1. Design Realization lecture 21 John Canny 11/4/03

2. Last time  Mechanics  Physics revisited  Electric motor characteristics

3. Next time  Assignment review/crit. Please bring a graphic of your board design and schematic.

4. This time  Some more physics:  Bending and stretching  Construction methods:  Molding  Welding  Structural components  Modular systems

5. Bending: moment of inertia again  The 2D moment of inertia about the x-axis is  For a rectangle: h b y x

6. Bending of a beam  We can make a beam bend by applying a moment (torque) to its end. The radius of curvature satisfies: which is for a rectangular beam. E is the elastic (Young’s) modulus. r M y z

7. Beam “spring”  The vertical displacement of the tip t is approximately t  L 2 /2r  The bending moment due to force F at tip is M=FL  The spring constant at the tip is k = F/t which is r M L t

8. Beam stretching  On the other hand the spring constant for stretching a rectangular beam is:  Compared with the bending spring constant which is:  The ratio is h 2 /6L 2. Assuming L >> h, the beam is much stiffer in stretching than in bending.

9. I-beams and honeycomb  Bending stiffness can be increased by moving material outward (h 3 term).  This is the principle of I-beams and honeycomb.

10. Mass-spring systems  A mass at the end of a spring can vibrate with a natural frequency which is

11. Example  Vibration in linear actuators:  Natural frequency of the cantilever, ¼” Aluminum, is about 100 Hz (!)

12. Example  Diagonal bracing:  Bending becomes a streching mode. Natural frequency increases to over 1 kHz

13. Vibration in plastics  Metals have relatively low loss when deformed. Vibration is often an issue.  Plastics have much higher loss, so vibrational energy dissipates much faster.

14. Making shapes: sculpting  Molding kits are available from Tap Plastics and others.  Two part epoxy “magic-sculp” provides a clay- like consistency for about two hours, then sets to a hard plastic model.  The model can still be worked when hard by cutting or sanding.

15. Making shapes: molding  From a plastic, wood, or metal model, a negative mold can be cast from a flexible plastic such as silicone or urethane.

16. Making shapes: molding  From the negative mold, copies can be cast. The casting materials are typically urethanes or polyester. Can be clear or colored.

17. Attaching shapes: Gluing  For plastics, glues are available that closely approximate the strength of the original plastic.  This generally gives best results. Excessive strength in a joint can create strain in the material near the joint.

18. Attaching shapes: Gluing  Many glues are available for wood. At the high end, epoxies are stronger than the wood itself.  Woodworking “yellow glues” provide very good performance as well and have similar strength to the wood being joined.  Dowels or dovetailing can be used to increase the contact surface – but may not necessarily increase strength.

19. Welding  Welding is joining pieces of similar metal using molten material of the same type.  The most common joining weld is a “fillet weld”

20. Welding  The size of the weld adds strength.  The shape of the weld relieves stress that can occur at sharp concavities in a part.

21. Arc Welding  Creates a thick weld using flux/wire which is part of the electrode:

22. Oxy-Acetylene Welding  Oxygen-Acetylene torch creates heat, flux/wire is fed separately:  Aside: Oxy-acetylene often used for cutting

23. MIG (Metal Inert Gas) Welding  Aluminum oxidizes instantly in air and requires an inert gas during welding. MIG welding uses an arc surrounding by gas flow (e.g. Argon).

24. Spot welding  Normally used to join sheet material.  Sheets are placed together and very high current passed through the join.

25. Truss systems Trussworks Inc.

26. Truss systems  Come in either aluminum or steel, 2, 3, 4-leg.  Fast-connect screw connections between elements.

27. Modular construction systems  Can be used to build artifacts from linear pieces.

28. Modular construction systems  “T-slot” systems comprise extruded aluminum beams that are joined using standard fasteners. Examples of “Minitec” framing:

29. Modular construction systems  Joining Minitec elements:

30. Modular construction systems  Minitec includes active elements (motorized motion stages):