This invention provides a stacker for use in forming stacks of cut sheets received from an upstream utilization device (e.g. a printer, cutter, etc.) that allows for positive driving of sheets into a stack using a stacking unit that includes a series of grippers that are adapted to grip and release a leading edge of each sheet at the appropriate time. In this manner, each sheet is gripped as it arrives from the upstream operation and is passed downstream into the stack, being released so as to properly decelerate at the stack's backstop. The grippers are mounted on a continuous belt between a pair of opposing drive sprockets. An edge sensor located upstream of the stacking unit triggers motion of the belts. The grippers are actuated by a mechanical cam arrangement to selectively grip and release at predetermined positions as the belt is driven.