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Math. Comput. Appl. 2016, 21(4), 40; doi:10.3390/mca21040040

The Modeling and Calculation of the Heading Machine Based on Differential Geometry

1
School of Mechanical Electronic & Information Engineering, China University of Mining and Technology, Beijing 100083, China
2
Mechanical & Electrical Engineering School, Beijing Information Science & Technology University, Beijing 100192, China
*
Author to whom correspondence should be addressed.
Academic Editor: Fazal Mahomed
Received: 7 July 2016 / Revised: 7 September 2016 / Accepted: 9 September 2016 / Published: 23 September 2016
View Full-Text   |   Download PDF [1614 KB, uploaded 27 September 2016]   |  

Abstract

The kinematic sketch of the heading machine’s cutting part is plotted and the kinematic relation is analyzed. The pose-attitude model of the cutting part is derived from the geometry method, and the velocity and acceleration relations are derived by the differential geometry method. According to the recurrence relation among the pose-attitude, the velocities and the accelerations, the numerical solving strategy is designed. The nonlinear part of the kinematics model is solved by the Newton iterative method. The kinematics model is simulated by MATLAB. The trigonometric functions are avoided by using the differential geometry method, and the derivation process and the results are simplified simultaneously. The simulation results give the curves of each kinematic parameter which verifies the validity of the kinematic model. View Full-Text
Keywords: the heading machine; spatial differential geometry; spatial mechanism; nonlinear; Newton iterative the heading machine; spatial differential geometry; spatial mechanism; nonlinear; Newton iterative
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Bai, L.; Ma, L.-H.; Ge, X.-S. The Modeling and Calculation of the Heading Machine Based on Differential Geometry. Math. Comput. Appl. 2016, 21, 40.

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