Mechanisms for MachinesME122, 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/lever.htm

• https://bvg8science.wikispaces.com/Chris+A%27s+IMA

• http://curriculum.vexrobotics.com/curriculum/mechanical-power-transmission/gear-ratios

http://www.ohio.edu/people/williar4/html/haped/nasa/simpmach/lever.htmhttps://bvg8science.wikispaces.com/Chris+A's+IMAhttp://curriculum.vexrobotics.com/curriculum/mechanical-power-transmission/gear-ratios

Definitions

• Mechanism = assembly of moving parts

• Machine = any device that helps you do work

• Mechanical Work = Force x Distance

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

Main uses of machines

• Transform energy

• Transfer energy

• Multiply and/or change direction of force

• Multiply speed

Levers

= 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 Lever: 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 belt.

• Closed pulley 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)

• If input force is applied to the axle, MA = r/R (always

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: screw jack)

• MA = 2π x radius / pitch r

Gears

• 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 gearBig MA and no back drive

• Planetary: combination of spur gears with internal and externalteeth. 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