1.5. Métodos de aislamiento de Campylobacter termofílicos
2.2.4. PCR-MULTIPLEX
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Chapter 4: Design(f)
A concavity in the track prole will produce unsupported regions across the CS that may appear as isolated islands or entire swaths along the direction, as shown in Figure 4.18(f)
. Unlike the supported regions in case(e)
, however, these unsupported regions may be very useful by themselves since they may be used to intercept and terminate selected motion paths. The track prole produced by the cutout operation of Section 4.2.2 produces such features.zz The support regions generated on the CS for cases (d) - (f) assume a simple CS surface, as in case (a).
We could, of course, generate even ner taxonomies of feeder features than those given in either Table 4.1 or Table 4.3. However, there is a tradeo between the information gained from a ner classication and both the increased size and added complexity of indexing and interpreting the combinations of feature types. Detailed taxonomies have in fact been developed for more general types of feeder than are treated here (see Boothroyd et. al. 8]). The disadvantage of such classication schemes quickly becomes apparent when we observe minor changes made to a feeder geometry within a given class producing major changes in feeder behavior, making it necessary to rene even further the classications forming the taxonomy. Further-more, the notion of similarity among classications is not easily represented in terms of proximity within such a taxonomy { similar classes could be placed in dierent regions whereas markedly dierent classes could become closely grouped. These were among the primary motivations behind our choice of motion constraints vs. raw ge-ometry as a representation of function. Once again we stress that the primary role of the taxonomies described here is to identify promising feeder classes with which to start the detailed design process that we will describe in the following section.
4.4: The Design of Vibratory Bowl Feeders
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In Section 3.2 we illustrated a functional description for a vibratory bowl feeder as a lter on the motions of parts (see Figure 3.9). We identied two primary classes of interactions: (i) reorienting of part motions by causing parts traveling in one orientation to reorient themselves (i.e. cause one path to transition or merge with another path), and (ii) selective removal of support from part motions by allowing parts traveling in a desired orientation to continue through the feeder while forcing those in other orientations to fall o the support track. The motion constraint repre-sentations described in Section 3.2 can capture both classes of ltering interactions, although we will focus most of our attention on the latter as it best characterizes the majority of bowl feeder types, and is in general easier to achieve in practice.
The basic strategy used for designing feeders is to rst dierentiate undesired part orientations from the desired orientation as the parts pass through the feeder by means of the interaction between the parts and the feeder bowl wall. Then,lter out those parts moving in the undesired orientations by means of their interaction with the support track. In terms of motion constraints, part motion paths are redirected by modications made to both the CS and dynamics parameters, and selected paths are made to terminate by intercepting them with unsupported regions manipulated on the surface of the CS.
Given a part geometry, we approach the task of designing a feeder in three phases:
Initial problem formulation
{ getting started. In this phase we essentially\rough out" an initial design starting with the simplest appropriate feeder geometry, typically a class 1 narrowed track feeder from Table 4.2 consisting of a straight bowl wall and support track. From the motion constraints generated by this choice we select the desired part orientation that we wish the feeder to accept, with the remaining orientations to be rejected.
Constraint manipulation
{ the heart of the design process. With the initial design problem dened above, we begin exploring the surrounding region of de-sign space.14 We rst examine the inherent dierentiability of the stable part orientations with a narrowed track. If we are able to obtain only the desired orientation by this method, i.e. if the part geometry is naturally orientable into the desired orientation, then we are done. Otherwise, we begin the de-tailed feeder design process, with the goal of reducing complexity as much as possible by varying only a few parameters at time. We do this by alternatively focusing on apparent inversion of either the CS $bowl wall or of the support transition boundaries $ support track. We explore a wide range of variations to a selected set of parameters before moving on to another set since, due to the nonlinear behavior of the constraints, larger variations may have charac-teristically dierent eects than small ones. We use the non-parametric cutout14In exploring a local area in design space we're basically assuming that the space is locally smooth and continuous, as noted in Section 4.1.4.
