Abstract: 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.

Key words: Angular stroke of rocker, Crank-rocker mechanism, Extreme position angle, Mechanism design