  We provide a constructive characterisation of circuits in the simple
(2,2)-sparsity matroid. A circuit is a simple graph G=(V,E) with |E|=2|V|-1 and
the number of edges induced by any $X \subsetneq V$ is at most 2|X|-2.
Insisting on simplicity results in the Henneberg operation being enough only
when the graph is sufficiently connected. Thus we introduce 3 different join
operations to complete the characterisation. Extensions are discussed to when
the sparsity matroid is connected and this is applied to the theory of
frameworks on surfaces to provide a conjectured characterisation of when
frameworks on an infinite circular cylinder are generically globally rigid.
