用虚设铰链法求解平面高级机构位置问题

Solve the Position problem of the Advanced Mechanism With Virtual Hinge Method

提出了解决平面高级杆组位置问题的一种新的方法———虚设铰链法。此法主要是在高级杆组中任意定长杆中间任意设定一个铰链点 ,外点与机架相联 ,形成一个由II级杆组组成的自由度为 1的虚拟II级机构。然后 ,将原杆长与虚拟机构中两端点的距离的差作为逼近函数 ,对逼近函数求解即得平面高级杆组的位置。这种方法简单有效 ,解的可靠性好 ,同时对初始值的要求也大大降低。应用这种方法针对实例开发的VC程序运行结果表明 :该种方法收敛速度快 ,精度高。

In this paper,a new method called virtual hinge method to solve the position of the advanced mechanism is put forward.We can just set one hinge point at random at any place in the middle of any fixed-length bar with exterior points connected with rack.In this way we can get a second-class mechanism composed of second-class bar group with one degree of freedom. Then the approximating function can be defined by the difference of the length of original bar and the distance of the two endpoints in the virtual mechanism.The position of the advance bar group will be got if the approximating function is worked out.This method is very simple,effective and reliable.At the same time,the requirement of initial value is lower dramatically.Through this way the result of the VC programm which is based on instance indicates that this solution is of high speed of convergence on the one hand,and high accuracy on the other.