“…During the second half of the 20th century, the productive results to find general methods for determination of the mobility of any mechanisms had been obtained by Moroshkin [15], Voinea and Atanasiu [16], Paul [17], Rö ssner [18], Boden [19], Ozol [20], Waldron [21], Manolescu [22], Bagci [23], Antonescu [24], Freudenstein and Alizade [25], Hunt [26], Herve [27], Gronowicz [28], Davies [29], Agrawal and Rao [30], Dudita and Diaconescu [31], Angeles and Gosselin [32], Alizade [33], McCarthy [34]. In the calculation of mechanism mobility, the following new parameters were used (Table 1), as the rank of linear independent loop equations or the order of the equivalent screw system of the closed loop (r), relative displacements of the joint (m), number of independent, scalar, differential loop-closure equations (k K ), the rank of the coefficient matrix (r(j)), finite dimensional vector space (d(v)), new formula of the number of independent loops (L = j B À B À c b , where j B is the total number of joints on the platforms, and c B is the total number of branches between moving platforms and B is the number of moving platforms), serial open chains connecting to ground or total number of robot legs (c l ), and the degree of constraint of the platform (U).…”