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Polynomial solutions for the direct kinematic problem of planarthree-degree-of-freedom parallel manipulators
Gosselin, C.M. Sefrioui, J.
Dept. de Genie Mecanique, Laval Univ., Ste-Foy, Que.;
This paper appears in: Advanced Robotics, 1991. 'Robots in Unstructured Environments', 91 ICAR., Fifth International Conference on
Publication Date: 19-22 Jun 1991
On page(s): 1124-1129 vol.2
Meeting Date: 06/19/1991 - 06/22/1991
Location: Pisa, Italy
ISBN: 0-7803-0078-5
References Cited: 12
INSPEC Accession Number: 4474225
Digital Object Identifier: 10.1109/ICAR.1991.240405
Current Version Published: 2002-08-06
Abstract
Presents a general solution for the direct kinematics of planar three-degree-of-freedom parallel manipulators. It has been shown elsewhere, using geometric considerations, that this problem can lead to a maximum of six real solutions. The formulation developed leads to a polynomial of the sixth order which is hence minimal. This is illustrated with an example, taken from the literature, for which six real solutions have been found. Moreover, for a special geometry in which the three joints on the platform and on the base are respectively aligned, it is shown that the solution can be cascaded in two steps involving the solution of a cubic and a quadratic respectively. This particular class of planar parallel manipulators can therefore be solved in closed-form and no more than four real solutions have been found in this case. Examples of this class of manipulators are also solved
Link:
http://ieeexplore.ieee.org/xpl/freea...&isnumber=6178