Capitulo 2. MARCO TEÓRICO
2.1. Residuos sólidos
2.1.4. Gestión integral de los residuos sólidos
Figure 3.23 shows the planar representations of the four example domains discussed in this section, and Figure 3.24 shows their corresponding representations in cong-uration space. We have noted a number of similarities between these representations throughout our discussion that are worth recalling here. First, we have focused a considerable amount of attention on the role of kinematic motion constraints rep-resented by the surface of the CS and determined by interactions between object shapes. In the examples of assembly, parts xtures, and the APOS feeder we saw how some of these constraints took the form of features on the CS surface that we likened tofunnelsorwellsthat guide motions toward a specic state or set of states in conguration space. In the bowl feeder and APOS examples we saw parallel valleys in the -dimension on the CS that acted to sort and guide parts into dierent stable orientations. In addition to kinematic constraints we saw representations of dynamic motion constraints in terms of forward projections determined by the mechanics of object interaction. For the peg-in-hole assembly and vibratory bowl feeder exam-ples we were able to generate detailed representations of object motions as a set of paths, or trajectories, from initial states in conguration space and constrained by contact with the CS. For the xture and APOS feeder examples we were unable to generate exact motion descriptions, but instead bounded the set of reachable states in conguration space through which any trajectory would pass.
In addition to their similarities, the four example domains were also chosen for
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(a) (b)
(c) (d)
Figure 3.23: The four planar application examples:
(a)
peg-in-hole assembly,(b)
vibratory bowl feeder,
(c)
xture, and(d)
APOS feeder.100
Chapter 3: Visualization and Application DomainsFigure 3.24: Conguration space representations for the four planar application ex-amples: peg-in-hole assembly, vibratory bowl feeder, xture, and APOS feeder.
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their dierent usage of the resources made available within the conguration space representation. Specically, both the assembly and xture examples focused on a rel-atively small region of conguration space where the local set of CS facets were su-cient to describe the kinematic motion constraints of interest, whereas the functional description of both the vibratory bowl and APOS feeders required the consideration of kinematic motion constraints over large regions of the CS. On the other hand, the assembly and bowl feeder examples utilized exact integration of motion paths to construct forward projections, whereas the xture and APOS feeder examples relied on bounded energy models to generate their non-kinematic constraints. This particular set of four example domains was chosen to combine dierent constraint representations in dierent ways in an attempt to span the class of problems that might be considered using the motion constraint representations developed.
In each of the four examples, we presented functional metaphors intended to abstract the important relationships between object motions and their constraints without distraction by geometrical or physical details. Of course, these \details" are crucial for ensuring that a particular instance of a system has the desired functional characteristics. In this sense, the conguration space representation is meant to act as a kind of bridge between the abstract function common to all instances or artifacts from a particular domain, and the detailed information that makes each particular instantiation unique. Specically, the motion constraint representations in congu-ration space, including the CS, forward projections, and support regions, all possess both the topological properties that map to the abstract functional metaphors, as well as detailed metric information that ensures delity with the behavior of the actual example under consideration.
Finally, in each of the examples we attempted to give a sense of how a given system might be modied, or designed, to achieve the desired functional character-istics. Although the motion constraint representations allow us to conrm whether or not a particular system has the desired behavior, and in some cases a sense of how robust that behavior is to potential variations in system parameters, we still do not have an a priori means of reliably generating the desired constraints from scratch. This topic will be addressed more fully in the next chapter for the rst two examples: peg-in-hole assembly and vibratory bowl feeders. The remaining two examples, although proting from the developments made for the other examples, await further research into the implementation of conservative and non-conservative energy bounded forward projections.
The purpose of this chapter was to make the representations and visualization techniques introduced in Chapter 2 more concrete by introducing a set of example applications. These examples were chosen to span the available set of constraint rep-resentations, as well as to highlight similarities and dierences between the various functional constraints. In the next chapter we will consider in detail themanipulation of the representations developed so far, and in particular we will apply the
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Chapter 3: Visualization and Application Domains ing tools to the rst two example domains introduced in this chapter: peg-in-hole assembly and vibratory bowl feeders.Design
Chapter 4
You can't always get what you want... But if you try some time, you might nd, you get what you need.
{ M. Jagger & K. Richards, 1969
In this chapter we will take the representations of function in terms of motion constraint that were developed in the previous chapter and examine how they may be utilized for the purposes of design. We begin by considering a number of poten-tial methods by which objects with the desired constraint characteristics might be generated, and consider a subset of these methods that appear to be both feasible and suitable for design. We then provide an overview of an implemented toolkit for the design of motion constraints in the form of an interactive computer aided design environment. This toolkit is applied to the design of artifacts from two of the ex-ample domains in the previous chapter: vibratory bowl feeder tracks and compliant peg-in-hole assemblies. Finally, we discuss some additional characteristics of design using motion constraints and examine the possibility of extending the scope of the toolkit to include fully or partially automated design methodologies.