Forward Displacement Analysis of a General 6‐3 Stewart Platform Using Conformal Geometric Algebra

Wei, Feng; Wei, Shimin; Zhang, Ying; Liao, Qizheng

doi:10.1155/2017/4687638

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…The kinematics [5], singularity [6], dynamics [7], modeling and control [8] of this PM have been a major topic of research in the past and it continues up until now, e.g. [9]. Some applications require less than 6-DoF.…”

Section: Introductionmentioning

confidence: 99%

Kinematic analysis and dimensional optimization of a 2R2T parallel manipulator

Araujo-Gómez

Díaz‐Rodríguez

Mata

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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The need of a device providing two translational (2T) and two rotational (2R) movements led us to the design a 3UPS-1RPU parallel manipulator. The manipulator consisted on a mobile platform connected to a base through four legs. That is, the manipulator layout has one central leg and three external legs at the same radial distance. By studying different locations of the legs anchoring point, we improved the first layout design, yet not the optimal one. On this basis, this paper focus on the optimal dimensional design of the manipulator. To this end, we put forward the kinematics equations of the manipulator in accordance to the anchoring points coordinates. Through a numerical approach, the equations enable to find the manipulator workspace. Also, we find a global manipulability index using a local dexterity measure. The latter index serves as optimal function. The optimization process considers joint constraints. Thus, we built a nonlinear optimization problem solved through sequential quadratic programming algorithms. We start by optimizing only a small set of parameters rather than the entire set, which gives us insights on the initial guess to optimize using the entire set. The optimal design layout varies from the original layout. Findings suggest that a task-oriented reconfiguration strategy can improve manipulator performance.

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Section: Introductionmentioning

confidence: 99%

Kinematic analysis and dimensional optimization of a 2R2T parallel manipulator

Araujo-Gómez

Díaz‐Rodríguez

Mata

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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“…Huo et al [18] and Li et al [19] proposed a mobility analysis approach for PMs based on geometric algebra. Zhang et al [20,21] and Wei et al [22] applied CGA to solve the direct kinematics of parallel mechanisms.…”

Section: Introductionmentioning

confidence: 99%

A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms

Zhang

Liu

Wei

et al. 2018

Mathematical Problems in Engineering

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A geometric modeling and solution procedure for direct kinematic analysis of 6-4 Stewart platforms with any link parameters is proposed based on conformal geometric algebra (CGA). Firstly, the positions of the two single spherical joints on the moving platform are formulated by the intersection, dissection, and dual of the basic entities under the frame of CGA. Secondly, a coordinate-invariant equation is derived via CGA operation in the positions of the other two pairwise spherical joints. Thirdly, the other five equations are formulated in terms of geometric constraints. Fourthly, a 32-degree univariate polynomial equation is reduced from a constructed 7 by 7 matrix which is relatively small in size by using a Gröbner-Sylvester hybrid method. Finally, a numerical example is employed to verify the solution procedure. The novelty of the paper lies in that (1) the formulation is concise and coordinate-invariant and has intrinsic geometric intuition due to the use of CGA and (2) the size of the resultant matrix is smaller than those existed.

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

Shim

Lee²,

Joo

et al. 2022

Journal of Mechanisms and Robotics

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This paper presents a new forward kinematic approach for the 3-6 Stewart platform. In the 3-6 Stewart platform, the position and orientation of the moving platform can be determined through kinematic constraint equations that indicate the possible trajectories of the three joints on the platform from the base coordinates. In most previous studies, the constraint equations were obtained through vector equations, which involves many complicated steps and multiple variables. Based on Denavit-Hartenberg (D-H) notation, the proposed approach allows a constraint equation representation with only four parameters. In addition, to implement the forward kinematics with the fewest possible D-H parameters, the 3-6 Stewart platform is reconfigured into three virtual revolute joints sharing base coordinates. Consequently, the constraint equations can be intuitively derived, and the computation process becomes more concise. The feasibility of the proposed approach is verified through an iterative numerical analysis and a simulation comparison with the general inverse kinematics.

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Forward Displacement Analysis of a General 6‐3 Stewart Platform Using Conformal Geometric Algebra

Cited by 5 publications

References 14 publications

Kinematic analysis and dimensional optimization of a 2R2T parallel manipulator

Kinematic analysis and dimensional optimization of a 2R2T parallel manipulator

A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms

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

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