Abstract: Given frame points, the point on the expectant straight-line and the direction of the task straight-line, this paper presents a syntbesis method of approximate straigbt-line four-bar linkages, which has four-point contact with its tangent. The traditional synthesis methods are difficult to obtain the optimal mechanism since only parts of the mechanism solutions are synthesized. After solution regions are determined, an infinite number of mechanism solutions satisfied the designers' needs can be expressed on a finite coordinate ptane. The mechanism property graphs are displayed to enable the designers to find out all the mechanism types and properties more intuitively for getting the optimal mechanism directly. So the problem of blindness of choosing mechanisms is solved efficiently, and the design period will be shortened.