Engineering Chapter 8

Involute

most common shape; type of teeth we see in our robots. The tooth has a curve made by base circle

Crankshaft

rotating axle that takes power from the engine

Driveshaft

runs under car that ultimately powers wheels

Calculations compound gear reduction

- First and last gear only matter - Count the number of teeth - Divide the driven gear by the driver gear (size doesn't matter)

Gear reduction required equation

- Gear Reduction Required = Output Torque / Input Torque Or - Gear Reduction Required = Input Speed / Output Speed No units

Examples of power

- How fast a student can carry a backpack holding 15 lbs of books up a flight of stairs. - How fast can a student transfer the chemical energy in their muscles into mechanical energy to lift the backpack up the flight of stairs.

Power transmission in cars

- In front-engined rear-wheel-drive, power is transmitted from the engine through the clutch and gearbox to the rear axle by tubular propeller shaft - Rear axle must be able to move up and down on suspension - For constant movement to occur, splines on the front end of the propeller shaft slide in and out of the gearbox as distance changes - Last part of transmission is the final drive, which incorporates the differential - Front-wheel-drive cars use same transmission principles as rear-wheel- drive cars, but mechanical components vary in design according to engine and gear layout

Going uphill

- Load is high - Use gear ratio with increased output torque at low speed

Going down hill

- Load is low; rider has limited power. - Use gear ratio with increased speed at low output torque

Teeth qualities

- Prevent slippage between gears - Make it possible to determine gear ratio (Ex:) one wheel has 60 teeth and the other has 20; ratio is 3:1

Smaller gears driving larger gears result in?

- Result in a torque increase and a speed decrease. - Large gears driving small gears result in a torque decrease and a speed increase..

Power

- The rate at which work is performed. - The rate that energy is transferred.

Gear qualities

- Wheels with teeth. - Mesh together and make things turn. - Transfer motion or power. - Allows mechanical advantage to adjust the whole system

Stall current

- amount of current a motor will draw when it is stalled (amp) - sum of all motor stall currents.

Free current

- amount of current a motor will draw when it is under no load (amp) - sum of all motor free currents.

Stall torque

- amount of load placed on a motor that will cause it to stop moving (N*m) - sum of all motor stall torques

Free speed

- maximum rotational speed a motor will run at when it is under no load (RPM) - same no matter how many motors

Driven gear

Gear that moves as a result of the motion of the driving gear. the output gear. The gear that work is being done on.

Lever equations

Levers = output length / input length No units

Pitch

- the distance between corresponding points on successive teeth (measurement of the tooth itself). - Pitch is measured about halfway between root and tip of tooth.

Common gear ratios

12, 36, 60, 84

Fundamental Law of Gear-Tooth Action

2 teeth (one from each gear) act at the contact point K. All action is driven from one point

Gear Train

A connected set of rotating gears that transmits power from an input to an output and can have any number of gears in a single row

What kind of shaft does VEX use?

A four-sided polygon (square) shaft as part of its motion system. This means that the shaft will transfer torque directly to anything which has a matching square hole. This square shaft also has rounded corners, which allow the shaft to spin freely in a larger-size round hole.

Gear reduction is seen as?

A fraction that is often reduced to simplify the expression.

Why is it necessary to use gear ratios

A motor that is very fast but has only a little bit of torque would not be suitable to lift a heavy load It is necessary change the outputs to a more appropriate balance of torque and speed.

Gear reduction equation

Gear reduction = (Driven gear teeth) / (Driving gear teeth) (No math, just ratio) No units

How can mechanical power be transmitted?

Across large distance in a variety of ways. Unit will focus on mechanical energy in the form of rotational motion.

Gears

Another method of mechanical power transmission. 7 common types.

Crown Gears

Are a type of bevel gear in which the teeth project perpendicular to the gear face. They can mesh with other bevel gears and spur gears so that motion is transferred between shafts with intersecting axes of rotation.

Bevel Gears

Are conically shaped, and transmit power between shafts that have intersecting axes of motion. They can transmit power between shafts at a variety of angles, but are most commonly used to transmit power 90-degrees.

Compound gear reduction equation

Compound Gear Reduction = Gear Reduction 1 x Gear Reduction 2

What is a series of a number of gears fixed together called?

Compound Gears.

Cycloid

Consists of 2 separate curves; type of gear we see in clocks.

For gears of the same pitch Tooth count and diameter are what?

Directly proportional

The only gets that matter in a series are the ____ and ____ gears

First Last

What are the motor specifications?

Free speed Stall torque Stall current Free current.

Gear ratio equation

Gear ratio = (Driving gear teeth) : (Driven gear teeth) (No math, just ratio) No units

Motor specifications

Important information on how the motors behave. all motors are different and have different properties based on their type, configuration, and manufacture

More teeth is equal to

Larger diameter

What is the process of changing the direction the gear is turning?

Motion reversal

Is there one point K for each gear, or are there mutiple points?

Multiple; there is a point K for each individual gear.

An example of a epicyclic/planetary gear

One might use the sun gear as the input and the planet carrier as the output while the ring gear is held stationary, or one might use the ring gear as the input and the sun gear as the output while the planet carrier is held stationary.

Gears naturally turn in ____ ways

Opposite

Wheels spinning in _____ directions wont drive anywhere.

