retraction space of each undercut facet [29]. The retraction space represents a set of candidate translation vectors that can be used by side action to completely disengage from the undercut facet. A discrete set of feasible and non dominant restrictions is generated. The shape of the side actions is generated after the identification of undercut regions. In Fu’s recent research, by employing the  proposed  notions  of  the  demoldability map of surfaces and undercut features of the molding [30], the most preferred demolding direction and the grouping of undercut features are conducted. The side core is then designed.

Although the inner undercut is defined as an imperfect surface region in a molding as it is difficult to be manufactured, some inner undercuts are needed for certain functions or assembly requirements. However, the existing methods for undercut recognition mostly deal with outer undercuts, which are molded by side cores or side-cavities. In this paper, research on the design of internal pins is conducted. The complete invisible surfaces and their adjacent surfaces are recognized, and the undercut types are classified. The inner undercuts are then identified and the internal pins for molding of the inner undercuts are generated by extracting the appropriate geometrical entities of the undercuts. Finally, the moldability assessment is given according to the three criteria for detection of deep inner undercuts. The feasible internal pins are identified or redesign is recommended.

2. Methodology

In this research, the potential undercuts are first recognized. The potential undercuts will be the real ones if they cannot be molded by the main core or cavity. To represent the technology developed in this research, the following definitions and lemmas are firstly articulated.

2.1. Definitions

Main core, main cavity and side core

Generally, a two-piece mold consists of a set of plates which are pided into two halves. The stationary half is called the cavity, while the movable half is called the core. The pair of directions along the opening path of the main core and main cavity are called the parting direction and anti-parting direction, as shown in Fig. 1. In an injection molding, the surface regions which prevent the typical two-piece molds from opening by their local molding tools after the plastic solidified are called undercuts. The local tools are the so-called side-core and internal pin. The side core needs to withdraw outwards, while the internal pin needs to release inwards to facilitate the opening of main core and cavity. Fig.    1

illustrates these definitions.

Type n surfaces and edges (n = I,II,III)

The undercuts are classified into two types, outer undercut and inner undercut. The outer undercuts are the geometrical features molded by side cores, while the inner undercuts are those molded by internal pins. In this research, the surfaces of molding are classified into three types, as shown in Fig. 2.

Fig. 2 shows the surface classification for the given parting directions Pd and −Pd. Type I surfaces are the convex surfaces of the molding, extending which would form the convex hull of   the

molding. It can be seen from Fig. 2(b) that they have the largest boundary loop along the parting direction. Type II surfaces are the surfaces forming the concave features in the molding along the parting direction. Type III surfaces are the surfaces which form the undercuts. They are the surfaces whose edges could be completely

invisible along Pd  or −Pd, as shown in Fig. 2(d). The edges in the

outside loop of the Type n surfaces are designated as Type n edges (n = I, II, III).

  The main mold components.

(a)