PLANAR RATIONAL B-SPLINE MOTIONS

Nonuniform rational B-spline (NURBs) curves and their associated techniques are of major importance in computer aided geometric design. The paper discusses planar rational B-spline motions. These are planar motions in which all point paths are NURBs curves. Such motions are connected with a linear control structure, which can be used to apply algorithms developed for the design of curves and surfaces directly to the design of planar motions. The first part of the paper gives a brief introduction to plane kinematics and the theory of kinematic mappings. Rational motions and the application of the corresponding control structures are discussed in detail. The second part of the paper presents a C-2 interpolation scheme with rational motions of degree 4, which is the minimum degree for motions which have positions with vanishing angular velocity.