Multilayer structures containing 24 Å thick DyBa2Cu3O7 layers, separated by 96 Å of an (Y0.6Pr0.4)Ba2Cu3O7 alloy, are studied to investigate the effect of coupling on vortex dynamics. With the magnetic field perpendicular to theab plane, and as a function of the number of superconducting layers in the structure, we find that the activation energy for flux motion increases, first linearly, and then saturates. This linear increase is taken as evidence that pancake vortices belonging to different DyBa2Cu3O7 layers are stacked and have a coupled motion. Above a characteristic number of superconducting layers,N c , shear of the vortex structures becomes important and the thermally activated process only displaces a stack ofN c pancake vortices, meaning that the vortex lattice is turning three dimensional. In these structures we findN c to be 2 to 3.