Abstract Rapid prototyping technologies are capable of directly manufacturing physical objects from CAD models and have been increasingly used in product development, tool and die making and fabrication of functional parts. Solid ground curing (SGC) technology, one of the rapid prototyping technologies, is suitable of  building multiple parts with different geometry and dimensions in batch production of rapid prototypes to minimize the cost of prototypes. However, the layout of CAD models in a graphic environment is time-consuming. Because of high cost of the resin, the layout of models in a batch is critical for the success of the SGC operations in any industrial environment. This paper presents the layout optimization using simulated annealing techniques. A software system was developed to assist Cubital operators to layout CAD models with various geometric shapes. The system accepts STL files from any solid modeling environment. Several examples are provided to illustrate the techniques and effectiveness of the approach.6374
1. Introduction
Increasing global competition requires product oriented manufacturing firms to become more flexible and responsive to the ever-changing market. Substantial reduction of  product development time will improve firms’ response to market demands and therefore gain competitive advantages.
Rapid prototyping and manufacturing technologies have been improving manufacturers’ responsiveness in several aspects such as rapid creation of 3D models and prototypes; and cost-effective production of patterns and moulds with complex surfaces [1]. Rapid prototyping technologies are capable of directly generating physical objects from CAD models. A variety of rapid prototyping technologies have emerged including stereolithography,  selective laser sintering (SLS), fused deposition manufacturing, laminated object manufacturing, 3D printing and solid ground curing (SGC). They have a common feature: the prototype is produced by adding materials, rather than removing or deforming materials as in traditional manufacturing processes [2]. These technologies can fill the uncertainty void  between the conceptual design and an actual part. The technologies can also significantly improve the efficiency of pattern and mould making processes.
SGC processes can produce multiple parts with different geometries and dimensions in a single setup and therefore are suitable for batch production. In the building process of SGC (Fig. 1), a mask is generated by electrostatically charging a glass plate with a negative image of the cross-section of the part, which is similar to the process used in the laser printer. In the meantime, a thin layer of liquid photo-curable resin is spread across the surface of the work place. Then, the glass plate with the mask is placed between the lamp and the surface of the workspace. Instead of using a laser beam, an UV lamp is used to flood the chamber and expose and solidify the entire layer. After the residual liquid resin is wiped off by a vacuum cleaner, the model tray moves back under the UV lamp for a second exposure that solidifies the liquid resin that is not totally cleaned by the vacuum. The voids in this layer are filled with hot liquid wax, which acts as support for overhangs and isolated parts. After the wax is cooled down to solid by a cold metal plate, this resin/wax layer is milled with a fly cutter to a specified thickness. The new layer of resin is applied when the model tray moves from the milling station back to the exposure chamber. The SGC process can produce multiple parts at the same time by simply slicing a batch of CAD  models and charging the glass plate with a negative image of multiple cross-sections. Thus, Cubital machines can be used for production of multiple models in batches.
However, in the building process of SGC, the resin that does not contribute to the part and is wiped off cannot be reused because it has been partially cured during the initial exposure. If one needs to build a single part and there are no other parts to share the block, this part can be very expensive unless it occupies most of the model tray. Moreover, most of the other rapid prototyping machines have to weave the cross-sections of each part in a batch one by one. Although the lead time on these machines can be reduced by producing multiple parts, the production time does depend on the number of parts and the parts geometry. In the SGC process, the UV lamp exposes every layer with the same time span as predetermined by the operator. Thus the resin consumption and fabrication time per layer are constant, independent of the parts’ geometry and the number of the parts in the batch. Consequently, the time and the cost of producing a batch of parts simply depend on the number of layers produced in the fabrication. In order to maximize productivity and minimize cost, parts in every batch should be ‘packed’ as low as possible within the given area of the model tray so that the fabrication layers for the batch of parts can be minimized. Model layout optimization for solid ground curing rapid:http://www.751com.cn/yingyu/lunwen_3890.html