平面Ⅲ级杆组装配构形的特殊位置分析

CONFIGURATION ANALYSIS OF PLANAR TWO-LOOP CHAIN AT SPECIAL POSITION

研究了使用数值法求解平面Ⅲ级杆组位置构形可能失效的原因。认为从拆副法看平面III级杆组中心副位置求解可归结为连杆曲线与圆的交点 ,当连杆曲线出现奇异点时 ,杆组位置构形出现奇异解。文中导出了用杆组结构参数表示的奇异点坐标计算式及产生奇异点的结构参数关系式。分析了奇异点数目、形态以及杆组中各构件在奇异点处各种可能的装配模式。

According to disconnecting kinematic pair, the configuration analysis of planar two loop chain becomes locating a set of points that lie on the intersection of the coupler curve of compound link and the circle with the end of binary link connecting with other link outside the chain as center and the length of the link as radius . In this paper, it is indicated that the numerical approaching to configurations of the chain, which involves the nonlinear displacement equations of the chain and the coupler curve of the sixth order ,may fail to converge at special position that a pair position of Compound link coincides with double point of coupler curve. To solve this problem, the formulas computing Cartesian coordinate and criteria generating singularity characterized by structure parameters of the chain are developed with algebraic method . And the number of special position and all kinds of configurations of the chain are analyzed in detail.