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Research Papers

Natural Frequency Computation of Parallel Robots

[+] Author and Article Information
Coralie Germain

Institut de Recherche en Communications
et Cybernétique de Nantes IRCCyN,
UMR CNRS 6597,
1, rue de la Noë,
Nantes 44321, France
e-mail: coralie.germain@ens-rennes.fr

Sébastien Briot

Institut de Recherche en Communications
et Cybernétique de Nantes IRCCyN,
UMR CNRS 6597,
1, rue de la Noë,
Nantes 44321, France
e-mail: Sebastien.Briot@irccyn.ec-nantes.fr

Stéphane Caro

Institut de Recherche en Communications
et Cybernétique de Nantes IRCCyN,
UMR CNRS 6597,
1, rue de la Noë,
Nantes 44321, France
e-mail: Stephane.Caro@irccyn.ec-nantes.fr

Philippe Wenger

Institut de Recherche en Communications
et Cybernétique de Nantes IRCCyN,
UMR CNRS 6597,
1, rue de la Noë,
Nantes 44321, France
e-mail: Philippe.Wenger@irccyn.ec-nantes.fr

Note that each robot link can be composed of one element or several elements.

It is assumed that the generalized velocities are equal to d/dt(δqt)=q·t.

Note that index ij is written i, j in this section for a better understanding of the equations.

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 30, 2013; final manuscript received September 11, 2014; published online January 12, 2015. Assoc. Editor: Arend L. Schwab.

J. Comput. Nonlinear Dynam 10(2), 021004 (Mar 01, 2015) (11 pages) Paper No: CND-13-1194; doi: 10.1115/1.4028573 History: Received July 30, 2013; Revised September 11, 2014; Online January 12, 2015

The characterization of the elastodynamic behavior and natural frequencies of parallel robots is a crucial point. Accurate elastodynamic models of parallel robots are useful at both their design and control stages in order to define their optimal dimensions and shapes while improving their vibratory behavior. Several methods exist to write the elastodynamic model of manipulators. However, those methods do not provide a straightforward way to write the Jacobian matrices related to the kinematic constraints of parallel manipulators. Therefore, the subject of this paper is about a systematic method for the determination of the mass and stiffness matrices of any parallel robot in stationary configurations. The proposed method is used to express the mass and stiffness matrices of the Nantes Variable Actuation Robot (NaVARo), a three-degree-of-freedom (3DOF) planar parallel robot with variable actuation schemes, developed at IRCCyN. Then, its natural frequencies are evaluated and compared with those obtained from both Cast3m software and experimentally.

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Figures

Grahic Jump Location
Fig. 1

Schematic of a parallel robot for its dynamic modeling: (a) kinematic chain and (b) virtual tree structure

Grahic Jump Location
Fig. 2

Schematics of the flexible elements into consideration: (a) parameters of one flexible body j and (b) assembly of two flexible bodies

Grahic Jump Location
Fig. 3

The NaVARo (a) prototype of the NaVARo located at IRCCyN, Nantes, France and (b) Shematics of the NaVARo

Grahic Jump Location
Fig. 4

The eight configurations used for the experiments: (a) pose 1 x = 0 m, y = 0 m, θ = 0 rad; (b) pose 2 x = 0 m, y = 0 m, θ = −π/3 rad; (c) pose 3 x = 0.117 m, y = 0.068 m, θ = −π/3 rad; (d) pose 4 x = 0.182 m, y = 0.105 m, θ = −π/3 rad;(e) pose 5 x = −0.117 m, y = 0.068 m, θ = −π/3 rad; (f) Pose 6 x = −0.182 m, y = 0.105 m, θ = −π/3 rad; (g) pose 7 x = 0 m, y = −0.135 m, θ = −π/3 rad; and (h) pose 8 x = 0 m, y = −0.21 m, θ = −π/3 rad

Grahic Jump Location
Fig. 5

Experimental setup: DataBox

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