基于模糊集理论的四杆机构优化设计

Optimization of four-rod mechanism based on fuzzy set theory

以曲柄摇杆机构为例,根据在设计中参数值的不确定性,使从动件在原动件运动规律一定的条件下能准确地按一定规律运动,并以理论和实际运动规律之间的偏差最小为设计目标,建立了模糊集理论设计的数学模型,给出了设计方法,并利用MTLAB软件编写的计算机程序运算出优化结果.通过和常规的优化方法惩罚函数法在结果上的数据对比表明,理论运动轨迹和实际机构的运动轨迹之间偏差的平方和减少了11.89%,充分体现了模糊集理论在四杆机构设计上的优越性.

Taking crank and rocker mechanism as an example and according to the uncertainty of parameters of the mechanism to be designed, the driven component was made move exactly in accordance to a definite pattern specified by the motion pattern of driving component. Taking the minimized deviation between theoretical and actual motion patterns as designing objective, a mathematical model was set up with fuzzy set theory and a design method was also given. Finally, optimization result was computed with a computer program worked out by using the software MATLAB. Compared the result with that obtained by using traditional optimization method （penalty function method）, it was found that the sum of squared deviation between the loci of theoretical motion and actual motion of the mechanism designed was decreased by 11.89%, illustrating the superiority of fuzzy set theory in the design of four-rod mechanism.