Title | **Configuration space analysis of rigid mechanisms.** |

Author(s) | Samuli Piipponen, Jukka Tuomela |

Type | Article in Journal |

Abstract | In 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. |

Keywords | mechanisms; robotics; holonomic constraints; algebraic geometry; computational algebraic geometry; Gröbner basis |

ISSN | 1787-2405; 1787-2413/e |

Language | English |

Journal | Miskolc Math. Notes |

Volume | 14 |

Number | 2 |

Pages | 685--695 |

Publisher | Miskolc University Press, Miskolc |

Year | 2013 |

Edition | 0 |

Translation |
No |

Refereed |
No |