZL.01107247.4 (2003-08-6)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, Q., Luo, K., Wang, Jg. (2008). Symbolic Solutions for Direct Displacement and Manipulability Analyses of 3-DOF Parallel Machine Tools Using Groebner Base Method. In: Xiong, C., Liu, H., Huang, Y., Xiong, Y. (eds) Intelligent Robotics and Applications. ICIRA 2008. Lecture Notes in Computer Science(), vol 5315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88518-4_109
Download citation
DOI: https://doi.org/10.1007/978-3-540-88518-4_109
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88516-0
Online ISBN: 978-3-540-88518-4
eBook Packages: Computer ScienceComputer Science (R0)