Spatial rational motions based on rational frenet-serret curves

Abstract

The aim of This work 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 spatial rational motion design. 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. Furthermore we provide an analysis on spatial frames (frenet-serret frame and rotation minimizing frame). Also we derive and algorithm for computation of rotation minimizing frames on RF curves.