吉林大学学报(工学版) ›› 2013, Vol. 43 ›› Issue (05): 1241-1246.doi: 10.7964/jdxbgxb201305015

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Forward kinematics solution of bogie 6-DOF platform based on the orthogonality of rotation matrix

WANG Xiu-gang, SU Jian, CAO Xiao-ning, XU Zhen, LU Hai-ge, TIAN Zong-ju   

  1. College of Transportation, Jilin University, Changchun 130022, China
  • Received:2012-05-14 Online:2013-09-01 Published:2013-09-01

Abstract:

The paper employed the orthogonality of rotation matrix of homogeneous transfer matrix and Newton iteration to obtain the solution of forward kinematics of the space attitude simulation bogie. First, according to the orthogonal relationship between the elements of the rotation matrix and the length constraints of the hydraulic cylinder rods, the mathematical model with nonlinear equations was established. In this model, the elements of the homogeneous transformation matrix were taken as the unknowns, and the number of equations was equal to the number of the unknowns. Then, the approximate solution was obtained with Newton-Raphson method. Finally, the corresponding position and pose were solved on the basis of the relationship between the elements of the homogeneous transformation matrix and the position variables. The method avoids the iterative calculation of trigonometric function with Newton-Raphson method, improving the speed to solve the forward kinematics. Also, the method of forward kinematics of the bogie 6-DOF platform provides the possibility of realizing the space attitude simulation of bogie. It provides the theoretical basis and technical support for the pose solution of other forms of 6-DOF platform.

Key words: railway transportation, space attitude simulation platform, forward kinematics, homogeneous transfer matrix, Newton iteration

CLC Number: 

  • U260

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