基于结式消去法的并联机构位置解析

Parallel manipulator site analysis based on resultant elimination

目的并联机构位置解析的核心问题是求解一组非线性方程组,为此提出一种消去法使并联机构位置方程降维,以便采用同伦方法求得位置方程全部解。方法从并联机构位置约束方程出发,采取狄克逊结式对位置正解方程进行消元,从而得到机构位置正反解封闭方程;采用同伦方法和利用MATLAB数学软件进行求解。结果利用MATLAB数学软件编制的狄克逊结式消元和同伦算法的数学机械化程序,得到Delta型并联机构位置问题的全部数学解。结论结式消去法为并联机构位置解析提供了十分有效的通用方法,而且可用于解决其他更为复杂的体系。

Aim To find methods of resolving nonlinear equations, becaues the cornerstone of the parallel mechanism site analysis is that nonlinear equations are solved. Methods The elimination method, homotopy method and Matlab mathematic software were used to solve the nonlinear equations. Results The complete mathematical solution of Delta parallel mechanism site was gotten by Matlab software. Conclusion The resultant elimination we employ here provides an effective mechod for parallel mechamism site analysis, and may solve other complex systems.