The theory ofrobotsor reproducing power‐amplifying systems is considered. After a general terminological orientation the study in the first part is confined tosimple robots, the theory of which is equivalent to that of non‐linear springs with inertia and friction. The alacrity and fidelity of control are well exhibited by studying the behavior of a robot under constant tracking. Special emphasis is placed on the specification of conditions foroptimum performance, i.e., minimum deviation or maximum fidelity after any given time. Curves are given for both proportional and on‐off robots, from which the parameter values for optimum performance may be read.In Part II the theory of proportional robots is analyzed in detail, especially from the point of view of conditions for optimum performance. Two subsequent papers will contain the theory for the on‐off case and the general non‐linear robot case. The paper is organized as follows:Part I. Descriptive accountA. Terminology and kinematic descriptionB. Dynamical equation of robots with usual loadC. Optimum performance curves. Practical examplesPart II. Theory of simple robots with proportional controlA. Complete solutions as functions of time. Optimum performance curvesB. Path curves in the position‐velocity plane