  We describe the family of minimal graphs on strips with boundary values
$\pm\infty$ disposed alternately on edges of length one, and whose conjugate
graphs are contained in horizontal slabs of width one in $\mathbb{R}^3$. We can
obtain as limits of such graphs the helicoid, all the doubly periodic Scherk
minimal surfaces and the singly periodic Scherk minimal surface of angle
$\pi/2$.
