A mobile cart for a three-dimensional object printing system includes a mechanism that enables vertical movement of the platen with reference to ejector heads in the system. The mobile cart includes a pair of links at each end of a cart that pivotally connect a member positioned between the cart and the platen to the cart and the platen. An actuator is configured to laterally move the member bi-directionally and along an axis that is orthogonal to the member. This movement of the member pivots the links to raise and lower the platen depending on the direction in which the member is urged by the actuator.