A spatial–structural design process can be investigated via a so-called research engine, in which a spatial design is transformed into a structural design and vice versa. During the transformation from a spatial into a structural design, it is necessary to obtain a stable structural model, so that a structural analysis can be carried out. This article presents four methods to automate the (normally carried out intuitively) stabilisation process, using data related to a structural design’s geometry and its instability modes. The methods all use the null space and associated null vectors of the structural stiffness matrix. Then each null vector is resolved by either (a) rod addition, (b) plane addition, (c) hinge fixation by single rod substitution, or (d) hinge fixation by coupled rod substitution. The methods have been implemented in C++ and several test cases have been carried out. The test cases explain why (a) rod addition provides the most realistic solutions, (b) if several methods are used subsequently for one problem, superfluous elements are inevitable, (c) there is a serious influence on the performance for various systems of key point numbering, (d) the efficiency of the methods is not optimal and may be improved by some suggested strategies.