Denavit-Hartenberg Notation-Based Kinematic Constraint Equations for Forward Kinematics of the 3–6 Stewart Platform

Shim, Seongbo; Lee, Seongpung; Joo, Subin; Seo, Joonho

doi:10.1115/1.4053822

Cited by 11 publications

(2 citation statements)

References 16 publications

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“…In Equation ( 8 K denotes the element of stiffness matrix, which reflects the relationship between the displacement of the moving platform and the external force. The elements of the stiffness matrix can be calculated from the geometric parameters of the platform and the stiffness of the legs [32].…”

Section:  mentioning

confidence: 99%

Computer Simulation Study of Stiffness Variation of Stewart Platform under Different Loads

Zhao,

Liu,

et al. 2024

ijacsa

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The ability of Stewart platform to resist deformation is an important target for designing and optimizing the platform, and studying the variation rule of stiffness of Stewart platform under different loads can help us to understand the dynamic characteristics of the platform, guide the design and control of the platform, and improve the performance and stability of the platform. The purpose of this paper is to change the law of stiffness variation and influence factors of Stewart platform under different loads, aiming to study the change of stiffness of Stewart platform under different loads as well as the influence factors, and the influence of stiffness change on the performance and stability of the platform. Firstly, using MATLAB software, the kinematic and mechanical model of Stewart platform was established, the analytical expression of the stiffness matrix of the platform was deduced, and the stiffness characteristics and stiffness singularity of the platform were analyzed. Then, using ADAMS software, the dynamic simulation model of the Stewart platform was established, and the stiffness of the platform was simulated and analyzed. The results show that the stiffness of the Stewart platform will appear singularity or sudden change under some special positions or loads, which should be avoided as much as possible so as not to affect the performance and stability of the platform. There is a certain correlation between the dynamic and static stiffness, but it is also affected by the nonlinearity of the structure, damping, coupling and other factors.

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Section:  mentioning

confidence: 99%

Computer Simulation Study of Stiffness Variation of Stewart Platform under Different Loads

Zhao,

Liu,

et al. 2024

ijacsa

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show abstract

“…In addition, a mathematical toolkit of the absolute nodal coordinate was introduced to solve the positioning of the soft parallel robots [27]. An analytical approach applying the Denavit-Hartenberg (D-H) notation to the forward kinematics of the 3-6 Stewart platform was proposed by Shim et al [28], but it was not intended to improve the speed or precision of the endeffector. Nevertheless, it is of crucial significance to calculate the forward kinematics of parallel robots in real-time control.…”

mentioning

confidence: 99%

Kernel extreme learning machine‐based general solution to forward kinematics of parallel robots

Jun-hai

Zhang

2023

CAAI Trans on Intel Tech

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The forward kinematics of parallel robots is a challenging issue due to its highly coupled non‐linear relation among branch chains. This paper presents a novel approach to forward kinematics of parallel robots based on kernel extreme learning machine (KELM). To tackle with the forward kinematics solution of fully parallel robots, the forward kinematics solution of parallel robots is equivalently transformed into a machine learning model first. On this basis, a computational model combining sparrow search algorithm and KELM is then established, which can serve as both regression and classification. Based on SSA‐optimised KELM (SSA‐KELM) established in this study, a binary discriminator for judging the existence of the forward kinematics solution and a multi‐label regression model for predicting the forward kinematics solution are built to obtain the forward kinematics general solution of parallel robots with different structural configurations and parameters. To evaluate the proposed model, a numerical case on this dataset collected by the inverse kinematics model of a typical 6‐DOF parallel robot is conducted, followed by the results manifesting that the binary discriminator with the discriminant accuracy of 88.50% is superior over ELM, KELM, support vector machine and logistic regression. The multi‐label regression model, with the root mean squared error of 0.06 mm for the position and 0.15° for the orientation, outperforms the double‐hidden‐layer back propagation (2‐BP), ELM, KELM and genetic algorithm‐optimised KELM. Furthermore, numerical cases of parallel robots with different structural configurations and parameters are compared with state‐of‐the‐art models. Moreover, these results of numerical simulation and experiment on the host computer demonstrate that the proposed model displays its high precision, high robustness and rapid convergence, which provides a candidate for the forward kinematics of parallel robots.

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Time-varying external archive differential evolution algorithm with applications to parallel mechanisms

Wen

Ji²,

Che³

et al. 2023

Applied Mathematical Modelling

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Denavit-Hartenberg Notation-Based Kinematic Constraint Equations for Forward Kinematics of the 3–6 Stewart Platform

Cited by 11 publications

References 16 publications

Computer Simulation Study of Stiffness Variation of Stewart Platform under Different Loads

Computer Simulation Study of Stiffness Variation of Stewart Platform under Different Loads

Kernel extreme learning machine‐based general solution to forward kinematics of parallel robots

Time-varying external archive differential evolution algorithm with applications to parallel mechanisms

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