A vast number of mechanisms have been synthesized to augment the requirements of automation industry, but still there is need to invent useful mechanisms. To bridge this gap and to fulfill the requirement of motion between two extreme positions, various planar kinematic linkage mechanisms have been proposed by different researchers. In this paper, an effort has been made to propose a mechanism along with its analytical dimensional synthesis that makes use of two binary links having two offset tracing points. The proposed mechanism transmits motion between two extreme positions by alternately temporarily fixing a different binary link in two distinct stages. The analytical equations have been written using dyadic and triadic approach of mechanism synthesis for common standard kinematic task of path generation. The proposed method is noniterative and reduces the solution space.