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Some algebraic geometry problems arising in the field of mechanism theory

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Book cover Algorithms in Algebraic Geometry and Applications

Part of the book series: Progress in Mathematics ((PM,volume 143))

Abstract

Mechanism theory deals with kinematic chains, i.e., rigid bodies (called links) connected by joints. These joints enable motion between the links and are characterized by the type of motion they allow. The main joints allow only one motion, either a rotation around a given axis (rotary joint) or a translation along one given axis(prismatic joint). More complex joints can be constructed with these basic joints, e.g., the ball-and-socket joint enabling every rotation around a point. Note that a finite set of parameters defines the status of the joint. For example, for a rotary joint the rotation angle fully defines the joint. The independent parameters of the joints will be called the articular coordinates of the mechanism.

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References

  1. Freudenstein F. On the variety of motion generated by mechanisms. Transaction of the ASME, pp. 156–160, February 1962.

    Google Scholar 

  2. Gosselin C. and Merlet J.-P.. On the direct kinematics of planar parallel manipulators: special architectures abd number of solutions. Mechanism and Machine Theory, March, 1994.

    Google Scholar 

  3. Gosselin C., Sefrioui, and Richard M. J. Solution polynomiale au problème de la cinématique directe des manipulateurs parallèles pains à 3 degrés de liberté. Mechanism and Machine Theory, 27(2): 107–119, March, 1992.

    Article  Google Scholar 

  4. Hartenberg R. S., Denavit J. Kinematic synthesis of linkages. MacGraw- Hill, 1964.

    Google Scholar 

  5. Hunt K. H. Kinematic geometry of mechanisms. Clarendon Press, 1978.

    MATH  Google Scholar 

  6. Innocenti C. Analytical determination of the intersection of two coupler- point curves generated by two four-bar linkages. In Computational Kinematics (eds J. Angeles, P. Kovacs and G. Hommel), pp. 251–262. Kluwer, 1993.

    Google Scholar 

  7. Lazard D. Generalized Stewart Platform: How to compute with rigid motions?. In IMACS, pp. 85–88, Lille, May, 1993.

    Google Scholar 

  8. Merlet J.-P. An algorithm for the forward kinematics of general parallel manipulators. In ICAR, pp. 1131–1135, Pise, June, 1991.

    Google Scholar 

  9. Merlet J.-P. Singular configurations of parallel manipulators and Grass- mann geometry. International Journal of Robotics Research, 8(5): 45–56, Ocotber, 1989.

    Article  Google Scholar 

  10. Merlet J.-P. Les robots parallèles. Hermès, Paris, 1990.

    Google Scholar 

  11. Mourrain B. Enumeration problems in geometry, robotics and vision. This volume.

    Google Scholar 

  12. Raghavan M. and Roth B. Kinematic analysis of the 6R manipulator of general geometry. In 5th Int. Symp. of Robotics Research, pp. 263–270, Tokyo, 1990.

    Google Scholar 

  13. Ronga F. and Vust T. Stewart platforms without computer. Preprint, 1992.

    Google Scholar 

  14. Wampler C. and Morgan A. Solving the 6R inverse position problem using a generic-case solution methodology. Mechanism and Machine Theory, 26(1): 91–106, 1991.

    Article  Google Scholar 

  15. Wampler C., Morgan A. and Sommese A. J. Numerical continuation methods for solving polynomial systems arising in kinematics. ASME J. of Mechanical Design, 112: 59–68, March, 1990.

    Article  Google Scholar 

  16. Wampler C., Morgan A. and Sommese A. J. Complete solution of the ninepoint path synthesis problem for four-bar linkages. ASME J. of Mechanical Design, 114: 153–159, March, 1992.

    Article  Google Scholar 

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© 1996 Birkhäuser Verlag Basel/Switzerland

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Merlet, JP. (1996). Some algebraic geometry problems arising in the field of mechanism theory. In: González-Vega, L., Recio, T. (eds) Algorithms in Algebraic Geometry and Applications. Progress in Mathematics, vol 143. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9104-2_13

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  • DOI: https://doi.org/10.1007/978-3-0348-9104-2_13

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9908-6

  • Online ISBN: 978-3-0348-9104-2

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