Introduction to Parametric Design

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Introduction to Parametric Design

• Sophomore Engineering Clinic I

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Example from Architecture.

• Design of Columns

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Example from Architecture.
Capital

• Design of Columns

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Example from Architecture.
Capital
Shaft

• Design of Columns

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Example from Architecture.
Capital
Shaft
Base

• Design of Columns

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A Single Column.
Height between ceiling and floor is fixed

• Design of Columns

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A Single Column.
Capital Diameter
Capital Height
Shaft Top Diameter
Shaft Height
Shaft Bottom Diameter
Base Height
Base Diameter

• Column has 7 dimensions

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Consider Constraint

• Capital Height Shaft Height Base Height
  Height of Ceiling (fixed)
• 7 dimensions 1 constraint 6 DOF

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A Single Column.
Capital Diameter
Capital Height
Shaft Top Diameter
Shaft Height
Shaft Bottom Diameter
Base Height
Base Diameter

• Column has 7 dimensions
• Column has 6 independent DOF

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Variables

• Our drawing suggests relative relations between
  the different variables, but we have not yet
  attached any numbers (values) to them.
• When we assign actual numbers to the variables,
  the shape of the column might look quite
  different.

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A Family of Columns

• Our definition of the column admits a wide range
  of possibilities, called design instances all
  belonging to the same family of columns.

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Parametric Design

• When we define the column in a general sense,
  using variable attributes (parameters) we allow
  for a large (possibly infinite) number of
  specific design instances.
• When we use parameters to define a large number
  of instances, and then select the best one, we
  are performing parametric design.

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Reading Assignment
Expiatory Temple of the Sagrada Familia, in
Barcelona, Spain Designed by Antonio Gaudi
between 1883 and 1926.

• C.R.B. Hernandez, Thinking parametric design
  introducing parametric Gaudi, Design Studies, 27
  (2006) 309-324.

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Parametric Design

• When the values of parameters are real numbers,
  we call this parametric variation.
• Parameters can also have entities besides real
  numbers as values. For examples
• A list of available materials (material)
• Number of wings (integer)
• A list of available circuits (component)

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Parametric Design

• Hernandez talks about parametric combinations and
  parametric hybrid models, depending on what type
  of entities the parameters are.
• We will use the term parametric models in a more
  general sense, and admit parameters with
  different types of entities.

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Developing Parametric Models
2
3

• Start with a rectangle
• Identify a family of shapes by defining one
  parameter

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Parametric Model Case I
Parameter Width Height 2 (we say it is
constrained)
2
Width

• We have defined a family with 1 parameter

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Parametric Model Case I
Parameter Width Height 2 (we say it is
constrained)
2
Width

• We have defined a family with 1 parameter
• We have defined an infinite number of design
  instances

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Parametric Model Case II
Parameter Height Width 3 (constrained)
Height
3

• We have defined a family with 1 parameter.
• We have defined an infinite number of design
  instances.

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Parametric Model Case III
2
3

• x- and y-coordinates of 3 nodes are parameters

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Parametric Model Case III

• Instances are not constrained to rectangles

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Comments

• 3 different parametric models were defined. Cases
  I and II had a single parameter, Case III had
  more parameters.
• All parametric models allow the design instance
  of a 2x3 rectangle.
• Case III allows all the design instances allowed
  by Cases I and II, and more.
• The parametric models for Cases I and II were
  constrained to have 4 right angles it might not
  have been apparent this was a constraint when
  they were first defined.

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For Next Week

• Develop a parametric model for a rocket with 3
  parameters
• Amount of water in rocket,
• Mass of clay used,
• 1 parameter to describe a family of fins.

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Constraints

• Clay is placed only in front of rocket, in a
  rounded shape.
• Exactly 3 wings, placed 120o apart.
• Duct tape is used only to secure wings and clay
  to bottle.
• Fin size and shape belong to a family that is
  defined by a single parameter. (you define the
  appropriate parametric model for the wings)

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An example fin family

• Right triangles with height to length ratio of
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• Size and shape of fins are defined by either
  height or length

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Whats Next?

• Next week, come to lab with a parametric model
  for your rocket. (check with a faculty member
  before lab)
• Over the next three weeks, perform experiments to
  determine the set of parameters that maximizes
  the distance that your rocket can fly.

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Example test results
Distance (ft)
Water (liters)

• Holding 2 parameters constant while varying the
  third allows a systematic study of behavior.
• Be careful the optimal value of one parameter
  might depend on the values of the other two
  parameters.

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Note

• Your grade for the report will be based on the
  technical description of the parametric model you
  develop, your discussion of parametric design,
  etc. (assignment sheet will be passed out later)
• The grade of your report for this project will
  not be based on your final distance.

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FAQs

• Can I change the parametric model for the rocket
  after a few tests?

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FAQs

• Can I change the parametric model for the rocket
  after a few tests?
• No. It is more important to systematically
  search the 3 DOF design space to find the best
  solution for your parametric rocket than to
  maximize the distance flown.

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FAQs

• What if we realize that the family of fins that
  we defined with our parametric rocket does not
  lead to an especially effective rocket?

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FAQs

• What if we realize that the family of fins that
  we defined with our parametric rocket does not
  lead to an especially effective rocket?
• Thats OK. Find the best solution for the
  parametric model you developed.

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Food for Thought

• When developing a parametric model, a designer is
  likely to purposely introduce constraints
  thereby limiting the design instances that are
  available. Why would a designer do this?
• What other things might introduce constraints
  into a design?

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Food for Thought

• What are the advantages of using only a single
  parameter to define the family of fins for your
  rocket?
• What are the disadvantages of using only a single
  parameter to define the family of fins for your
  rocket?

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Food for Thought

• What happens if you define the family of fins
  using a parameter that does not have a strong
  effect on the performance of your rocket? (e.g.,
  the color of the wing in an extreme case)
• What happens if you define the family of fins in
  a way that does not admit any specific instances
  that are effective? (e.g., circumferentially
  oriented wings)