Analytical synthesis of mechanisms is a useful tool towards computer-aided machinery design and production. 4-bar planar mechanisms have wide applications in industry and thus receive more attention from machinery design researchers. The proposed approach relies on forming a mathematical model for the mechanism position incorporating the 2 coupler positions. The model consists of 6 nonlinear equations considering the transmission angle of the mechanism in the 2 coupler positions. A case study is presented as a justification for the proposed approach. Exact coupler positions are attained with transmission angles not more than 7 % of the optimum value of 90 degrees.