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Kinetostatics and Optimal Design of a 2PRPU Shoenflies-Motion Generator

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Multibody Mechatronic Systems (MuSMe 2017)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 54))

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Abstract

Schoenflies-motion generators (SMGs) are 4-degrees-of-freedom (dof) manipulators whose end effector can perform translations along three independent directions and rotations around one fixed direction (Schoenflies motions). The authors, in a previous paper, showed that a 2PRPU SMG has a simple position analysis and singularities that leave a wide free-from-singularity workspace. The present paper addresses the kinetostatics and the optimal design of this SMG.

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Notes

  1. 1.

    Hereafter, R, P, U, and C stand for revolute pair, prismatic pair, universal joint, and cylindrical pair, respectively. The underlining indicates the actuated joints and the sequence of joint types, which are encountered by moving from the base to the platform on a limb, is given with a string of capital letters.

  2. 2.

    Hereafter, f = (fx, fy, fz)T is the resultant force and m = (mx, my, mz)T is the resultant moment about A1 of the force system the platform applies to the external world.

  3. 3.

    The “singular values” of a real matrix A are the square roots of the eigenvalues of the positive-semidefinite matrix A T A. Also, the spectral norm of A is the square root of the largest eigenvalue of A T A; thus, the spectral norm of A is equal to its largest singular value.

  4. 4.

    These geometric values have been found in [5] acceptable to have a dexterous workspace wide enough for practical applications.

References

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Acknowledgments

This work has been developed at the Laboratory of Advanced Mechanics (MECH-LAV) of Ferrara Technopole, supported by FIR2016 funds, by Regione Emilia Romagna (District Councillorship for Productive Assets, Economic Development, Telematic Plan) POR-FESR 2007–2013, Attività I.1.1, and by the Raul Guenther Laboratory of Applied Robotics (LAR-UFSC) of Federal University of Santa Catarina, supported by Brazil’s federal agencies for research: CNPq, CAPES and FINEP.

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Authors and Affiliations

  1. Federal University of Santa Catarina, Florianópolis, Brazil

    H. Simas

  2. University of Ferrara, Ferrara, Italy

    R. Di Gregorio

Authors
  1. H. Simas
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  2. R. Di Gregorio
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Corresponding author

Correspondence to H. Simas .

Editor information

Editors and Affiliations

  1. School of Mechanical Engineering, Federal University of Uberlândia, Uberlândia, Minas Gerais, Brazil

    João Carlos Mendes Carvalho

  2. Mechanical Engineering, Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil

    Daniel Martins

  3. Mobility Engineering Center, Federal University of Santa Catarina, Joinville, Santa Catarina, Brazil

    Roberto Simoni

  4. Mechanical Engineering, Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil

    Henrique Simas

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Simas, H., Di Gregorio, R. (2018). Kinetostatics and Optimal Design of a 2PRPU Shoenflies-Motion Generator. In: Carvalho, J., Martins, D., Simoni, R., Simas, H. (eds) Multibody Mechatronic Systems. MuSMe 2017. Mechanisms and Machine Science, vol 54. Springer, Cham. https://doi.org/10.1007/978-3-319-67567-1_13

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  • DOI: https://doi.org/10.1007/978-3-319-67567-1_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67566-4

  • Online ISBN: 978-3-319-67567-1

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