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The passive modular groups mentioned in the classical theory of mechanisms are the basis modules in the construction of planar mechanisms with one degree of mobility corresponding to their linkages with four degrees of freedom. Even if thirteen solutions are presented [3,4,5,6] only some of them are found in practice and apparently there are groups never met in the mechanisms structure.The effectors extremity of bi mobile mechanisms describes any curve in an adequate domain. When the bi mobile mechanisms become main mechanical structures for robot arms and legs for mobile platforms two new notions are put into evidence -the inverse and the direct modelling. The inverse structure modelling of bi mobile mechanisms is based on the passive modular groups. By using the numerical operators such new structures with zero degree of mobility obtained from Baranov trusses may be obtained. In the paper there are also presented such new groups and their applying for the design of optimal bi mobile mechanisms. The paper is the result of intensive research to obtain new solutions applied and designed for various branches of robotics. The bi mobile systems thus obtained are patentable.

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