THE PRINCIPLES OF INTERPOLATION FOR HIGHER ORDER CURVES

So far in numerical-controlled machine tools the principal methods of interpolation arethe straight line method and the circular are method. But with the development of scienceand technology, the requirement for processing complicate-shaped parts arises in some indus-trial departments and production areas. Most of the parts, for example, are of higher orderor cubic curves as in the wings of an airplane, the hull of a ship and, the nonsphericalcurves.So far as we know the higher order curves are treated by dividing them into anumber of small segments and every one of which can be approximated by a straight line ora circular are. However there are some shortcomings in this treatment as stated below: theerror produced in the interpolation may be great, the prceision in processing low. and theprograming complicated; in addition, more programing fields may be required to deal withand the tape may be very long, so it is difficult to carry out.It has been proposed in thispaper that the profile in higher order curve can be interpolated more accurately so long assome simple data are given. The distinguishing characteristics of this method are simple inoperation and easy in speed control. The maximum interpolation error is estimated as lessthan 0.707 pulse equivalent.