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Systematic Use of Velocity and Acceleration Coefficients in the Kinematic Analysis of Single-DOF Planar Linkages

  • Raffaele Di GregorioEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

In single-degree-of-freedom (DOF) mechanisms, velocity coefficients (VCs) and their 1st derivative with respect to the generalized coordinate (acceleration coefficients (ACs)) only depend on the mechanism configuration. In addition, if the mechanism is a planar linkage, complex numbers are an easy-to-use tool for writing linkage’s loop equations that are formally differentiable. Here, both these results are combined to propose an algorithm that systematically uses VCs and ACs for solving the kinematic-analysis problems of single-DOF planar linkages. The proposed algorithm is efficient enough to be the kinematic block of any dynamic model of these linkages; also, it lends itself to present planar kinematics in graduate and/or undergraduate courses.

Keywords

Planar Linkage Velocity Coefficient Acceleration Coefficient Higher Education 

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Notes

Acknowledgments

This work has been developed at the Laboratory of Advanced Mechanics (MECH-LAV) of Ferrara Technopole, supported by FAR2018 UNIFE funds and by Regione Emilia Romagna (District Councillorship for Productive Assets, Economic Development, Telematic Plan) POR-FESR 2007-2013, Attività I.1.1

References

  1. 1.
    Paul, B.: Kinematics and Dynamics of Planar Machinary. Prentice-Hall, Inc., Englewood Cliffs N.J. (1987).Google Scholar
  2. 2.
    Nikravesh, P.E.: Planar Multibody Dynamics. CRC Press, Boca Raton FL (2018).Google Scholar
  3. 3.
    Marghitu, D.B.: Mechanisms and Robots Analysis with MATLAB. Springer-Verlag, London, (2009).Google Scholar
  4. 4.
    Galletti, C.U.: A Note on Modular Approaches to Planar Linkage Kinematic Analysis. Mech. Mach. Theory 21(5), 385-391 (1986).Google Scholar
  5. 5.
    Bràt, V., Lederer, P.: KIDYAN: Computer-Aided Kinematic and Dynamic Analysis of Planar Mechanisms. Mech. Mach. Theory 8, 457-467 (1973).Google Scholar
  6. 6.
    Wampler, C.: Solving the Kinematics of Planar Mechanisms. J. Mech. Des 121(3), 387-391 (1999).Google Scholar
  7. 7.
    Wampler, C.: Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation. J. Mech. Des 123(3), 382-387 (2001).Google Scholar
  8. 8.
    Di Gregorio, R.: An Algorithm for Analytically Calculating the Positions of the Secondary Instant Centers of Indeterminate Linkages. J. Mech. Des 130(4), 042303-(1-9) (2008).Google Scholar
  9. 9.
    Di Gregorio, R.: A novel dynamic model for single-degree-of-freedom planar mechanisms based on instant centers. ASME J. of Mechanisms and Robotics 8(1), 011013-(8pages) (2016).Google Scholar
  10. 10.
    Di Gregorio, R.: On the Use of Instant Centers to Build Dynamic Models of Single-dof Planar Mechanisms. In: Lenarcic J., Parenti-Castelli V. (eds) Advances in Robot Kinematics 2018. Springer Proceedings in Advanced Robotics, vol 8, pp. 242-249. Springer, Cham (2018).Google Scholar
  11. 11.
    IFToMM Commission A: Terminology for the Theory of Machines and Mechanisms. Mech. Mach. Theory 26(5), 435-539 (1991).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of EngineeringUniversity of FerraraFerraraItaly

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