Opposite

Output speed equation

Output speed = (Input speed) / (Gear Reduction) Units is RPM

Equation for pitch

Pitch = # of teeth (z) divided by diameter (in inches) of gear (d) P = z/d No units

Gear ratios

Provides an opportunity to adjust the mechanical advantage of a mechanism. As the mechanical advantage changes, the speed of motion also changes. As work increases speed decreases

A _____ connects the pairs of gears.

Shaft/axel

Sprocket and Chain

Similar to gears, can be calculated by counting their teeth. Find gear ratio and reduction the same way

Steps of finding gear ratio

Step 1: Find torque Step 2: Find torque load Step 3: Find gear reduction Step 4: Determine gear ratio

Equation for torque load

T motor = T stall x (i max - i free) / i stall - i free T motor - torque at max allowed current i max - maximum allowed current draw T stall - stall torque i free - motor free current i stall- motor stall current.

Tooth profile

The curve made by the shape of the tooth

What happens if one single gear in the system is broken?

The entire system is defunct and can't work

Idler gears don't affect what?

The gear ratio between input and output shafts. Gear ration or gear reduction, regardless of the number of teeth they have. Size and number of idler gears don't matter, they just transmit power.

Pressure angle (α)

The leaning angle of a gear tooth

The larger diameter the gear, then?

The longer levers

Spur Gears

The most common type of gear. When most people think of gears, they think of this one. They transfer motion between two shafts running parallel to each other. Are characterized by their teeth, which are straight and parallel to the gear's axis of rotation. These are the primary form of mechanical power transfer used in the VEX Robotics Design System. In addition, they are found in the real world in everything from automobiles to the mechanism that opens the tray on a DVD player.

Power Transmission

The transfer of energy from its place of generation or storage to a location where it does work. Transmits power from one shaft to another. Usually associated most with electrical power transmission. Usually performed with overhead lines

Compound gears

There are multiple gear pairs. Each pair has its own Gear Ratio, and a shared axle connects the pairs to each other. The resulting Compound Gear system still has a Driving Gear and a Driven Gear, and still has a Gear Reduction

Rack Gears

They are mounted to a straight rod, such that it moves in a linear fashion when torque is applied to it by a spur gear (known as the pinion gear). They are commonly used to convert rotational motion to linear motion. Cars utilize this type of gear set to convert the rotary motion of a steering wheel into a linear left/right motion required to steer the car. Within competition robotics there are many applications where they can be used to create linear actuators for driving mechanisms.

Worm Gears

They come in pairs: has gears and wheels that mate together to transfer power between perpendicular shafts that have axes of rotation offset from each other. They resemble screws; as they spin, they turn their mating worm wheel. This type of gear pair is very useful for creating a high mechanical advantage in a small form factor. In this type of gear pair, they can drive the worm wheel forward, but it is very difficult to do that in a the reverse. For this reason, these gears are useful for applications where the designer doesn't want a mechanism to be back-driven.

Epicyclic (Planetary) Gear

They consists of one or more planet gears moving along an outer ring gear as a central sun gear drives them. As the they are driven, they typically move a planet carrier plate along with them. They can be used in a variety of ways with different gears serving as the inputs and outputs. The overall mechanical advantage of this gear set changes depending on the configuration used.

Belt and Pulley

They don't have teeth, but their ratio can be calculated by comparing their diameters and radius. Find gear ratio and reduction the same way.

Helical Gears

They resemble spur gears, only their teeth are curved in the shape of a helix. These gears can be used to transmit power between two parallel axes of motion, or between perpendicular non-intersecting axes of motion.

What is the purpose of motion reversal?

To get two gears (the driver and the driven gear) to go in the same direction. Gears naturally go opposite ways.

Applied torque on the center of rotation equation

Torque = Force x Distance from Center of Rotation Units: Nm

Output torque equation

Torque = Input Torque x Gear Reduction Units: Nm

Large Gears driving small Gears result in a?

Torque decrease and a speed increase.

Shafts

Transfers motion from point to point along their axis of motion. (Ex.) the drive axle of a car. Power is transferred into shafts via keys, splines, or polygonal shafts.

Gears can what?

Transmit power from one part of a machine to another. Help a car move

Idler gear

Used to make the output (driven) gear spin in the same direction as the input (driving) gear. Can be useful, especially for spanning long distances.

What do you do if the Gears you are using have different sized and/or shaped teeth?

You have to get a new gear

Designs sometimes require what?

certain speeds, which motors must be geared up or down to achieve.

DC motors sometimes have?

current limits they must stay under or other load limits

Gears can provide what?

gear reduction in motorized equipment

Driving Gear

gear that intimates the motionof the other gears, it is usually connected to a power source such as a motor.

Adjustments to the mechanical advantage are

important to the design of DC motor systems

Gear

one of a set of toothed wheels that work together to create movement in an object

Gear tooth

part of the gear that mates/clings with other toothed parts of a gear to transmit torque

Pitch point

point of contact of the pitch lines of two gears

(Ex) Gears in a car can transmit what?

power from the crankshaft to the driveshaft

Gear ratios

ratio of the number of rotations of a driver gear to the number of rotations of a driven gear

Diametral pitch

the number of teeth of a gear per inch of its pitch diameter

For two Gears to mesh, they must?

they must have the same size and shape teeth on the same ratio of spacing.

Torque

torque = force x distance Linear force at the edge of a circle Units is in Nm

Torque Load

torque the motor inputs to gears