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提出了一种基于结式消元的Stephenson-Ⅲ型六杆机构死点位置识别的新方法。Stephenson-Ⅲ六杆机构输入-输出方程的重根和机构的死点与双点位置是一一对应的。将Stephenson-Ⅲ六杆机构看作由一个四杆链和一个五杆链组成,首先分别建立这两个运动链的闭环矢量方程,然后利用消元法和正切半角替换推导出机构的输入-输出多项式方程和关于机构双点的一元六次方程;基于Sylvester结式定理求得机构输入-输出方程的重根和双点方程的实数根;从输入-输出方程的重根中删除机构的双点位置即得到机构的死点位置构型。
A new method to identify dead center position of Stephenson-Ⅲ type six-bar mechanism based on knot elimination is proposed. The Stephenson-III six-bar mechanism input-output equation of the root and the dead center of the mechanism and the two-point position is one-to-one correspondence. The Stephenson-III six-bar mechanism is considered as a four-bar chain and a five-bar chain. First, the closed-loop vector equations of the two kinematic chains are established respectively. Then the input-output of the mechanism is deduced by the elimination method and the tangent- Polynomial equation and the six-point equation about the double point of the mechanism; the real root of the double-point equation of the input-output equation of the mechanism is obtained based on the Sylvester knot theorem; the double point position of the mechanism is deleted from the double root of the input-output equation Get the organization’s dead center position configuration.