Abstract
Coherent lines are generally more complex spatial curves, and the study of coherent lines is the basis for studying cutting trajectories of spatial coherent cutting machines. In this paper, the spatial geometry problem is transformed into an algebraic problem solving by establishing a mathematical model of spatial coherent line to find its parametric equations. Interpolation refers to the process of data densification. In this paper, a speed planning method that adapts to the curvature change of the Non-Uniform Rational B-Splines ( NURBS ) curve is proposed. After inputting the starting points and endpoints to the Computer Numerical Control (CNC), the computer will calculate the coordinate data of each step according to the characteristics of the line segment, carry out the speed planning and then complete the curve trajectory interpolation. The accuracy of the algorithm is verified by comparing the theoretical coherent trajectory and interpolated trajectory.
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