关于曲柄摇杆机构极位夹角的若干命题及其应用

SOME PROPOSITIONS RELATED TO EXTREME POSITION ANGLE OF CRANK-ROCKER MECHANISMS AND THEIR APPLICATIONS

针对具有急回特性的Ⅰ、Ⅱ型曲柄摇杆机构,通过深入分析极位夹角与构件尺寸之间的内在关系,获得了Ⅰ型曲柄摇杆机构极位夹角分别小于、等于或大于90°的几何条件以及Ⅱ型曲柄摇杆机构极位夹角一定小于90°的结论,揭示了曲柄摇杆机构设计时作为已知条件的极位夹角和摇杆摆角之间应满足的要求。首次将研究结果综合形成为5个定理,并通过实例说明了这些定理的应用。

Based on deeply analysis of inherent relations between the extreme position angle and the link dimensions of type Ⅰ and type Ⅱ crank-rocker mechanisms with quick return characteristics, the geometrical conditions are put forward, by which we can judge whether the extreme position angle of type Ⅰ crank-rocker mechanisms is less than, equal to or lager than 90°, It is proved that the extreme position angle of type Ⅱ crank-rocker mechanism is certainly less than 90°. The relations between the extreme position angle and the angular stroke of the rocker are brought to light, which should be satisfied during the kinematic design of crank-rocker mechanisms. For the first time, the study results are synthesized as five theorems. Several examples are given to show the correctness and applications of these theorems.