DOF in engineering problems (2)
A reflection on verbal and visual skills to take advantage of the "degrees of freedom (DOF)" present in engineering problem statements.
To this end, some results of the challenge posed are used as an excuse to address these ideas:
https://grabcad.com/groups/weekly-challenge-group/discussions/a-mechanism-to-move-the-green-orange-rectangle
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Step 1: Improve and systematize
Part 1 of this tutorial was dedicated to reflecting on certain design practices that could be improved, some of which could be seen in the orange-green rectangle challenge.
Any errors cited are not attributable to lack of experience or technical knowledge. On the contrary, they are more frequent among those who know certain topics well and act driven by tradition, rushing to use, over and over again, the same recipes without even managing to put them in crisis.
Even more than errors, it is advisable to consider them "opportunities for improvement" achievable with some systematization in the creative process, which is usually tinged with mysticism and its prominent actors seem to depend on innate abilities that cannot be understood or taught.
The existence of "natural talents" for different activities, including design and problem solving, seems undeniable, which should be detected, cultivated and used. But what is within everyone's reach are not those innate abilities, but rather those that can be acquired through training (learning and teaching, regardless of natural talents).
We will dedicate this part 2 of the tutorial to mention and exemplify some practices of systematization of the creative process in the hope of improving our thinking and design processes.
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Step 2: Remove restrictions and expand the spectrum
For the example of the rectangle, which is very simple, to help us observe some characteristics of large and complex problems, we will have to be willing to extrapolate some situations and imagine them on a larger scale.
One of the common techniques in such problems is to relax or remove some restrictions from the problem statement, temporarily, to facilitate the flow of ideas and develop a broader spectrum of solutions.
In this way, the solutions to the original problem become a subset of such a spectrum, but the rest of them provide a greater degree of understanding and imaginative resources to reach useful solutions.
How would this technique be applied to the rectangle example?
We should first take the original problem statement:
- Original statement: be a rectangle with one side green (front) and the other side orange (back). Its initial position leaves the orange face visible, with its long edges in a horizontal position. Its final position leaves the green face visible, with its long edges in a vertical position. It is requested to design a mechanism capable of moving it between both positions.
- Graphic: in the following figure the orange and green colors are associated with two different faces of the rectangle:
Then analyze it and create a new version in which we relax or remove some restriction that, a priori, is complex to satisfy and may be limiting the fluidity of our ideas. This is arbitrary and there is no one way to do it, but here is an example of an alternative:
- Simplification: let's forget (for a moment) the requirement to differentiate both sides of the rectangle (orange and green) and simply ask to go from the initial position to a final position with the long edges vertical.
- New statement: be a rectangle located with its long edges in a horizontal position that requires moving to a final position where its long edges are vertical. It is requested to design a mechanism capable of moving it between both positions.
- Graph: although the following graph is the same as the original, its meaning is different, more general, less restrictive. The colors now simply represent the starting position (landscape) in orange and the final position (vertical) in green:
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Step 3: Use the simplified statement
The simplified statement is used like any other, with the advantage that it represents a somewhat simpler problem than the original.
It is advisable to make good drawings to make the instructions clear before proposing solutions. This will lead us to realize that the rectangle has two faces (front and back) although without the obligation to condition the movement to them:
Identifying the faces (front and back) of the rectangle will make it easier for us to recognize all the “orientations with long vertical edges”:
How many different cases will there be?
In this example, a simple analysis allows us to recognize four different cases or ways in which the rectangle can be placed in its final position starting from a certain initial position:
CASE 1: facing the FRONT with counterclockwise turn
CASE 2: facing the FRONT with clockwise rotation
CASE 3: showing the BACK with counterclockwise rotation
CASE 4: showing the BACK with clockwise rotation
As a summary and visual stimulus, we graph these cases together to anticipate the structure of the future SCS (Solution Concept Spectrum):
Note:
At this point someone might ask... why were the other four cases in which the rectangle in its initial position leaves its "back" visible not analyzed?
Such cases exist and are valid but totally symmetrical to those already raised. That is, two situations will be found again in which the same face (the back in the previous figure) appears in two possible final positions (with counterclockwise rotation and with clockwise rotation) and another two situations where it is the other face ( the front in the previous figure) which appears in the final position in two possible orientations.
In this way, the same mechanisms that resolve cases 1, 2, 3 and 4 are those that could resolve the other four additional cases.
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Step 4: Deepen understanding
In a more complex case, it would be essential to deepen the analysis to ensure complete understanding of the simplified statement.
In the previous step we illustrated the different cases that show the initial and final positions of the movement.
Now, it is possible to "glimpse the movements" through vectors with a start and end at different points of the object to be moved. Of course, these vectors cannot be considered "paths of the movement of the points" since they are straight segments that can hardly be traversed simultaneously by said points.
However, these straight segments already give us a good idea of at least one alternative movement between the initial and final positions considered:
Locating a plane (such as a rectangle) in space requires only 3 non-collinear points, but adding other points helps to think because, as will be seen later, each object has points with complex movement and others (which should be found) that move. in a linear or circular way, and they are usually the most convenient to implement future mechanisms (we have not talked about them yet, nor are we trying to define them: we are talking about "movement").
All of the above is usually systematized in what we call "support graphs for mobility analysis" that are summarized for this step.
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Step 5: Make supporting graphics
The previous task (joining initial and final positions of various points of the object) is something that should be done systematically since it constitutes a strong visual stimulus for the design of the movement and, subsequently, the mechanism.
