<p class="MsoNormal" style="margin-bottom: .0001pt; text-align: justify; line-height: 150%">One of the most significant issues investigated in the CAD/CAM developments is the swept envelope formation by a moving tool. The goal is to determine the outer boundary of the tool during its motion. There is a bunch of attempts to get envelopes based on the evaluation of tangency constraint. The core operation of this method is to pick the input values one at a time and consider the solutions of constraint for various dependent values at a particular time instance. Then repeat this until finding all elements of swept profiles located on the envelope. Such a pathway causes excessive computational effort and time that must be spent to implement the tangency constraint. Recently some research [1-5] has been conducted to completely eliminate the need for evaluating tangency-constraint. In these techniques in order to obtain a closed-form representation of the envelope, the tangency constraint is written explicitly in terms of the dependent variable then it is embedded into the tool surface equation. There are some benefits. As a single composite form, it provides better integration with downstream applications. It eliminates the arduous calculations that would be required for a large number of constraint evaluations at different inputs, and thus reduce the manufacturing cycle time. While this sounds straight forward there are some important inevitable consequences of these restructurings. In the new form, there are no restrictions on the domains of the input variables. For milling tools of moderate geometric complexity calculating these domains is simple, provided one level-cut. On the other hand, in many molds and die-making industries the form-cutting tool shapes are quite complex having multiple level-cuts. As a consequence of this, the whole set of input values need to be partitioned into a number of disjoint ordered-subsets for which correspondence check between domain and eliminated variables must be performed. The computational cost associated with this type of calculation can become impractical when looking at all the benefits we get from eliminating the tangency-constraint evaluation. To overcome this issue, in this paper first, we introduce a powerful test that takes the domain restrictions into account when the swept profiles of the form cutters are calculated. Later, using this test we will systematically investigate the distribution patterns of swept profiles which normally form closed loops or open-branches on tool surfaces. Finally, we present algorithms for forming the domains of composite forms under different motion kinematics. In this section, also some examples are given to illustrate the effectiveness of the methodology.</p>

Investigating the Effects of Branching on the Constraint-Embedded Swept Profile Calculations

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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