Delta DLP 3-D Printing of Large Models

Abstract

This paper presents a 3-D printing system that uses a low-cost off-the-shelf consumer projector to fabricate large models. Compared with traditional digital light processing (DLP) 3-D printers using a single vertical carriage, the platform of our DLP 3-D printer using delta mechanism can also move horizontally in the plane. We show that this system can print 3-D models much larger than traditional DLP 3-D printers. The major challenge to realize 3-D printing of large models in our system comes from how to cover a planar polygonal domain by a minimum number of rectangles with fixed size, which is NP-hard. We propose a simple yet efficient approximation algorithm to solve this problem. The key idea is to segment a polygonal domain using its medial axis and afterward merge small parts in the segmentation. Given an arbitrary polygon $\Omega $ with $n$ generators (i.e., line segments and reflex vertices in $\Omega $ ), we show that the time complexity of our algorithm is $O(n^{2}\log ^{2}~n)$ and the number of output rectangles covering $\Omega $ is $O(Kn)$ , where $K$ is an input-polygon-dependent constant. A physical prototype system is built and several large 3-D models with complex geometric structures have been printed as examples to demonstrate the effectiveness of our approach. Note to Practitioners —Low-cost 3-D printers and 3-D printing of large models are two important but often conflicting goals in manufacturing industry. Usually low-cost devices such as DLP 3-D printer using an off-the-shelf consumer projector cannot print large models, due to the small projection area of the projector. In this paper, we propose to horizontally move the platform such that a large area can be printed by the composition of multiple small projection areas. Based on this new mechanism, we propose a simple yet efficient algorithm to cover an arbitrary polygonal shape (possibly with holes or multiple disjoint polygons) by a small set of rectangles with fixed size. Our algorithm is theoretically sound and can be easily implemented. We built a physical prototype system of the proposed low-cost Delta DLP 3-D printer, which successfully prints several large models with satisfied mechanical properties.