SUPPORT GRAPHICS FOR MOBILITY ANALYSIS
CASE 1:
CASE 2:
CASE 3:
CASE 4:
We can now refine the Spectrum of Solution Concepts that we achieved in step 3, which only cited the start and end positions of the movement, adding information on the mobility of certain points:
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Step 6: Analyze mobility
With the support graphics for the analysis of mobility as a "visual stimulus" it is advisable to "give time for ideas to mature" by observing them repeatedly to "imagine different ways to achieve each case of mobility."
As each mobility case has infinite ways to be implemented, it is advisable to have some strategies for its analysis. In this tutorial we will mention two of them: Detection of stationary points and Definition of components.
DETECTION OF STATIONARY POINTS
A stationary point on a support graph is one whose coordinates do not change while the moving object only rotates around it. It corresponds to a vector of zero modulus that we represent as a curved arrow that leaves and returns to the same point. It can inspire interesting and relatively easy-to-generate solutions, as exemplified below for the stationary point that appears at a vertex of the rectangle for mobility CASE 4:
It is a very determining fixed point for movement, but the rest of the points still have infinite ways to get from their initial positions to their final ones. In few cases these shapes will include some line segment (vectors) like those already graphed, but in most cases such a thing will not be possible because "it would imply deforming the object"... and deforming the object (or converting it into a mechanism capable of sticking) is a very interesting creative proposal!
DEFINITION OF COMPONENTS OF THE MOVEMENT
Another very useful strategy for the analysis of mobility is the arbitrary definition of "movement components" compatible with each mobility case presented.
Like any system of "components" its definition is arbitrary and there are infinite possibilities. As in the case of a vector of a certain module, direction, sense and initial point in space: it is possible to represent it in infinite coordinate systems, for which "it will have different components" that reflect the same physical reality. That is, if some invariant is calculated from these components (such as the vector module), obviously the result must be the same from any coordinate system and its respective components.
An example of mobility by components for CASE 1
Note that the order of these three component movements can be interchanged, which provides additional creative freedoms. But even more so if we consider that, for each definition of components it is possible to define different "combined movements". That is, the component movements can be executed individually and successively (in any order) or in combination and simultaneously... creating infinite movement solutions, without having yet spoken of the artifact (mechanism) capable of providing it.
For example, by combining (by simultaneous execution) the first two linear motion components defined above, a translational motion with rotation is generated that can be physically solved even more simply than the individual components and, furthermore, by reducing the number of degrees of freedom. That is: to move these two components individually, two motors would have to be used, but for combined movement only one and, for example, a simple system of linear guides would be sufficient.
Another example of component definition:
Note: this option collides with the context of the garage, but we must remember that it is fictitious and there are no space restrictions in the lockers.
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Step 7: Tolerate divergence
Perhaps one of the least intuitive questions for engineers who have been trained in a classical way, with analytical content, a rational mentality and vertical (convergent) thinking, is the convenience of tolerating divergence and its multiple alternative solutions, exploring them before trying to fully develop them.
It happens that strongly rational formation induces us to rapidly converge and that, in the design process, is reflected in our anxiety to "find something that works and perfect it" without remaining too long in a "divergent state, managing multiple alternatives."
It may even seem like a waste of time, in addition to being tedious because we need to train our lateral (divergent/creative) thinking and learn to postpone detailed engineering in favor of the generation and evaluation of a greater quantity and diversity of ideas.
Training lateral thinking (divergent/creative) does not have the objective of displacing vertical thinking (convergent/rational) but rather "using it when it is most useful" since these are complementary abilities that do not come into conflict if one gets used to developing them. the design in its three consecutive stages:
1. Conceptual (in which divergent thinking predominates),
2. Basic (where both types of thinking are combined, although with a preponderance of convergent thinking) and
3. Detailed (where convergent/vertical/rational thinking predominates).
Tolerating the divergence that we have proposed so far, removing restrictions from the problem and making the set of solutions broader, implies having patience despite knowing that we are looking at a set of solutions where some clearly do not solve the original problem:
But then why do we waste time looking at them?
To get inspiration and glimpse new creative resources applicable to really valid solutions!
For example, if we had not made this effort, we would probably never have discovered movements as special as CASE 4 due to its stationary point. Simply put: this NO SOLUTION ended up teaching us something very valuable about how to move an object and we can apply that to the resolution of this same problem or any other in the future.
Of course I am not referring to something obvious and typical of this example (such as the stationary point and the rotations around it) but rather any other special knowledge specific to the real/complex problem that one is addressing.
But if you want a more forceful justification, just think that:
Any motion design from "the supposedly useless cases 3 and 4" can be made successful simply by "adding to it one or more motion components (out of many possible ones)":
Basically, the "prize for tolerating divergence" is learning. For this reason, I maintain that the design process is a learning process when one is willing to replicate the techniques used for it: observe, analyze, reflect, mature so that the concepts pass from working memory to short-term memory. , and from this (time and repetitions through) it manages to move to the long term, becoming a resource that is easy to recover and apply to other problems.
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Step 8: Design the mechanism
So far we have talked about "designing movements" with abstraction from the artifact (mechanism) capable of providing it.
Since this tutorial would be too long, we will leave it to the next one to deal with this issue so that the phrase we have been using makes sense: design the movement first and then the mechanism!
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Step 9: Links
This tutorial comes from:
DOF in engineering problems (1)
and continues in:
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