Maximal primitive hindering systems for convex figures

In (Dokl. Math. 64 (2001) 385) we formulated shortly the results which contain a complete classification of compact, convex planar figures with respect to the maximal cardinality of their fixing systems and also a complete classification of compact, convex figures with respect to the maximal cardinality of their hindering systems. For fixing systems the results were proved in details in (Discrete Geometry Marcel, Dekker, New York-Basel, 2003, 85). Here we give detailed proofs for hindering systems. The obtained theorems generalize and make more precise the results obtained by Mani (Acta Math. Sci. Hungar. 22 (1971/72) 269). Some examples illustrate the text.