Institute for Systems Research

1. We give a general definition of the problem as the task of covering a target region without interfering with anobstruction region. This definition encompasses the task of milling a general 2-D profile that includes bothopen and closed edges.

2. We discuss three alternative definitions of what it means for a cutter to be feasible, and explain which of thesedefinitions is most appropriate for the above problem.

3. We present a geometric algorithm for finding the maximal cutter for 2-D milling operations, and we show thatour algorithm is correct.

Our methodology has the following three benefits over the state-of-the-art. First, by using multi-piece molds we can create complex 3D objects that are impossible to create using traditional two piece molds. Second, we make use of sacrificial molds. Therefore, using multi-piece sacrificial molds, we can create parts that pose disassembly problems for permanent molds. Third, mold design steps are significantly automated in our methodology. Therefore, we can create the functional part from the CAD model of the part in a matter of hours and so our approach can be used in small batch manufacturing environments.

The basic idea behind our mold design algorithm is as follows. We first form the desired gross mold shape based on the feature-based description of the part geometry. If the desired gross mold shape is not manufacturable as a single piece, we decompose the gross mold shape into simpler shapes to make sure that each component is manufacturable using CNC machining. During the decomposition step, we account for tool accessibility to make sure that (1) each component is manufacturable, and (2) components can be assembled together to form the gross mold shape. Finally, we add assembly features to mold component shapes to facilitate easy assembly of mold components and eliminate unnecessary degree of freedoms from the final mold assembly.

The main contribution is that, for all the real and synthetic point- sets we tried, the average number of neighbors for a given point of the point-set follows a power law, with D2 as the exponent. This immediately solves the selectivity estimation for spatial joins, as well as for ﲢiased range queries (i.e., queries whose centers prefer areas of high point density).

We present the formulas to estimate the selectivity for the biased queries, including an integration constant (K hape' ) for each query shape. Finally, we show results on real and synthetic points sets, where our formulas achieve very low relative errors (typically about 10%, versus 40% - 100% of the uniform assumption).

Even after one has decided upon al abstract set of features to use for representing manufacturing operations, the set of feature instances used to represent a complex part is by no means unique. For a complex part, many (sometimes infinitely many) different manufacturing operations can potentially be used to manufacture various portions of the part - - and thus many different feature instances can be used to represent these portions of the part. Some of these feature instances will appear in useful manufacturing plans, and others will not. If the latter feature instances can be discarded at the outset, this will reduce the number of alternative manufacturing plans to be examined in order to find a useful one. Thus, what is required is a systematic means of specifying which feature instances are of interest.

This paper addresses the issue of alternatives by introducing the notion of primary feature instances, which we contend are sufficient to generate all manufacturing plans of interest. To substantiate our argument, we describe how various instances in the primary feature set can be used to produce the desired plans. Furthermore, we discuss how this formulation overcomes computational difficulties faced by previous work, and present some complexity results for this approach in the domain of machined parts.

In particular, the lack of pre- and post-processors suited for the finite element analysis of the bridges is one of the major reasons why the running of finite element program, as a standard part of bridge design, has always been a time consuming process. Currently available bridge software provides few facilities to easily set up, edit, and query information about the design problem description, and the response output to various truck loading conditions. Often the designer is given a textual echo of the input, but no graphical verification that a problem has been well formed. This problem is particularly acute when the design problem definition, and ensuing finite element analysis, needs to be repeated several times.

Furthermore, general purpose finite element packages often do not provide for automatic generation of moving truck and lane loads for the maximum effect.

The purpose of this study is development of an interactive graphically based pre-processor for the finite element analysis of highway bridges with high-speed engineering workstations. The pre-processor gives engineers the choice of using both keyboard and mouse styles of interaction to describe and edit bridge geometries, set boundary conditions, and place trucks at the desired positions on the bridge. For our program, entitled XBUILD, the finite element software along with the pre-processor and post-processor, execute on separate workstations. They communicate via message passing and socket- based Interprocess Communication.

The first method enumerates conventional graphs by deriving the vertex-to- vertex incident matrix directly. The second method derives conventional graphs from contracted graph families by the arrangement of binary chains. The row vector formed by listing of binary vertex chains is used instead of the vertex-to-vertex incident matrix. The third method uses the edge-to-vertex incident matrix as the expression of graphs instead of the vertex-to-vertex incident matrix. The dual of a conventional graph is derived from the dual of a contracted graph by the arrangement of parallel edges. A conventional graph is formed from the dual graph by the following definition of a dual graph.

Two tables of conventional graphs with seven and eight vertices, and with up to eleven edges have been developed. We believe that the results of these conventional graphs are new. Mechanisms of higher pair joints with six loops and seven or eight links can now be synthesized from these tables.