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Some aspects of a mathematical theory of rigidity and flexibility are developed for general infinite frameworks and two main results are obtained. In the first sufficient conditions, of a uniform local nature, are obtained for the existence of a proper flex of an infinite framework. In the second it is shown how continuous paths in the plane may be(More)
Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear(More)
A theorem of Laman gives a combinatorial character-isation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in R 2. A more general theory is developed for frameworks in R 3 whose vertices are constrained to move on a two-dimensional smooth submanifold M. Furthermore, when M is a union of concentric spheres, or a union(More)
The graphs G = (V, E) with |E| = 2|V | − that satisfy |E | ≤ 2|V | − for any subgraph G = (V , E) (and for = 1, 2, 3) are the (2,)-tight graphs. The Henneberg–Laman theorem characterizes (2, 3)-tight graphs inductively in terms of two simple moves, known as the Henneberg moves. Recently, this has been extended, via the addition of a graph extension move, to(More)
BACKGROUND AND OBJECTIVES An association exists between student participation in a family medicine clerkship and student selection of family practice as a career. The effect of student exposure to other generalist specialties on career choice is unknown. This study determined if the specialty of an assigned generalist preceptor during a third-year(More)