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Kinematics of a class of parallel manipulators which generates structures with three limbs

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Abstract

In this paper, the forward position analysis (FPA) of a class of parallel manipulators which can be modeled as structures with three limbs when the active joint rates, namely the generalized coordinates, are locked, is carried out using mixed and analytic procedures. The first option is a novel procedure which combines a numerical method and the closed-form solution of the geometry of a tetrahedron, that allows to find all the possible solutions for the FPA when specific requirements are satisfied. The second option is an analytic procedure capable of reducing a nonlinear system of three equations in three unknowns into a univariate 16th order polynomial equation, which evidently leads to a multiple solution. The introduction of linear equations, proposed in this contribution, obtained from the particular topology of these mechanisms simplifies considerably the FPA. In order to complement the kinematic analyses, the acceleration analysis of an exemplary parallel manipulator is approached by means of standard screw theory. Of course, as an intermediate step, this contribution also provides the velocity analysis of the chosen parallel manipulator. Finally, two numerical examples are provided.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Instituto Tecnológico de Celaya, Av. Tecnológico y A. García Cubas, 38010, Celaya, Gto., México

    J. Gallardo-Alvarado, H. Orozco-Mendoza & R. Rodríguez-Castro

  2. Universidad de Guanajuato, FIMEE, Calle Tampico No. 912, 36730, Salamanca, Gto., México

    J. M. Rico-Martínez

Authors
  1. J. Gallardo-Alvarado
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  2. H. Orozco-Mendoza
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  3. R. Rodríguez-Castro
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  4. J. M. Rico-Martínez
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Correspondence to J. Gallardo-Alvarado.

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Gallardo-Alvarado, J., Orozco-Mendoza, H., Rodríguez-Castro, R. et al. Kinematics of a class of parallel manipulators which generates structures with three limbs. Multibody Syst Dyn 17, 27–46 (2007). https://doi.org/10.1007/s11044-006-9033-3

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  • DOI: https://doi.org/10.1007/s11044-006-9033-3

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