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Parametric damped vibrations of Gough–Stewart platforms for symmetric configurations

Afzali Far, Behrouz LU ; Lidström, Per LU and Nilsson, Kristina LU (2014) In Mechanism and Machine Theory 80. p.52-69
Abstract
Abstract Modal behavior of a GoughâStewart Platform (GSP) is sensitive to several variables related to its inertia, damping and stiffness as well as its complex 3-D geometry. To optimize its dynamical performance, due to the complications of this system, it is crucial to have the equations parametrically at the neutral configuration. However, in the literature, no complete parametric solution to this problem is presented. In this paper, we establish a fully-parametric and closed-form model for the damped vibrations of GSPs. In particular, this analytical model can be used in order to design, optimize and control GSPs in high-precision/bandwidth applications. Parametric expressions of the damped eigenfrequencies and the corresponding... (More)
Abstract Modal behavior of a GoughâStewart Platform (GSP) is sensitive to several variables related to its inertia, damping and stiffness as well as its complex 3-D geometry. To optimize its dynamical performance, due to the complications of this system, it is crucial to have the equations parametrically at the neutral configuration. However, in the literature, no complete parametric solution to this problem is presented. In this paper, we establish a fully-parametric and closed-form model for the damped vibrations of GSPs. In particular, this analytical model can be used in order to design, optimize and control GSPs in high-precision/bandwidth applications. Parametric expressions of the damped eigenfrequencies and the corresponding eigenvectors as well as the Jacobian, stiffness and damping matrices are developed. Interestingly, despite the complexity of the system, it is shown how well-structured algebraic expressions are obtained using the Cartesian-space approach. Having analytically studied the eigenvectors, the conditions for decoupled vibrations are also analytically formulated. Finally, using a reference GSP, the sensitivity of the damped eigenfrequencies to stiffness and damping variations are investigated accompanied by a cross-check with an ABAQUS® simulation. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Gough–Stewart manipulators, Parallel robots, Hexapods, Parametric modal analysis, Mode shapes
in
Mechanism and Machine Theory
volume
80
pages
52 - 69
publisher
Elsevier
external identifiers
  • wos:000340993000004
  • scopus:84901471899
ISSN
1873-3999
DOI
10.1016/j.mechmachtheory.2014.04.018
language
English
LU publication?
yes
id
cba40109-e3d0-4883-91d3-13914a3120b6 (old id 4590315)
alternative location
http://www.sciencedirect.com/science/article/pii/S0094114X14001256
date added to LUP
2014-08-25 11:46:25
date last changed
2017-01-01 03:19:40
@article{cba40109-e3d0-4883-91d3-13914a3120b6,
  abstract     = {Abstract Modal behavior of a GoughâStewart Platform (GSP) is sensitive to several variables related to its inertia, damping and stiffness as well as its complex 3-D geometry. To optimize its dynamical performance, due to the complications of this system, it is crucial to have the equations parametrically at the neutral configuration. However, in the literature, no complete parametric solution to this problem is presented. In this paper, we establish a fully-parametric and closed-form model for the damped vibrations of GSPs. In particular, this analytical model can be used in order to design, optimize and control GSPs in high-precision/bandwidth applications. Parametric expressions of the damped eigenfrequencies and the corresponding eigenvectors as well as the Jacobian, stiffness and damping matrices are developed. Interestingly, despite the complexity of the system, it is shown how well-structured algebraic expressions are obtained using the Cartesian-space approach. Having analytically studied the eigenvectors, the conditions for decoupled vibrations are also analytically formulated. Finally, using a reference GSP, the sensitivity of the damped eigenfrequencies to stiffness and damping variations are investigated accompanied by a cross-check with an ABAQUS® simulation.},
  author       = {Afzali Far, Behrouz and Lidström, Per and Nilsson, Kristina},
  issn         = {1873-3999},
  keyword      = {Gough–Stewart manipulators,Parallel robots,Hexapods,Parametric modal analysis,Mode shapes},
  language     = {eng},
  pages        = {52--69},
  publisher    = {Elsevier},
  series       = {Mechanism and Machine Theory},
  title        = {Parametric damped vibrations of Gough–Stewart platforms for symmetric configurations},
  url          = {http://dx.doi.org/10.1016/j.mechmachtheory.2014.04.018},
  volume       = {80},
  year         = {2014},
}