ScholarLens Back to search
2018•Journal of Advanced Mechanical Design Systems and ManufacturingOpen access

A numerical method for forward kinematics of general Stewart manipulator using natural coordinates

Ruobing Wang, Hongtao Wu, Yanli Liu, Xiaolong Yang, Xuexiang ZHANG

Open full text 4 citations

Abstract

In this paper, a numerical method for forward kinematics of general Stewart manipulator using natural coordinates is presented. The kinematic equations are in quadratic forms and the corresponding Jacobian matrix is a linear function of coordinates because of using natural coordinates. According to the characteristics of the kinematic equations, the Newton-Raphson algorithm is simplified to decrease the renewal time of iterations between equations and Jacobian matrix, and used to solve the kinematic equations. The singularity and convergence problems of the algorithm are discussed. Furthermore, the method using natural coordinates is compared with the traditional method using rotation matrix through numerical examples. Comparison results show that the method using natural coordinates is very accurate, more efficient, and has a greater convergence domain.

Open-access reader

About this research paper

What this paper is about

In this paper, a numerical method for forward kinematics of general Stewart manipulator using natural coordinates is presented. The kinematic equations are in quadratic forms and the corresponding Jacobian matrix is a linear function of coordinates because of using natural coordinates. According to the characteristics of the kinematic equations, the Newton-Raphson algorithm is simplified to decrease the renewal time of iterations between equations and Jacobian matrix, and used to solve the kinematic equations. The singularity and convergence problems of the algorithm are discussed. Furthermore, the method using natural coordinates is compared with the traditional method using rotation matrix through numerical examples. Comparison results show that the method using natural coordinates is very accurate, more efficient, and has a greater convergence domain.

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper, a numerical method for forward kinematics of general Stewart manipulator using natural coordinates is presented. The kinematic equations are in quadratic forms and the corresponding Jacobian matrix is a linear function of coordinates because of using natural coordinates. According to the characteristics of the kinematic equations, the Newton-Raphson algorithm is simplified to decrease the renewal time of iterations between equations and Jacobian matrix, and used to solve the kinematic equations. The singularity and convergence problems of the algorithm are discussed. Furthermore, the method using natural coordinates is compared with the traditional method using rotation matrix through numerical examples. Comparison results show that the method using natural coordinates is very accurate, more efficient, and has a greater convergence domain.

Key concepts: Jacobian matrix and determinant, Kinematics, Mathematics, Generalized coordinates, Forward kinematics, Singularity, Convergence (economics), Mathematical analysis

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
A numerical method for forward kinematics of general Stewart manipulator using natural coordinates — Research Paper | ScholarLens