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Mechanical Sciences An open-access journal for theoretical and applied mechanics
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Volume 7, issue 1
Mech. Sci., 7, 9–17, 2016
https://doi.org/10.5194/ms-7-9-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Mech. Sci., 7, 9–17, 2016
https://doi.org/10.5194/ms-7-9-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 18 Jan 2016

Research article | 18 Jan 2016

Solving the dynamic equations of a 3-PRS Parallel Manipulator for efficient model-based designs

M. Díaz-Rodríguez1, J. A. Carretero2, and R. Bautista-Quintero2,3 M. Díaz-Rodríguez et al.
  • 1Departamento de Tecnología y Diseño, Facultad de Ingeniería, Universidad de los Andes, Mérida, 5101, Venezuela
  • 2Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3A 5A3, Canada
  • 3Departamento de Ingeniería Mecánica, Instituto Tecnológico de Culiacán, Sinaloa, 80220, Mexico

Abstract. Introduction of parallel manipulator systems for different applications areas has influenced many researchers to develop techniques for obtaining accurate and computational efficient inverse dynamic models. Some subject areas make use of these models, such as, optimal design, parameter identification, model based control and even actuation redundancy approaches. In this context, by revisiting some of the current computationally-efficient solutions for obtaining the inverse dynamic model of parallel manipulators, this paper compares three different methods for inverse dynamic modelling of a general, lower mobility, 3-PRS parallel manipulator. The first method obtains the inverse dynamic model by describing the manipulator as three open kinematic chains. Then, vector-loop closure constraints are introduced for obtaining the relationship between the dynamics of the open kinematic chains (such as a serial robot) and the closed chains (such as a parallel robot). The second method exploits certain characteristics of parallel manipulators such that the platform and the links are considered as independent subsystems. The proposed third method is similar to the second method but it uses a different Jacobian matrix formulation in order to reduce computational complexity. Analysis of these numerical formulations will provide fundamental software support for efficient model-based designs. In addition, computational cost reduction presented in this paper can also be an effective guideline for optimal design of this type of manipulator and for real-time embedded control.

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Three methods for formulating the dynamic model of parallel manipulators are compared in terms of their computational efficiency. The first two have been previously presented in the literature while the last one is introduced in this paper. Analysis of these numerical formulations provides a guideline for computational cost reduction for optimal design of this type of manipulator and for real-time embedded control.
Three methods for formulating the dynamic model of parallel manipulators are compared in terms...
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