Abstract: The coupler curve which is near the zero-curvature point on the inflection circle is close to the straight line, the mechanism is often as the approximate straight-line guidance mechanism. When the instant center of linkage is infinitely far, there is no inflection circle in the linkage of four-bar linkage mechanism. It is difficult to synthesize approximate straight- line mechanism by the old methods. According to the intuitionistic analysis, a logical superposed formula for curvature of every spot locus on the linkage of four-bar linkages is presented, when the instant center of linkage is infinitely far. Afterward the formula is deduced by relativistic kinematics. The superposed formula is correct, and a diagrammatizing method getting zero-curvature spot on the linkage is gained by this formula, then the formula is successfully applied to synthesize the four-bar approximate straight-line linkages with infinitely far instant center. The method has such advantages: simplicity, visualization and practicality, which strongly supplements the theory of the inflexion circle.

Key words: Approximate straight-line, Four-bar linkage mechanism, Synthesis