Using geometric algebra to represent and interpolate tool poses

Abstract

In conventional computer-aided manufacturing techniques, a tool path is sent to the machine tool controller as a sequence of precision points. This means that errors are introduced when the controller interpolates between the points to recover the intended path. For 4- and 5-axis machining, a sequence of precision poses (positions and orientations) is needed. The use of geometric algebra in representing poses is discussed. The form of algebra used can represent rigid-body transforms exactly and can interpolate, in a natural way, between two or more poses using spherical linear interpolation. Sequences of poses from free-form surfaces are investigated. Tool motions are generated and compared with tool paths derived from purely positional information. It is found that the motion paths more naturally follow the original surface so that the interpolation errors are smaller.

Keywords:

• tool poses
• numerical control
• interpolation
• geometric algebra

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors gratefully acknowledge the support of the Engineering and Physical Sciences Research Council (EPSRC) in funding a project entitled ‘Algebraic modelling of 5-axis tool path motions’ [ref: EP/L006316/1].