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In optimal design problems we have to determine a set of design parameters such that a given mechanism satisfies a list of requirements. In practice however these requirements may be classified as either compulsory or relaxable. For classical optimal design methodologies, it is very difficult to find the solutions that satisfy compulsory requirements simultaneously and make the best compromise between these two kinds of requirements. So in this paper we propose and illustrate on an example of parallel robots an approach based on interval analysis that allows to determine almost all possible mechanism geometries such that all compulsory requirements will be satisfied simultaneously. As using interval analysis all possible solutions will be obtained as a set of regions in the parameter spaces, the best design compromise for the relaxable requirements will be determined by sampling the solution regions.