A universal design method for synthesis problems of mechanisms that realize the approximate straight-line trajectory is presented in this paper. First, given the expected straight line and prescribed fixed pivots, a general mathematics model with angles as design parameters to determine the initial position of two side links is established, through which all infinite possible straight-line mechanisms are obtained. Then, kinematic constraints are imposed, including type, transmission angle, size, straightness, and defect. All feasible solution mechanisms that meet the constraints are calculated and can be expressed in solution regions. It is intuitive and comprehensive for designers to observe the distribution pattern of the solution. In the end, an optimal high-precision straight-line mechanism can be selected in the feasible solution regions by setting an optimization aim. The second-order osculating mechanism synthesis method can provide more solutions for designers, but designers can use the third-order osculating mechanism synthesis method when a higher straightness requirement is imposed. This method addresses the synthesis problem of this kind of mechanism for straight-line guidance and the problem of choosing an optimal solution from an infinite number of solutions.