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Coordinate‐free kinematic analysis of overconstrained mechanisms with mobility one
Author(s) -
Lerbet J.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200110195
Subject(s) - mathematics , jacobian matrix and determinant , constraint (computer aided design) , holonomic constraints , singularity , kinematics , rank (graph theory) , gravitational singularity , closure (psychology) , holonomic , manifold (fluid mechanics) , algebra over a field , set (abstract data type) , pure mathematics , topology (electrical circuits) , mathematical analysis , computer science , geometry , combinatorics , mechanical engineering , physics , classical mechanics , artificial intelligence , economics , engineering , market economy , programming language
We propose to analyse some classical overconstrained mechanisms by using explicitely the relations of singularity and not only the closure equation A 1 ˆ...ˆ A n = e . Using the fact that their configuration space manifold is such that the constraint jacobian is permanently not of full rank, we apply our earlier developed analysis strategy for singularities to analyse overconstrained mechanisms. By theorem 1, the holonomic constraints A 1 ˆ...ˆ A n = e are linearized and formulated in an appropriate form on the Lie algebra ... This gives a redundant set of linear equations which is solved. The used method is coordinate‐free and the solution of the Bennett and Bricard mechanisms is given as illustration of the method.