Dynamics and control of the Stewart platform

Леонов, Г. А.; Зегжда, С. А.; Ershov, B. A.; Kazunin, D. V.; Kostygova, D. M.; Kuznetsov, Nikolay V.; Товстик, П. Е.; Товстик, Т. П.; Yushkov, M. P.

doi:10.1134/s102833581409002x

Cited by 15 publications

(6 citation statements)

References 9 publications

(13 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Other approaches based on Newton-Euler equations are detailed in [16,20], while in [17] the equations of motion are obtained using the Kane equations.…”

Section: Forced Vibrationsmentioning

confidence: 99%

“…The dynamics of a platform acted on by a pneumatic actuator, considering the inertia of the actuators, is studied in [16], while the dynamics of the platform acted on by linear actuators is described in [17,18]. The dynamics of the Stewart platform are studied with the aid of the principle of virtual work [19], or with the aid of the equations of classical mechanics considering a certain delay for the answer [20]. Reference [21] considers a Stewart platform for which a combination of methods are presented for the mathematical representation of its direct kinematics as well as algorithms of optimization.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Vibrations of a Rigid Solid Hung by Kinematic Chains

et al. 2022

View full text Add to dashboard Cite

In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical.

show abstract

“…Other approaches based on Newton-Euler equations are detailed in [16,20], while in [17] the equations of motion are obtained using the Kane equations.…”

Section: Forced Vibrationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Vibrations of a Rigid Solid Hung by Kinematic Chains

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Кроме того, имеет место нелинейная зависимость кинематики и динамики механизма в зависимости от точки рабочей области, что приводит к анизотропии и неоднородности динамических, упругих и скоростных свойств. В связи с этим решение данных вопросов привлекает внимание многих исследователей [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: совместное моделирование движения параллельного манипулятора...unclassified

Co-Simulation Parallel Manipulator Movements Using Adams-Matlab

Duyun

Горлов

Duyun

2022

Bulletin of Belgorod State Technological University Named After. V. G. Shukhov

View full text Add to dashboard Cite

The article presents the methods and results of the analysis of the movement of a modeling manipulator such as the Hugh-Stewart platform using Adams-Matlab in order to check and develop a possible trajectory of the working body. Application of Matlab Simulink for solving kinematics problems: determining the extension length of rods along a given trajectory of the movement of the working body. A feature of the Simulink application scheme is the export of physical and mechanical parameters of a solid model from Adams. Mutual integration of Matlab Simulink and Adams View evaluate the implementation of the possibility of implementing a kinematic, comprehensive and force analysis of the mechanism, taking into account its design features due to the use of an apparent prototype. The proposed method of joint modeling is presented in the form of a detailed description of the content of Simulink circuit blocks, their interaction in modeling, the exact mathematical apparatus and the conditions for implementing mutual thoroughness of the Matlab and Adams software packages. The technique was tested on the ascent from constructive platforms while moving along a sexual character such as a given trajectory. The results of a computational experiment are proposed and an analysis is made of the coordinate correspondence of the actual trajectory obtained as a result of modeling in joint simulation with the initial given trajectory for various types of motion.

show abstract

“…The dynamics and control of Gough-Stewart platforms (single hexapod platforms) has been intensively studied in the last two decades (e.g., see [1][2][3][4]), using Newton-Euler approach [1,4], the Lagrange formulation [2] or the virtual work method [3], etc.…”

Section: Introductionmentioning

confidence: 99%

“…These parallel robots dynamics studies use various rotation parameterizations, e.g., the Euler angles are still very popular to parameterize 3D rotations [1][2][3], sometimes in the framework of Denavit-Hartenberg convention.…”

Section: Introductionmentioning

confidence: 99%

Direct Dynamics of Gough-Stewart Hexapod Platforms Using the Redundant Parameterization of Rotations by Full Rotation Matrices

2017

IJOMAM

View full text Add to dashboard Cite

-The direct dynamics study of Gough-Stewart hexapod platforms presented in this paper represents a preparatory step towards the direct dynamics study of a double hexapod, i.e., two Gough-Stewart platforms mounted in parallel one above the other. The direct dynamics model used here is based on the redundant parameterization of rotations by full 3 dynamics of each solid of the hexapod platform comprises 12 scalar differential equations (3 for each translation and 9 for each solid rotation) and 6 algebraic scalar orthogonality equations, plus the algebraic constraints characterizing the joints. For the entire hexapod, the overall differentialalgebraic system comprises 156 scalar differential equations and 78+72=150 scalar algebraic equations. Of course, a number of 150 scalar Lagrange multipliers are introduced in association with fulfilling the algebraic equations. So, our dynamic modelling technique involves an increased number of parameters and equations, but this disadvantage is compensated by the fact that the dynamic equations can be written in a systematic way, being structurally similar for each solid of the hexapod multibody system. From the numerical point of view, the differential-algebraic system is solved by an iterative "shooting method", using classical adaptive step size Runge-Kutta integration. No convergence troubles were encountered so far, when studying the direct dynamics of the Gough-Stewart hexapod platform considered as case study.

show abstract

Dynamics and control of the Stewart platform

Cited by 15 publications

References 9 publications

On the Vibrations of a Rigid Solid Hung by Kinematic Chains

On the Vibrations of a Rigid Solid Hung by Kinematic Chains

Co-Simulation Parallel Manipulator Movements Using Adams-Matlab

Direct Dynamics of Gough-Stewart Hexapod Platforms Using the Redundant Parameterization of Rotations by Full Rotation Matrices

Contact Info

Product

Resources

About