This study is to develop a practical control scheme called three-step input method whereby a flexible robot arm is moved from one position to another in the least amount of time with a minimum of residual vibration when the arm reaches its defined end point. The basic premise is to use open loop self-adjusting input signals that take system dynamic characteristics into account;In particular, the class of problem addressed in this thesis is restricted to the elimination of residual vibration when the fastest response is done in time steps of one half of the robot's fundamental natural period;Unfortunately, real structural systems have small amounts of damping. The flexible manipulator in this study is modeled as two lumped masses connected by a spring with a damper. A self-adjusting command input function used in the three-step input method consists of three step inputs, each with different step sizes and switching times that work in concert with the system's dynamic response;This research work is concerned with defining a simple practical method to utilize step inputs to achieve optimum response. The optimum response is achieved by using a self-adjusting command input function that is obtained during a real time processing;The practicality of this control scheme is demonstrated experimentally by using an analog computer to simulate a simple flexible robot and a conventional servo controller in two ways. First, the experiments focus on point-to-point movement. Second, a multiple level procedure is used to achieve large movements. The three-step procedure is also shown to require a small amount of digital computing resources.