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6。Conclusions

When designing packaging machinery, there is a clear need to simulate the action of the machine itself to check that it functions correctly。 There is also a need to simulate the motion of the carton itself during the various stages of the erection process。 This is to ensure that unwanted interference between faces of the carton net does not occur。 This is particularly the case when reconfigurable equipment is being used to check that the configuration is correct and to establish what motion control is required。

It has been seen that it is possible to obtain a simulation by handling the transforms applied to the carton faces。 Reducing the face graph to a spanning tree imposes a hierarchy on the faces and allows the required driving motions to be established。 The cuts effectively made in forming the tree correspond to dyads in which the angular positions of two adjoining faces need to be established。 This can be done by imposing constraints which say that the edges on either of each cut must come together。

Such constraints can be dealt with within a constraint mod- elling environment。 The necessary commands can be created au- tomatically from a data file which defines the net of the carton (in terms of nodes and faces) and identifies where the cuts (and dyads) are deemed to lie。 Since each dyad normally can have two solu- tions, care is needed to ensure that the correct one is found。 This can be done by imposing bounds on the allowable angles for the faces or by imposing suitable values with which to start the search for the solution。

These ideas have been demonstrated successfully on two typi- cal forms of cartons, namely a tray and a skillet with a gable-end。 In addition, the approach has been shown to work well with the more complicated folding pattern required for an origami bird。

Acknowledgements

The work reported in the paper was carried out within the Innovative Design and Manufacturing Research Centre at the University of Bath。 This is funded by the Engineering and Physical Sciences Research Council (EPSRC)。 Additionally, the work relates to a project on reconfigurable packaging systems sponsored by the Department of the Environment, Food and Rural Affairs (DEFRA)。 This support is gratefully acknowledged。摘要：纸箱包装是一种常见的包装方式，用来包装各种各样的物品。纸箱包装通常是由专门的机器来折叠，通过运用平面网格来折叠纸板使之成形。当有需要使用的新形状的纸箱时，专用机械可能就不适用而重构系统则可以使用。有需要来模拟纸板折叠直立过程,以确保这种行为达到预期的效果。这篇论文研究基于约束技术来进行这样一个仿真。必要的指令来自于纸箱网格的几何学。几何约束是确保网格保持完整并且解决呈现出来的面循环情况。论文网