Parametric damped vibrations of Gough–Stewart platforms for symmetric configurations

Far, Behrouz Afzali; Lidström, Per; Nilsson, K. Peter R.

doi:10.1016/j.mechmachtheory.2014.04.018

Cited by 25 publications

(27 citation statements)

References 36 publications

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“…The angle M J represents the rotation of the strut-pairs. Considering the six GSP variables [6] as well as M J , the geometric design space s G for GGSPs is defined by seven geometric variables as ^7 , , , , , , , , 0,…”

Section: Kinematicsmentioning

confidence: 99%

“…10 as well. This rotation matrix is based on Bryant angles due to the motivations presented in [6,15]. However, it could also be written based on e.g.…”

Section: Kinematicsmentioning

confidence: 99%

“…The stiffness matrix can be calculated directly using the Jacobian matrix [6]. The Jacobian matrix J is defined as the transformation between the Cartesian velocities C q of the platform and the length rates J q of the struts …”

Section: Stiffnessmentioning

confidence: 99%

“…1. Thus, the inertia matrix in the Cartesian space is diagonal and is given by [6] According to Eq. 15, the stiffness matrix is required to be proportional to the inertia matrix.…”

Section: Dynamic Isotropymentioning

confidence: 99%

“…In particular, the linearized equations of motion at the neutral configuration are of interest. These are well-known for GSPs from the literature [4][5][6][7][8][9]. However, despite the importance of dynamic isotropy as an optimal design solution, there exist a limited number of publications dealing with dynamic isotropy in GSPs.…”

Section: Introductionmentioning

confidence: 99%

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A Class of Generalized Gough-Stewart Platforms Used for Effectively Obtaining Dynamic Isotropy – An Analytical Study

Far

Lidström

2015

MATEC Web of Conferences

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Abstract. In this paper, we propose a class of Generalized Gough-Stewart Platforms (GGSPs) used, as a novel approach, to eliminate the classical isotropic constraint of GSPs (hexapods). GGSPs are based on the standard GSP architecture with additional rotations of the three strut-pairs. Despite the architectural generalization introduced in GGSPs, they do not require much more effort in order to be fabricated. This is due to the fact that all the struts (actuators) can be chosen identical, similar to standard GSPs. We analytically show how effectively the classical isotropic constraint is removed and that still sufficient simplicity is retained. Furthermore, this paper gives an intuitive understanding of dynamic isotropy in GGSPs as well as GSPs.

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Section: Kinematicsmentioning

confidence: 99%

“…10 as well. This rotation matrix is based on Bryant angles due to the motivations presented in [6,15]. However, it could also be written based on e.g.…”

Section: Kinematicsmentioning

confidence: 99%

Section: Stiffnessmentioning

confidence: 99%

“…1. Thus, the inertia matrix in the Cartesian space is diagonal and is given by [6] According to Eq. 15, the stiffness matrix is required to be proportional to the inertia matrix.…”

Section: Dynamic Isotropymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Class of Generalized Gough-Stewart Platforms Used for Effectively Obtaining Dynamic Isotropy – An Analytical Study

Far

Lidström

2015

MATEC Web of Conferences

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A Joint-Space Parametric Formulation for the Vibrations of Symmetric Gough-Stewart Platforms

Far¹,

Lidström²

2015

Progress in Systems Engineering

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Mathematical modelling of linear motion error for Hexarot parallel manipulators

Pedrammehr

Qazani

Asayesh

et al. 2016

Applied Mathematical Modelling

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a b s t r a c tHexarot is a robotic manipulator that belongs to the family of axis symmetric parallel mechanisms. The robot is able to move the robot platform or tool center point in six degrees of freedom (DOF). This paper presents the kinematics model of the robot including the inverse and forward kinematics, and its time derivatives. Then using the kinematics formulations, investigation of the nonlinear motion of the Hexarot robot for a desired linear motion path is performed. For this purpose, the concept of curvature of the robot path is used for measuring the nonlinearity of the actual motion of the robot. The nonlinear motion error of the robot is analyzed for the scenario where the platform moves on a linear path between two arbitrary points of the robot workspace. The effects of different parameters on the nonlinear motion error of the mechanism are demonstrated and strategies for motions with low error values are proposed.

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Parametric damped vibrations of Gough–Stewart platforms for symmetric configurations

Cited by 25 publications

References 36 publications

A Class of Generalized Gough-Stewart Platforms Used for Effectively Obtaining Dynamic Isotropy – An Analytical Study

A Class of Generalized Gough-Stewart Platforms Used for Effectively Obtaining Dynamic Isotropy – An Analytical Study

A Joint-Space Parametric Formulation for the Vibrations of Symmetric Gough-Stewart Platforms

Mathematical modelling of linear motion error for Hexarot parallel manipulators

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