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In this paper, the design of reactionless 3-degree-of-freedom (DOF) and 6-DOF parallel manipulators is presented. At first, the design and dynamic balancing of a novel 3-DOF parallel mechanism referred to as the parallelepiped mechanism are addressed. Two types of actuation schemes of the mechanism are considered, and the two corresponding mechanical structures are designed. The balancing equations are derived by imposing that the center of mass of the mechanism is fixed and that the total angular momentum is constant with respect to a fixed point. Optimization is performed to determine the counterweights and counter-rotations based on the balancing conditions. Numerical examples of reactionless 3-DOF parallelepiped mechanisms are given. The dynamic simulation software ADAMS is used to simulate the motion of the mechanisms and to verify that the mechanisms are reactionless at all times and for arbitrary trajectories. Finally, the 3-DOF parallelepiped mechanisms are used as legs to synthesize reactionless 6-DOF parallel manipulators.