Based on the enveloping hexahedron constructed by Bennett mechanism，the instantaneous relative position and orientation relation between the Bennett linkage configuration and the hyperboloid defined by its joint axis are derived. The dynamic mapping between the Bennett mechanism，the enveloping hexahedron，and the hyperboloid is visually explored，the geometric characteristics of the enveloping hexahedron configuration of the Bennett linkage with equal diagonals are analyzed. It is found that the projection of the enveloping hexahedron's bottom surface of the Bennett linkage at the given configuration coincides with the short axis of the waist ellipse through visualization of the projection of the hyperboloid on waist cross-section，which sparks inspiration of exploring the pressure angle of the mechanism. The research discovers that when the input angle is equal to,$n\mathrm{\pi }+\mathrm{\pi }/\mathrm{2}(n\in N)$,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17184716&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17184713&type=,26.07733345,3.47133350,，the configuration of the Bennett linkage happens the minimum pressure angle，which equals the twist angle of the output link. The visualization research on the mechanism with specific structural parameters and its associated geometry characteristics，such as geometric surfaces and curves，get inspiration and can provide ideas to reveal the general rules of kinematics.