In a number of industrial, space, or mobile applications, reaction forces and moments transmitted by a manipulator to its base are undesirable. In this paper, we analyze the problem of force and torque transmission in robotic systems, and propose design and planning methods that can eliminate it, or reduce it. Based on force and moment transmission analysis, a three DOF redundant manipulator design is selected. Dynamic reaction forces are eliminated by force balancing. Reaction moments are eliminated by following reactionless paths, whose planning is simplified by rendering the dynamics configuration-invariant. Reactionless Workspaces are defined in which any end-effector path can result in zero dynamic reactions. An example is used to demonstrate the usefulness of the proposed methods. An important advantage of these methods is that the manipulator can be used either as a redundant, or as a reduced DOF reactionless system.