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Smooth continuous spiral tool paths are preferable for computer numerical control (CNC) machining due to their good kinematic and dynamic characteristics. This paper presents a new method to generate spiral tool paths for the direct three-axis CNC machining of the measured cloud of point. In the proposed method, inspired by the Archimedean spiral passing through the radial lines in a circle, 3D radial curves on the cloud of point are introduced, and how to construct the radial curves on the complex cloud of point is discussed in detail and then a practical and effective radial curve construction method of integrating boundary extraction, region triangulation, mesh mapping, and point projection is proposed. On the basis of the radial curves, the spiral tool path can be generated nicely by interpolating the radial curves using a spiral curve. Besides, the method of identifying and eliminating the overcuts and undercuts in the spiral tool path resulting from the interpolation error is also presented for good surface quality. Finally, several examples are given to validate the proposed method and to show its potential in practical applications when quality parametric models and mesh models are not available.

Kagome honeycomb structure is proved to incorporate excellent mechanical and actuation performances due to its special configuration. However, until now, the mechanical properties of 3D printed Kagome honeycomb have not been investigated. Hence, the objective of this work is to explore some mechanical properties of 3D-printed Kagome honeycomb structures such as elastic properties, buckling, and so on. In this paper, the analytical formulas of some mechanical properties of Kagome honeycombs made of 3D-printed materials are given. Effective elastic moduli such as Young's modulus, shear modulus, and Poisson's ratio of orthotropic Kagome honeycombs under in-plane compression and shear are derived in analytical forms. By these formulas, we investigate the relationship of the elastic moduli, the relative density, and the shape anisotropy–ratio of 3D-printed Kagome honeycomb. By the uniaxial tensile testing, the effective Young's moduli of 3D printed materials in the lateral and longitudinal directions are obtained. Then, by the analytical formulas and the experimental results, we can predict the maximum Young's moduli and the maximum shear modulus of 3D-printed Kagome honeycombs. The isotropic behavior of 3D-printed Kagome honeycombs is investigated. We also derived the equations of the initial yield strength surfaces and the buckling surfaces. We found that the sizes of the buckling surfaces of 3D printed material are smaller than that of isotropic material. The efficiency of the presented analytical formulas is verified through the tensile testing of 3D printed Kagome honeycomb specimens.