Mechanisms for ME122, Portland State University References

• Making Things Move: DIY Mechanisms for Inventors, Hobbyists, and Artists by Dustyn Roberts. • http://www.ohio.edu/people/williar4/html/haped/nasa/simpmach/le ver.htm • https://bvg8science.wikispaces.com/Chris+A%27s+IMA • http://curriculum.vexrobotics.com/curriculum/mechanical-power- /-ratios Definitions

• = assembly of moving parts

• = any device that helps you do work

• Mechanical Work = x Distance

• Mechanical Advantage (MA) = the relationship between the load (example: load being lifted) and the effort (example: required to lift it) Main uses of machines

• Transform energy • Transfer energy • Multiply and/or change direction of force • Multiply speed

= rigid object used with a pivot point to multiply the mechanical force on an object • Uses definition of moments to compute MA (mechanical advantage): MA = length of effort arm / length of load arm. • Three components: • Fulcrum (pivot point) • Input (effort or force) • Output (load or resistance) • Three classes: • First Class : seesaw, oars on a boat • Second Class Lever: wheelbarrow • Third Class Lever (the only one without mechanical advantage): fishing rod Pulleys

= wheel with a groove along the edge for a rope or . • Closed system • Example: timing belt in a car • Used to translate rotational motion between axes • Mechanical advantage if the driven pulley is smaller than the output pulley • Mechanical advantage= ratio of pulley diameters. • Open pulley system • Pulley fixed: • Example: flag hoist • No mechanical advantage but change of direction of movement • Pulley unfixed (“runner”): • Can magnify the force but needs longer distance pull Unfixed Pulley examples

• Single whip no MA (mechanical advantage) • Gun tackle 2:1 MA • Luff tackle 3:1 MA • Twofold Purchase 4:1 MA • Double luff 5:1 MA • Three fold purchase 6:1 MA Wheel and Axle

• If input force is applied to the wheel, MA = R/r (always >1) , r

• If input force is applied to the axle, MA = r/R (always <1) , R Inclined planes and wedges

• Inclined plane:

MA = DI / DO = total distance of effort exerted / vertical distance the load is raised

• Wedge: example: knife, axe MA = Wl / Wb = Length of wedge / Width of wedge Screws

• 2 main types: • For fastening parts together • For lifting or linear motion (example: jack) • MA = 2π x radius / pitch r

• Basic Types of gears: • Spur: Transmits motion between parallel shafts

• Rack-and-pinion: Converts from rotary to linear motion. Movement is usually reciprocating

• Bevel :Mesh at an angle to change the direction of rotation

• Worm: screw meshes with the teeth of a spur gear Big MA and no back drive

• Planetary: combination of spur gears with internal and external teeth. Used when space is limited, but significant MA needed. Mechanical Advantage of Gears: Gear Ratio

• Small gear = pinion

• GR = # of teethdriven / # of teethdriver • GR = τdriven / τdriver with τ, torque. τ = F x r • GR = ωdriver / ωdriven with ω, angular velocity (in rad/s). ω = v/r

• When gear is used to magnify force: • Pinion is the driver • GR >1 • When gear is used to magnify speed: • Pinion is the one being driven • GR< 1 • Example: The driver gear rotates 6 times slower than the driven gear Spur Gear Setups

• Idler gears: • Idler gear is placed between driver and driven gear. Allows driver and driven gear to go in same direction. • GR = # of teeth on driven gear / # of teeth on driver gear • Compound gears: • More than one gear on the same axle. Has multiple gear pairs. • Very efficient to increase torque and decrease speed • GR= multiplication of each gear ratios together • Example: GR = (60/12) x (60/12) = (5/1) x (5/1) = 25/1