This paper presents a novel model for fitting of spatial straight line based on Chebyshev norm. The problem is firstly formulated as a minimax problem, and then reformulated as a semidefinite programming (SDP) problem, which could be solved by many interior-point algorithms. The application of the proposed approach to two problems arising from manufacturing engineering, i.e. planning of the ... [Show full abstract] initial location of cylindrical cutter for flank milling and evaluation of the spatial straightness error, is discussed. Examples and numerical simulations illustrate the efficiency of the novel model.