A hyper-chaotic mathematical programming method for finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 30th 2-coupling-degree nine-link Barranov truss was completed. Four constrained equations were established by using the vector method with the complex number method according to four loops of the mechanism, and four supplement equations were also established by increasing four variables and the relation of sine function and cosine function. The established eight equations are necessary to forward displacement analysis of the mechanism. The hyper-chaotic mathematical programming method was created on the basis of combining the mathematical programming method with hyper-chaotic sequences and utilizing two dimensional discrete hyper-chaotic systems to obtain initial points to find all real solutions of the nonlinear questions. A numerical example of forward displacement analysis was given. The result proves the correctness and validity of the proposed method.%应用求解非线性方程组全部实数解的超混沌数学规划法完成了第30种二耦合9杆巴氏桁架的位置正解的求解.结合矢量法和复数法建立了该机构四回路的4个约束方程,利用正、余弦函数关系增设4变量,建立了4个补充方程,从而构造了该机构位置分析的8变量约束方程组.将超混沌序列和数学规划法相结合,应用二维离散超混沌系统产生迭代初始点,提出了应用超混沌映射的数学规划法求解非线性方程组全部实数解的新方法,完成了该机构的位置分析.给出了计算实例.实例表明了该方法的正确性和有效性.
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