3D auxetic linkage based on Kirigami

The structural design of 3D auxetic linkages is a burgeoning field in digital manufacturing. This article presents a novel algorithm for designing 3D auxetic linkage structures based on Kirigami principles to address existing limitations. The 3D input model is initially mapped to a 2D space using conformal mapping based on the BFF method. This is followed by 2D re-meshing using an equilateral triangle mesh. Subsequently, a 3D topological mesh of the auxetic linkage is calculated through inverse mapping based on directed area. We then introduce new basic rotating and nonrotating units, employing them as the initial structure of the 3D auxetic linkage in accordance with Kirigami techniques. Lastly, a deformation energy function is defined to optimize the shape of the rotating units. The vertex coordinates of the non-rotating units are updated according to the optimized positions of the rotating units, thereby generating an optimal 3D auxetic linkage structure. Experimental results validate the effectiveness and accuracy of our algorithm. Quantitative analyses of structural porosity and optimization accuracy, as well as comparisons with related works, indicate that our algorithm yields structures with smaller shape errors.