For conventional robots, manipulator motions result in forces and moments on the base to cause undesirable base excitations. The objective of this paper is to systematically analyze the fundamentals of reactionless robots. Based on this analysis, design of two distinct classes of planar robots is proposed. Due to the underlying principle of conservation of angular momentum for these robots, the trajectory planning must satisfy additional constraints, illustrated through computer simulations. Currently, we are fabricating reactionless robots to illustrate the underlying concepts.