基于牛顿迭代混沌特性的机构综合新方法

New approach for mechanism synthesis based on the chaotic property of Newton iteration

为进一步探索混沌理论在解决实际工程问题中的应用,提出了基于牛顿迭代混沌特性的平面四杆机构运动综合问题的快速求解方法.借助计算机代数系统将平面四杆机构的综合问题归结为一元多项式方程的求解,并利用牛顿迭代法的混沌特性快速找出多项式方程的全部解,取其中的实数解代入机构综合的数学模型,即可求出其他机构参数并进行优化设计.由刚体导引的铰链四杆机构和曲柄滑块机构综合的实例证明了该方法具有简单、快速、求解过程可视等优点.

A fast solving method of mechanism synthesis by utilizing the chaotic property of Newton iteration was put forward for further exploring the application of chaos theory in solving practical engineeringoriented problems. With the computer symbolic manipulating technique, a one variable polynomial equation was derived for the closed form solution of a planar four bar mechanism, and all the roots of the equation could be easily located based on the chaotic property of Newton iteration. Then other parameters of the mechanism were easily obtained by substituting the real roots of the one variable polynomial equation into the mathematical formulae of the mechanism synthesis problem. And the design of the planar mechanism could be optimized further. The successful applications in the syntheses of a four-bar hinge mechanism and a crank-slider mechanism show that the proposed method is simple, efficient and its iteration process is visible.