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This research presents a new synthesis method named the constraint force design method allowing topology optimization for planar rigid-body mechanisms.In conventional mechanism design procedures, the kinematics of a mechanism whose topology is pre-determined by engineer are analytical derived and the positions and types of joints as well as the lengths of rigid links are changed and optimized to obtain optimal rigid-body mechanisms tracking output trajectories.In these conventional mechanism design processes, commonly it is impossible to change the configuration or topology of joints and links.The existing mechanism synthesis methods having been limited workspace, the performance analyses of several fixed topologies appear to be essential.In order to circumvent the fixed topology limitation in optimally designing rigid-body mechanisms, we present the constraint force design method.In this new design method, distributed unit masses simulate revolute or prismatic joints depending on the number of assigned degrees of freedom.For rigid-body mechanisms, constraint forces simulating rigid-links defined among these unit masses are applied and the kinetics of these unit masses is analyzed for rigid-body mechanisms.To minimize the root-mean square error of the output paths of synthesized linkages and a target linkage, this method designs the existence of these constraint forces using a genetic algorithm.The applicability and limitations of the newly developed method are discussed by solving several rigid-body synthesis problems.