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A configuration p in r-dimensional Euclidean space is a finite collection ofpoints (p^1,...,p^n) that affinely span R^r. A bar framework, denoted by G(p),in R^r is a simple graph G on n vertices together with a configuration p inR^r. A given bar framework G(p) is said to be universally rigid if there doesnot exist another configuration q in any Euclidean space, not obtained from pby a rigid motion, such that ||q^i-q^j||=||p^i-p^j|| for each edge (i,j) of G.It is known that if configuration p is generic and bar framework G(p) in R^radmits a positive semidefinite stress matrix S of rank n-r-1, then G(p) isuniversally rigid. Connelly asked whether the same result holds true if thegenericity assumption of p is replaced by the weather assumption of generalposition. We answer this question in the affirmative in this paper.

On affine motions and bar frameworks in general position