Five-axis milling machine normally has three translational and two rotary degrees of freedom. These configurations allow to program any arbitrary tool axis orientation. Usually both rotary axes are perpendicular to each other and their orientation equals the direction of the linear axes. The primary rotary axes have a constant orientation, while the orientation of a secondary axis changes due to a rotation around the primary axis.
One rotary axis has a fixed inclination with respect to the tool axis. The second rotary axis has a fixed orientation with respect to the clamping table. To simplify the formulae in this section the rotary axis which orientation remains fixed with respect to the tool axis will be defined as the principal rotary axis.
If the conventional kinematics of a five axis milling machine is considered, the conclusion follows that each orientation of the tool-axis (i,j,k) can be achieved at two different positions of the rotary axes. However a limited range of the rotary axes often eliminates one of these solutions. If the principal B-axis is zero ( i=0, j=0, k=1) then any value for the second axis is satisfactory. This is called a degenerated position : the C-axis is parallel to the tool axis and therefore has no influence on the orientation of the tool axis with respect to the clamping plane. If the tool axis is moved from the first solution space (B > 0) into the other solution space (B < 0) then the tool axis goes through the degenerated position (B = 0 and i=0, j= 0, k=1).
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