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In our previous paper, we presented the combinatorial theory for minimal isostatic pinned frameworks–Assur graphs–which arise in the analysis of mechanical linkages. In this paper we further explore the geometric properties of Assur graphs, with a focus on singular realizations which have static self-stresses. We provide a new geometric characterization of Assur graphs, based on special singular realizations. These singular positions are then related to dead-end positions in which an associated mechanism with an inserted driver will stop or jam. [Copyright &y& Elsevier]

Abstract: Consider a polar space weakly embedded in a projective space . A secant of is the intersection of the point set of with a line of spanned by two non-collinear points of . The geometry consisting of the points of and as lines the secants is a so-called Delta space. In this paper we give a characterization of this and some related geometries. [Copyright &y& Elsevier]

Abstract: In [B. De Bruyn, P. Vandecasteele, Near polygons with a nice chain of sub near polygons, J. Combin. Theory Ser. A 108 (2004) 297–311], we determined all dense near -gons of order with a nice chain of subpolygons, i.e. a chain of convex subpolygons satisfying (i) , , is a near -gon, and (ii) , , is big in . In the present paper, we describe a method which can be used for classifying general dense near polygons with such a chain. We will use this method to determine all dense near polygons with a nice chain of subpolygons if every hex is either classical or glued. We will apply the latter result to determine all dense near octagons of order with a nice chain of subpolygons. [Copyright &y& Elsevier]