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Rigid Body Hyper-jerk Analysis Using Screw Theory

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Multibody Mechatronic Systems

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 25))

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Abstract

Few decades ago screw theory appears to be an ‘old fashioned’ mathematical tool confined to solve simple rigid-body first-order kinematic analysis. Still in our days the validity of the acceleration equations in screw form of kinematic chains introduced by Rico and Duffy in the 1990s has been bitterly disappointed by some kinematicians. This work deals with an application of the theory of screws not only in the rigid-body acceleration analysis but also in the jerk and hyper-jerk analyses of a six-degrees-of-freedom parallel manipulator. The Inverse/Forward kinematic equations of the robot are systematically obtained by resorting to reciprocal-screw theory. The contribution is a little proof that screw theory is a trusted and confident mathematical resource to investigate the rigid-body higher-order kinematic analyses. Numerical examples, which are verified with the aid of commercially available software, are provided in order to show the application of the method.

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Acknowledgments

This work has been supported by CONACyT of Mexico

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Authors and Affiliations

  1. Instituto Tecnologico de Celaya, Av. Tecnologico y A. Garcia Cubas, 38010, Celaya, GTO, Mexico

    Jaime Gallardo-Alvarado

  2. CICATA Queretaro-Instituto Politecnico Nacional, Mexico, Mexico

    Mario A. Garcia-Murillo

Authors
  1. Jaime Gallardo-Alvarado
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  2. Mario A. Garcia-Murillo
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Corresponding author

Correspondence to Mario A. Garcia-Murillo .

Editor information

Editors and Affiliations

  1. Laboratory of Robotics & Mechatronics LARM, University of Cassino and South Latium, Cassino, Italy

    Marco Ceccarelli

  2. Section of Graduate Studies and Section of Graduate Studies and, National Polytechnic Institute, Mexico, Distrito Federal, Mexico

    Eusebio Eduardo Hernández Martinez

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Gallardo-Alvarado, J., Garcia-Murillo, M.A. (2015). Rigid Body Hyper-jerk Analysis Using Screw Theory. In: Ceccarelli, M., Hernández Martinez, E. (eds) Multibody Mechatronic Systems. Mechanisms and Machine Science, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-09858-6_39

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  • DOI: https://doi.org/10.1007/978-3-319-09858-6_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09857-9

  • Online ISBN: 978-3-319-09858-6

  • eBook Packages: EngineeringEngineering (R0)

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