Influence of strut inertia on the vibrations in initially symmetric Gough–Stewart Platforms—an analytical study

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

doi:10.1016/j.jsv.2015.03.054

Cited by 15 publications

(8 citation statements)

References 38 publications

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“…A new dynamic equation of the Free-Hex is established in this section to analyze the dynamic characteristics by considering unequal attachment stiffness among the six feet, leading to a wider range of applications of the Free-Hex in in-situ environment with better performances; it also can be utilized to a derived family of parallel kinematics machines (e.g. 3RPS and 3UPU), which have removed base platforms [27,28].…”

Section: Dynamic Equation Of the Free-hexmentioning

confidence: 99%

Parametric vibration analysis and validation for a novel portable hexapod machine tool attached to surfaces with unequal stiffness

Dong

Palmer

et al. 2019

Journal of Manufacturing Processes

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The Free-Leg Hexapod (Free-Hex) machine tool is an advancement from the conventional Stewart platform, which has the fixed base platform removed to enable the limbs to be attached to a wider range of surfaces (e.g. non-flat and curved). However, in some scenarios (e.g. in-situ repair of industrial installations), the limbs of the Free-Hex need to be attached to the surfaces with unequal stiffness, which brings the challenge of predicting the dynamics of the system for conducting machining operations under dynamically stable conditions. In this paper, after introducing the attachment stiffness (i.e. feet attached to the environment with different materials) in the conventional dynamic model of the parallel manipulator, the dynamic behavior of the Free-Hex machine tools devoted to the insitu operation environments was studied. Then, the experimental validation was conducted to prove the dynamic model developed in this paper. It was found that the errors of the proposed model are under 6% (i.e. 5.1% at symmetrical limb configuration and 5.8% at the arbitrary configuration) when the limbs are attached to the surfaces with unequal stiffness. Further, by applying the validated model, the dynamic performance of the Free-Hex with a wider range of attachment stiffness was analyzed. Overall, it was found that the attachment stiffness has a remarkable influence on the natural frequencies of the machine tool (e.g. the frequency of mode 4 at the symmetrical configuration is increased by 36.8% when the attachment stiffness of one limb changes from 0 to 1e+12 N/m). Thus, the work discussed in this paper can be utilized to avoid the dynamically unstable configurations of parallel kinematic machine tools (e.g. Free-Hex) when mounting on the surface with unequal stiffness in the in-situ operation environments.

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Section: Dynamic Equation Of the Free-hexmentioning

confidence: 99%

Parametric vibration analysis and validation for a novel portable hexapod machine tool attached to surfaces with unequal stiffness

Dong

Palmer

et al. 2019

Journal of Manufacturing Processes

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“…With reference to the inertia matrix C M given in (18), the isotropic eigenfrequency is given by ( ) …”

Section: Conditions Of Dynamic Isotropymentioning

confidence: 99%

“…The reference platform is similar to the one of a GoughStewart platform given in [18], where the inertia properties of the platform are given by As explained earlier, on the one hand, we know that in the isotropic solution each cluster of struts is parallel to a principal axis of the platform. On the other hand, the position of the struts along their axes does not have any influence on the decoupled stiffness matrix.…”

Section: Examplementioning

confidence: 99%

Dynamic isotropy in 3-DOF Gantry Tau robots - an analytical study

Afzali-Far

Lidström

Robertsson

2016

2016 IEEE International Conference on Robotics and Automation (ICRA)

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3-DOF Gantry Tau is a type of parallel robot, consisting of six struts configured in three clusters, which provides three translational DOFs. It has increasing industrial use in applications where large workspace and high stiffness are required. In fact, the concept of dynamic isotropy, where all the natural frequencies of a system are equal, can be employed in order to effectively optimize the geometry of robots. However, no study on dynamic isotropy of Gantry Tau robots has yet been reported in the literature. In this paper, the problem of dynamic isotropy in 3-DOF Gantry Tau robots is analytically addressed. Firstly, the kinematics is established based on a general approach with 36 geometric variables. Jacobian and stiffness matrices are also investigated where the struts are considered to be axially flexible. Subsequently, analytical solutions to obtain both a decoupled stiffness matrix and a complete dynamic isotropy are presented. Finally, as an example, dynamically isotropic geometries of a Gantry Tau robot are calculated, for a reference platform, using the developed analytical method.

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“…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%

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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Influence of strut inertia on the vibrations in initially symmetric Gough–Stewart Platforms—an analytical study

Cited by 15 publications

References 38 publications

Parametric vibration analysis and validation for a novel portable hexapod machine tool attached to surfaces with unequal stiffness

Parametric vibration analysis and validation for a novel portable hexapod machine tool attached to surfaces with unequal stiffness

Dynamic isotropy in 3-DOF Gantry Tau robots - an analytical study

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

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