Exact Taylor series coefficients for variable-feedrate CNC curve interpolators
作者： Rida T. Farouki , Yi-Feng Tsai
DOI: 10.1016/S0010-4485(00)00085-3
关键词: Mathematics 、 Quadratic equation 、 Parametric equation 、 Applied mathematics 、 Curve fitting 、 Curvature 、 Arc length 、 Taylor series 、 Variable (mathematics) 、 Algorithm 、 Truncation error (numerical integration)
摘要: Abstract Recent papers [Yang DCH, Kong T. Computer Aided Design 1994;26:225–34; Yeh S-S, Hsu P-L. 1999;31:349–57] formulate real-time CNC interpolators for variable feedrates along parametric curves. These employ truncated Taylor series to compute successive reference-point parameter values, but in both an erroneous coefficient the highest (quadratic) term is cited. The derivation of proper coefficients a straightforward, although somewhat convoluted, exercise chain-rule differentiation. Compact recursive formulae are presented here correct coefficients, up cubic term, cases where feedrate depends on: (i) elapsed time; (ii) curve arc length; or (iii) local path curvature. and cumulative effects truncation errors on accuracy such interpolator schemes also assessed, compared with essentially exact Pythagorean-hodograph
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