Using the topology optimization can be an effective means of synthesizing planar rigid-body linkage mechanisms to generate desired motion, as it does not require a baseline mechanism for a specific topology. While most earlier studies were mainly concerned with the formulation and implementation of topology optimization-based synthesis in a fixed grid, this study aims to realize the simultaneous shape and topology optimization of planar linkage mechanisms using a low-resolution spring-connected rigid block model. Here, we demonstrate the effectiveness of simultaneous optimization over a higher-resolution fixed-grid rigid block-based topology optimization process. When shape optimization to change the block shapes is combined with topology optimization to synthesize the mechanism, the use of low-resolution discretized models improves the computation efficiency considerably and helps to yield compact mechanisms with less complexity, making them more amenable to fabrication. After verifying the effectiveness of the simultaneous shape and topology optimization process with several benchmark problems, we apply the method to synthesize a mechanism which guides a planar version of a human's gait trajectory.