Parametric damped vibrations of Gough–Stewart platforms for symmetric configurations
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4590315
- author
- Afzali Far, Behrouz LU ; Lidström, Per LU and Nilsson, Kristina LU
- organization
- publishing date
- 2014
- 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
- 2016-04-01 10:09:22
- date last changed
- 2022-04-27 19:04:35
@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}},
keywords = {{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}},
doi = {{10.1016/j.mechmachtheory.2014.04.018}},
volume = {{80}},
year = {{2014}},
}