Algebraic solution for the forward displacement analysis of the general 6-6 stewart mechanism

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• 作者：Feng Wei ; Shimin Wei ; Ying Zhang ; Qizheng Liao
• 关键词：general 6 ; 6 Stewart mechanism ; forward displacement analysis (FDA) ; conformal geometric algebra (CGA) ; Gröbner basis ; Sylvester resultant
• 刊名：Chinese Journal of Mechanical Engineering
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：29
• 期：1
• 页码：56-62
• 全文大小：527 KB
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• 作者单位：Feng Wei (1) (2)
  Shimin Wei (1)
  Ying Zhang (1)
  Qizheng Liao (1)
  
  1. Automation School, Beijing University of Posts and Telecommunications, Beijing, 100876, China
  2. School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, 454000, China
  
• 刊物主题：Mechanical Engineering; Theoretical and Applied Mechanics; Manufacturing, Machines, Tools; Engineering Thermodynamics, Heat and Mass Transfer; Power Electronics, Electrical Machines and Networks; Electronics and Microelectronics, Instrumentation;
• 出版者：Springer Berlin Heidelberg
• ISSN：2192-8258

文摘

The solution for the forward displacement analysis(FDA) of the general 6-6 Stewart mechanism(i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane) has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra(CGA). The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Gröbner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Gröbner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9´9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix. Keywords general 6-6 Stewart mechanism forward displacement analysis (FDA) conformal geometric algebra (CGA) Gröbner basis Sylvester resultant