中文摘要：

常规的板材切割是切割完一个零件后再去切割另一个零件,如果两个零件的边有公共部分,则利用共边切割方法只进行一次切割就可以完成,这不但能提高切割效率而且还能节省切割成本。然而目前有关共边切割方法的研究还不太深入,共边切割方法对于切割路径的优化效果还没有完全发挥出来。提出了基于图论的＂一笔画＂共边切割方法和针对阵列矩形的＂阶梯形＂共边切割方法,并给出了实例。实例结果表明,提出的共边切割方法比现有的方法在割嘴和空行程和打孔点数上都有了很大的优化。

英文摘要：

Generally the process of metal cutting is that another part can be done after one part has been cut.As for two parts that share common line,one cut is enough to finish the cutting with common line cutting method,which not only improves the cutting efficiency but also saves the cutting cost.However,the further research on common line cutting method is not carried out,which optimization effect of cutting path based on common line cutting method is far from the role play.In this case ＂one cut＂ common line cutting method based on graph theory and ＂ladder＂ common line cutting method specific to rectangular array parts is proposed in it and examples are given,which result show that the common line cutting method proposed by it is effective for optimizing the pierce points and vacant path of nozzle.