Polynomial and spline interpolation of machine tool orientations

Abstract

In a method and apparatus for guiding the motion of a moveable machine element, the orientation of the machine element is defined by an orientation vector that can be programmed in each set. The orientation vector can be obtained by a linear great circle interpolation in a plane spanned by a start vector and an end vector. In more general cases, polynomials can be used in the program, enabling an almost arbitrary definition of the path that determines how the end vector is obtained. The interpolated orientation vector can also be rotated out of the plane by an arbitrary angle. An extended interpolation permits a representation of orientation changes on a conical surface having an arbitrary orientation in space. This enables the orientation axes to move across several sets with continuous velocity and acceleration.

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