【摘要】 基于共形几何代数方法建立了Stephenson-Ⅲ型机构的闭环约束方程,运用欧拉公式将方程表示成复数指数形式,描述了公式中各参数与共形空间中各矢量的相互关系,推导出了求解连杆机构运动姿态的输入-输出方程组,并在给定输入下得到了机构位置解。根据各输入杆变量的Jacobian矩阵的行列式的值等于0,推导得出了机构死点位置的判别式,得到了在死点构型下机构的位置解,通过与传统数值法计算结果的比对,验证了该方法的正确性和有效性。更多还原

【Abstract】 Closed-loop constraint equations of Stephenson-Ⅲ linkage mechanisms are established based on the Conformal Geometric Algebra( CGA),by using Euler formula. The closed-loop equations are expressed as compound exponential form. Mutual relationships between various parameters in the formula and vectors in conformal space are described. Depending on given input,input-output equations are derived to solve the position of the link mechanism. The value of Jacobian matrix determinant equals to 0,so that the discriminative formulas of the dead-center positions are derived and the dead-center position solutions are gained. Finally,the effectiveness and accuracy of this method are verified by contrasting with traditional numerical methods.更多还原