1.4 - Simple Machines

Week 1 - Design

Simple Machine

Mechanical device that changes the direction or magnitude of a force using mechanical advantage

6 common simple machines

Lever, Wheel & Axle, Pulley, Inclined Plane, Wedge, Screw

Mechanical Advantage (MA)

Force multiplication ratio: MA = Fout / Fin

Conservation of Energy principle

Input Work = Output Work: F₁d₁ = F₂d₂

Force displacement relationship

Inverse relationship: to increase output force, increase input displacement or decrease output displacement

Ideal MA assumption

No friction, heat losses, or deflection; everything rigid

Lever

Rigid beam and fulcrum that moves a load with applied force

Lever MA formula

MA = input force distance / output force distance = a/b

First class lever

Fulcrum in middle, effort and load on ends (lifting bar)

Second class lever

Load in middle, fulcrum and effort on ends (wheelbarrow)

Third class lever

Input force in middle, fulcrum and load on ends (golf club)

First class lever MA

Can be greater than or less than 1; always changes force direction

Second class lever MA

Always greater than 1; does not change force direction

Third class lever MA

Always less than 1; does not change force direction

Wheel & Axle

Disc with shaft at center; radial equivalent of lever

Wheel & Axle MA formula

MA = input radial distance / output radial distance = R/r

Pulley

Grooved wheel supporting rope between input force and load

Pulley MA

Number of ropes attached to the load

Fixed vs moveable pulley

Fixed: attached to beam; Moveable: attached to load

Inclined Plane

Sloped surface for raising heavy objects

Inclined Plane MA formula

MA = slope distance / vertical distance = s/h

Wedge

Triangular tool for splitting, separating or lifting objects

Wedge MA formula

MA = tool length / tool width = l/w

Wedge MA characteristic

Decreases the farther you drive the wedge in

Screw

Inclined plane wrapped around a cylinder

Screw MA formula

MA = rotational distance / linear distance = 2πr/p

Thread pitch

Distance between threads; finer threads give greater MA

Compound Machine

Combination of one or more simple machines

Compound Machine MA

Product of MAs of each simple machine

Scissors compound machine

Lever (handle) + Wedge (blade)

Corkscrew compound machine

Lever + Screw

Axe compound machine

Lever + Wedge

Wheelbarrow compound machine

Lever + Wheel & Axle

Hand winch compound machine

Wheel & Axle + Gear

Gear pair MA

Ratio of numbers of teeth: output gear teeth / input gear teeth