The dual-rod slider rocker mechanism is equivalent to two traditional single-rod sliders that share a common rocker, where the sliders translate along two opposite directions. Unlike a single-rod system, the dual-rod mechanism is unique, in the sense that the two sliders do not translate the same distance for the same rocker rotation. In this paper, an optimal kinematic and dynamic analysis of the dual-rod slider rocker mechanism is presented. This analysis is supplemented by an application to modular robotic coupling, in which the mechanism is employed by a torque recirculation scheme to enable three independent modes of operation via a single motor. Simulation, finite element analysis, and experimental results validate the kinematic properties of this mechanism, the rigidity of the proposed docking interface, and its three modes of operation. We conclude that the compactness of the dual-rod mechanism, and its unique kinematic properties, exhibits a broad industrial value for applications where size and weight are a critical design constraint, such as space and mobile robotics.