The problem addressed in this paper is to discover the frequently occurred sequential patterns from databases. Basically, the existing studies on finding sequential patterns can be roughly classified into two main categories. In the first category, the discovered patterns are continuous patterns, where all the elements in the pattern appear in consecutive positions in transactions. The second category is to mine discontinuous patterns, where the adjacent elements in the pattern need not appear consecutively in transactions. Although there are many researches on finding either kind of patterns, no previous researches can find both of them. Neither can they find the discontinuous patterns formed of several continuous sub-patterns. Therefore, we define a new kind of patterns, called hybrid pattern, which is the combination of continuous patterns and discontinuous patterns. In this paper, two algorithms are developed to mine hybrid patterns, where the first algorithm is easy but slow while the second complicated but much faster than the first one. Finally, the simulation result shows that our second algorithm is as fast as the currently best algorithm for mining sequential patterns. r

Abstract. Variable pressure angle (VPA) hob is an important cutting tool for generating the twist-free tooth flanks on a crowned involute helical gear used in the high precision gear boxes. However, an appropriate method for generating the VPA hob surface has not proposed yet. Therefore, this paper presents a worm grinding method for generating the helical surface of VPA hob on a CNC worm grinding machine. A mathematical model of the proposed method is established based on a standard hob by controlling rotational motion of the hob axis in the worm grinding process. A numerical example is implemented to verify the merits of the proposed method.