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A novel coupled mechanism was synthesized based on the particular geometrical construction and high symmetry of the regular tetrahedron. Firstly, two simple types of substitutive element component were designed and implanted in the location of all vertexes and edges contained in the regular solid respectively. An equivalent geometrical basic model was obtained with combination of the element parts connected by revolution joints according to frame of regular tetrahedron. The relative studies of the basic geometrical model with four congruent sub-structures were converted into a 6-bar closed-loop linkage. Secondly, the mobility of geometrical basic model was determined on the basis of independent motion shunting measurement method. The approach of adding chains was adopted to allocate the constraint sets and rearrange the components spatially when the closed-loop linkage was rigid on the basis of the screw theory. The element unit loop structure was abstracted by the means of modifying the constraint set of the 6-bar closed-loop linkage with the corresponding added chains symmetrically. Finally, the novel quasi-regular tetrahedron coupled mechanism was established with regroup of the identical elementary units according to the same way of combining the equivalent geometrical model. To define the motion of the new mechanism, a three-dimensional model was developed based on the SolidWorks for simulation analysis and the displacement variation of the output part and the other two symmetrical node components was provided by Matlab. The results showed that the new-designed coupled mechanism had two translational degrees of freedom which belonged to a plane perpendicular to the base and the three node components located in the vertexes had the same radial motion trend directed to the geometrical centre of the new structure. The mobility and the centripetal characteristic of the mechanism were verified correctively. This new structure can be applied to the executing structure of the deployable mobile robot.