This paper presents systematically a new method for the displacement analysis (DA) of multi-loop spatial linkages (MLSLs) based on ordered simple-opened-chains (SOCs). In performing DA, a MLSL is converted into not a set of base points, a set of isolated links or a tree with/without isolated links in common use, but a weakly coupled MLSL in this paper. The characteristics of the proposed method are: (a) The number of unknowns in the set of equations for displacement analysis (EDA) of a MLSL is reduced to the minimum; (b) All the possible configurations corresponding to a given set of inputs of a weakly coupled MLSL or a strongly coupled MLSL with the coupled degree k = 1 can be obtained quickly. As compared with the other two methods available to find all the solutions to the DA in the case of MLSL with k = 1, the proposed method is superior to the resultant method in that it is applicable to more complex MLSLs and superior to the continuation method in that it takes much less CPU time to find all the solutions; (c) The set of EDA can be formulated and solved automatically; and (d) The new approach makes it possible to perform the kinematic and kineto-static analyses in a unified and simplified way.

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