The aim of this paper is to demonstrate that the techniques of Computer Aided Geometric Design such as spatial rational curves and surfaces could be applied to Kinematics, Computer Animation and Robotics. For this purpose we represent a method which utilizes a special class of rational curves called Rational Frenet–Serret (RF) curves for robot trajectory planning. RF curves distinguished by the property that the motion of their Frenet–Serret frame is rational. We describe an algorithm for interpolation of positions by a rational Frenet–Serret motion. Further more we present an algorithm for tracking the constructed RF motion to achieve the desired velocity distribution profile of robot arm.