Details:
Title  A GröbnerSylvester Hybrid Method for ClosedForm Displacement Analysis of Mechanisms  Author(s)  A. N. Almadi, Anoop K. Dhingra, Dilip Kohli  Type  Article in Journal  Abstract  The displacement analysis problem for planar and spatial mechanisms can be written as a system of multivariate polynomial equations. Elimination theory based on resultants and polynomial continuation are some of the methods that have been used to solve this problem. This paper presents a new approach to displacement analysis using the reduced Gröbner basis form of a system of equations under degree lexicographic (dlex) term ordering of its monomials and Sylvester's Dialytic elimination method. Using the GröbnerSylvester hybrid approach, a finitely solvable system of equations F is transformed into its reduced Gröbner basis G using dlex term ordering. Next, using the entire or a subset of the set of generators in G, the Sylvester's matrix is assembled. The vanishing of the resultant, given as the determinant of Sylvester's matrix, yields the necessary condition for polynomials in G (as well as F) to have a common factor. The proposed approach appears to provide a systematic and rational procedure to the problem discussed by Roth, dealing with the generation of (additional) equations for constructing the Sylvester's matrix. Three examples illustrating the applicability of the proposed approach to displacement analysis of planar and spatial mechanisms are presented. The first and second examples address the forward displacement analysis of the general 66 Stewart mechanism and the 66 Stewart platform, whereas the third example deals with the determination of the I/O polynomial of an 8link 1DOF mechanism that does not contain any 4link loop.  Length  8  Copyright  ASME 
File 
 Language  English  Journal  Journal of Mechanical Design  Volume  122  Number  4  Pages  431  438  Year  2000  Month  December  Translation 
No  Refereed 
No 
