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TitleConfiguration space analysis of rigid mechanisms.
Author(s) Samuli Piipponen, Jukka Tuomela
TypeArticle in Journal
AbstractIn mechanical engineering and robotics, the main problem is usually to solve the equations
of motion of a given rigid mechanism. The rigid mechanisms are sometimes restricted or controlled
to move along a constrained path. In engineering sciences, the most common constraints are called
ideal joint constraints. The ideal joint constraints are generally holonomic constraints involving only the
coordinates and orientation of a mechanism with respect to a fixed coordinate frame. An important aspect
is that ideal joint constraints can be formulated as a set of polynomial equations. This means that the
configuration spaces of typical rigid mechanisms can be treated as algebraic varieties and the components
of a constraint function as generators of a polynomial ideal. This geometry algebra equivalence and
the advances of computational commutative algebra and algebraic geometry gives us means to actually
compute the properties of configuration spaces.
Keywordsmechanisms; robotics; holonomic constraints; algebraic geometry; computational algebraic geometry; Gröbner basis
ISSN1787-2405; 1787-2413/e
JournalMiskolc Math. Notes
PublisherMiskolc University Press, Miskolc
Translation No
Refereed No