Computing a flattest, undercut-free parting line for a convex polyhedron, with application to mold design

AbstractA parting line for a polyhedron is a closed curve on its surface, which identifies the two halves of the polyhedron for which mold-boxes must be made. A parting line is undercut-free if the two halves that it generates do not contain facets that obstruct the de-molding of the polyhedron. Computing an undercut-free parting line that is as “flat” as possible is an important problem in mold design. In this paper, algorithms are presented to compute such a parting line for a convex polyhedron, based on different flatness criteria

Algorithms for generating multi-stage molding plans for articulated assemblies

Plastic products such as toys with articulated arms, legs, and heads are traditionally produced by first molding individual components separately, and then assembling them together. A recent alternative, referred to as in-mold assembly process, performs molding and assembly steps concurrently inside the mold itself. The most common technique of performing in-mold assembly is through multi-stage molding, in which the various components of an assembly are injected in a sequence of molding stages to produce the final assembly. Multi-stage molding produces better-quality articulated products at a lower cost. It however, gives rise to new mold design challenges that are absent from traditional molding. We need to develop a molding plan that determines the mold design parameters and sequence of molding stages. There are currently no software tools available to generate molding plans. It is difficult to perform the planning manually because it involves evaluating large number of combinations and solving complex geometric reasoning problems. This dissertation investigates the problem of generating multi-stage molding plans for articulated assemblies. The multi-stage molding process is studied and the underlying governing principles and constraints are identified. A hybrid planning framework that combines elements from generative and variant techniques is developed. A molding plan representation is developed to build a library of feasible molding plans for basic joints. These molding plans for individual joints are reused to generate plans for new assemblies. As part of this overall planning framework, we need to solve the following geometric subproblems -- finding assembly configuration that is both feasible and optimal, finding mold-piece regions, and constructing an optimal shutoff surface. Algorithms to solve these subproblems are developed and characterized. This dissertation makes the following contributions. The representation for molding plans provides a common platform for sharing feasible and efficient molding plans for joints. It investigates the multi-stage mold design problem from the planning perspective. The new hybrid planning framework and geometric reasoning algorithms will increase the level of automation and reduce chances of design mistakes. This will in turn reduce the cost and lead-time associated with the deployment of multi-stage molding process

MULTIPLE PARTING SURFACES FOR SAND CASTING

ABSTRACT Multiple parting surfaces are frequently used in sand casting, die casting and injection molding processes. However, most research in this area has focused on die casting and injection molding. Parting surfaces for die casting and injection molding are relatively easier to compute compared to sand casting because their orientations and shapes are less restricted. In sand casting, the parting surfaces have to be parallel to each other and perfectly flat to permit the use of flasks with more than two pieces. The concepts of visibility and object illumination can be used to divide an object into two parts using a single parting surface. These methods, however, cannot be directly used for multiple parting surfaces. In this paper, a methodology to generate multiple parting surfaces for sand casting is described. The method uses Gauss maps to identify potential casting directions, and global accessibility cones to determine which faces can be cast in the same part of the pattern. The pattern is sliced using parallel planes such that each slice can be withdrawn from the mold in at least one direction. After the object is sliced, the number of parting surfaces is reduced by combining adjacent middle sections depending on their accessible directions

Geometric aspects of the casting process

Manufacturing is the process of converting raw materials into useful products. Among the most important manufacturing processes, casting is a commonly used manufacturing process for plastic and metal objects. The industrial casting process consists of two stages. First, liquid is filled into a cavity formed by two cast parts. After the liquid has hardened, one cast part retracts, carrying the object with it. Afterwards, the object is ejected from the retracted cast part. In both retraction and ejection steps, the cast parts and the object should not be damaged, so that the quality of final object is guaranteed and the cast parts can be reused to produce another object. This mode of production is called ``mass production''. Due to the geometric nature of the casting process, many geometric problems arise in the automation of casting. The problems we address here concern this aspect: Given a 3-dimensional object, is there a cast for it whose parts can be removed after the liquid has solidified? An object for which this is the case is called castable. We consider the castability problem in three different casting models with a two-part cast. In the first casting model, two parts must be removed in opposite directions. There are two cases depending on whether the removal direction is specified in advance or not. The second model is identical to the first casting model, except that the cast machinery has a certain level of uncertainty in its directional movement. In the third model, the two cast parts are to be removed in two given directions and these directions need not be opposite. For all three casting models, we give complete characterizations of castability, and obtain algorithms to verify these conditions for polyhedral parts. In manufacturing, features of an object imply manufacturing information, which facilitates the process of analyzing manufacturability and the automated design of a cast for the object. A small hole or a depression on the boundary of an object, for example, restricts the set of removal directions for which this object is castable, since the portion of the cast in the hole or in the depression must be removed from the object without breaking the object. We define a geometric feature, the cavity, which is related to the castability of objects, and provide algorithms to extract it from objects

Computing a Flattest, Undercut-Free Parting Line for a Convex Polyhedron, With Application to Mold Design

A parting line for a polyhedron is a closed curve on its surface, which identifies the two halves of the polyhedron for which mold-boxes must be made. A parting line is undercut-free if the two halves that it generates do not contain facets that obstruct the de-molding of the polyhedron. Computing an undercut-free parting line that is as "flat" as possible is an important problem in mold design. In this paper, algorithms are presented to compute such a parting line for a convex polyhedron, based on different flatness criteria. Keywords: Casting/molding, computational geometry, optimization. Additional keywords: Arrangements, shortest paths, visibility, point-set width. 1 Introduction We consider a geometric problem arising in the design of molds for casting and injection molding. Consider the construction of a sand mold for casting a polyhedral solid. First a prototype, P, of the polyhedron is made. Two halves of P are then identified and a separate mold-box is made for each. This i..