1. Introduction to Parametric Design Sophomore Engineering Clinic I

2. Example from Architecture. Design of Columns

3. Example from Architecture. Design of Columns Capital

4. Example from Architecture. Design of Columns Capital Shaft

5. Example from Architecture. Design of Columns Capital Shaft Base

6. A Single Column. Design of Columns Height between ceiling and floor is fixed

7. A Single Column. Column has 7 dimensions Shaft Height Base Height Capital Height Base Diameter Capital Diameter Shaft Bottom Diameter Shaft Top Diameter

8. Consider Constraint Capital Height + Shaft Height + Base Height = Height of Ceiling (fixed) 7 dimensions – 1 constraint = 6 DOF

9. A Single Column. Column has 7 dimensions Column has 6 independent DOF Shaft Height Base Height Capital Height Base Diameter Capital Diameter Shaft Bottom Diameter Shaft Top Diameter

10. 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.

11. 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.

12. 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.

14. Reading Assignment C.R.B. Hernandez, “Thinking parametric design: introducing parametric Gaudi,” Design Studies, 27 (2006) 309-324. Expiatory Temple of the Sagrada Familia, in Barcelona, Spain Designed by Antonio Gaudi between 1883 and 1926.

16. 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)

17. 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.

18. Developing Parametric Models Start with a rectangle Identify a family of shapes by defining one parameter 2 3

19. Parametric Model – Case I We have defined a family with 1 parameter 2 Width Parameter = Width Height = 2 (we say it is constrained)

20. Parametric Model – Case I We have defined a family with 1 parameter We have defined an infinite number of design instances 2 Width Parameter = Width Height = 2 (we say it is constrained)

21. Parametric Model – Case II We have defined a family with 1 parameter. We have defined an infinite number of design instances. Height 3 Parameter = Height Width = 3 (constrained)

22. Parametric Model – Case III x- and y-coordinates of 3 nodes are parameters 2 3

23. Parametric Model – Case III Instances are not constrained to rectangles

24. 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.

25. 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.

26. Constraints Clay is placed only in front of rocket, in a rounded shape. Exactly 3 wings, placed 120 o 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)

27. An example fin family Right triangles with height to length ratio of 1:2 Size and shape of fins are defined by either height or length

28. What’s 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.

29. Example test results 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. Water (liters) Distance (ft)

30. 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.

31. FAQ’s Can I change the parametric model for the rocket after a few tests?

32. FAQ’s 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.

33. FAQ’s What if we realize that the family of fins that we defined with our parametric rocket does not lead to an especially effective rocket?

34. FAQ’s What if we realize that the family of fins that we defined with our parametric rocket does not lead to an especially effective rocket? –That’s OK. Find the best solution for the parametric model you developed.

35. 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?

36. 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?

37. 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)