Design Realization lecture 21 John Canny 11403 Last

Design Realization lecture 21 John Canny 11/4/03

Last time § Mechanics § Physics revisited § Electric motor characteristics

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

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

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

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

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

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 2/6 L 2. Assuming L >> h, the beam is much stiffer in stretching than in bending.

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.

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

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

Example § Diagonal bracing: § Bending becomes a streching mode. Natural frequency increases to over 1 k. Hz

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.

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

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.

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

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.

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.

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

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

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

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

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).

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

Truss systems Trussworks Inc.

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

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

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

Modular construction systems § Joining Minitec elements:

Modular construction systems § Minitec includes active elements (motorized motion stages):