Mathematical model of Stewart platform motion

Alyushin, Yu. A.; Elenev, S. A.

doi:10.3103/s1052618810040011

Cited by 4 publications

(2 citation statements)

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“…A Stewart platform is called a form of manipulator with six degrees of freedom, which allows one to provide a given position and orientation of the surface in the vicinity of any point of the platform on its three cartesian coordinates and projections of the unit normal vector [1]. A mathematical model of the mechanism of movement of an undeformed platform with six degrees of freedom is proposed [2]. The Stewart platform consists of two rigid frames connected by 6 variable length legs.…”

Section: Stewart Platformmentioning

confidence: 99%

Kinematics of Supination and Pronation with Stewart Platform

Karakaş

Baydaş

2021

Journal of Mathematical Sciences and Modelling

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This paper presents kinematics form of pronation and supination movement. The algorithm of Stewart platform motion can be used to create a new motion of supination (or pronation) motion. Pronation motion can be taken as Stewart motion which has not any rotation on x-axis and y-axis. In this case, pronation motion has only one parameter. Supination movement creates a helix curve. Additionally, the correlation between rotation angle and extension is 1. This allows us to use artificial intelligence in pronation motion. In this article, the algorithm and Matlab applications of pronation motion are given in the concepts of artificial intelligence approach. This is a new and important approach.

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Section: Stewart Platformmentioning

confidence: 99%

Kinematics of Supination and Pronation with Stewart Platform

Karakaş

Baydaş

2021

Journal of Mathematical Sciences and Modelling

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“…The dynamic of the platform for an asymmetric load is studied with the Lagrange equations [24]; the singularities of the platform and their analysis are described in [25], while the control using Lyapunov-type methods is studied in [26]. The equations of motion can be obtained with the aid of the principle of superposition [27,28]. Lazard and Merlet [29] proved that a Stewart platform can have a maximum of 12 configurations and constructed such a platform.…”

Section: Introductionmentioning

confidence: 99%

On the Vibrations of a Rigid Solid Hung by Kinematic Chains

et al. 2022

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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.

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