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Chapter 4: Design operation sparingly, if at all, and only early on in the design process. At all times we try to avoid terminating the desired path, and immediately restore it if we should inadvertently do so. Finally, we verify the behavior of the de-sign continually as it evolves by observing the representations of the motion constraints, and by occasionally animating the forward projected motion paths.
Problem redenition
{ guring out what to do when you get stuck. There is no guarantee that we will be able to nd a feeder design suitable for the given formulation of the problem, or that such a design even exists. We have two ways of redening the problem should we fail to make progress toward a solution.The rst is to simply choose a dierent orientation that we wish to accept, and begin the constraint manipulation process anew.15 The second approach is to subdivide the design problem by taking the output part orientations from whatever feeder design we obtained above and treat them as the input to a new feeder design problem.
Figure 4.19 illustrates a feeder design methodology, based on the above phases, in the form of a owchart. The functional blocks embedded within each of the phases are described in detail below.
1.
Select initial feeder class:
Begin with the simplest class of feeder (class 1 from Table 4.2 consisting of a straight bowl wall and track).2.
Generate motion constraints:
Construct the CS, support regions and mo-tion paths using the nominal feeder geometries and dynamics settings.3.
Select desired path:
Choose one path to pass through the feeder without losing support. To maximize feeder throughput, it is best to select the path corresponding to the part initial orientation with the highest probability, illus-trated in cspace-shellby thethickest path.4.
Try a narrowed track:
Try to exploit the natural dierentiation of part orientations (radius function) by varying the oset of the straight track edge from the straight bowl wall (class 1) so that only the desired path passes through the feeder.5.
Remove other paths:
If the remaining paths cannot all be terminated by unsupported regions while at the same time maintaining support for the desired path, we choose the next thickest unterminated path and:1615In some cases, the result of the constraint manipulation phase may be a feeder that accepts the wrong part orientation, but rejects all of the other orientations, including the desired orientation.
In this case, we may simply choose to accept the result and declare the problem solved.
16The majority of design activity will occur in step 5 between(ii)and(iii). We must continually monitor the desired path's status and stop modications short of terminating that path. If the desired pathdoes become terminated, we should rst attempt to restore it before continuing.
4.4: The Design of Vibratory Bowl Feeders
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(1) Select Initial Geometry
(2) Generate Motion Constraints
(3) Select Desired Path
(4) Try Narrowed Track
Remaining Paths Terminated?
(5) Select & Terminate Other Paths
(i) Generate Track Cutout
(ii) Redirect Paths
(iii) Modify Supports
(6) Keep Trying?
(7) Reconfigure Problem
(ii) Cascade Features (i) Select New
Desired Path
Done!
Y N
Y N
Formulate Initial Problem
Manipulate Constraint Representations (Core Design Loop)
Redefine Problem
Figure 4.19: Flowchart for a bowl feeder design strategy (see text).
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Chapter 4: Design(i) Track cutout:
Early on in the design process, we may try introducing acutout
near the unterminated path with the most dierentiated valley height from the desired path. (If the unterminated path is higher in y than the desired path (most likely case) then choose aleft
falling cutout near the unterminated path. Otherwise, choose a right or forward falling path near the unterminated path.) This corresponds to a class 3 feeder geometry from Table 4.2.(ii) Redirect paths:
Manipulate the CS surface to dierentiate the unter-minated path from the desired path by creating or modifying a ridge or valley on the CS (i.e. a bowl wall protrusion or cavity, features(b)
&(c)
from Table 4.3). This corresponds to a transition from a feeder class 1 ! class 2 transition from Table 4.2. For non-class 1 bowl wall geometries, we may also vary the applied force vector to further dierentiate paths across individual contact facets.
(iii) Modify unsupported CS regions:
Tointerceptthe unterminatedpath, manipulate the support transition boundaries on the CS near a portion of the unterminated path on the CS ridge or valley feature. This corresponds to a transition from a feeder class 2 ! class 4 transition from Table 4.2.6.