A method for assembling windshield assemblies for vehicles includes a conveyor for delivering at least two plys of glass to an assembly station, a first robot for lifting one of the two plys from the conveyor, a second robot for gripping and removing at least one adhesive sheet from a stack of adhesive sheets and placing the removed adhesive sheet adjacent the other one of the two plys, whereby the first robot places the one of the two plys adjacent the removed adhesive sheet to assemble the windshield assembly. The step of removing a top adhesive sheet from the stack of adhesive sheets includes moving a knife along an edge of the top adhesive sheet to separate the edge of the top sheet from the next lower sheet in the stack. Alternatively, a blade is moved along a longitudinal length of the top sheet to separate it from the next lower sheet in the stack.