GEARS
Robot Gears By using different gear diameters, you can exchange between rotational (or translation) velocity and torque. by looking at the motor datasheet you can determine the output velocity and torque of your motor. In robotics you want more torque than speed for better handling and control.
Different types of gears Spur gears Idler gears Worm gears Bevel gears Belts & Pulleys
Essential Terminology Driver gear with applied force Follower gear doing useful work Idler gear turned by driver & turns follower Gear Train many gears in a row Geared Up large driver, small follower to speed gear train up. Geared Down small driver, large follower to increase torque (turning force) Compound gears combination of gears and axles where one axle has 2 gears often of different sizes.
Basic Gear Properties When 2 gears mesh, driver makes follower turn in opposite direction Need odd number of idler gears to make driver and follower turn in same direction. Need 0 or even number of idlers to make driver and follower turn in opposite direction When large driver turns small follower, its called gearing up and speeds up gear train When small driver turns large follower, its called gearing down and increases torque (turning force).
Gear Geometry Radius D + Radius F Driver Follower
QUESTIONS: A B motor Which gear is the driver (A or B)? Which gear is the follower (A or B)?
ANSWERS A B motor Which gear is the driver (A or B)? A Which gear is the follower (A or B)? B
QUESTIONS motor wheel A B C Which gear is the follower (A, B, or C)? Which gear is the driver (A, B, or C)? Which gear is the idler (A, B, or C)?
ANSWERS motor wheel A B C Which gear is the follower (A, B, or C)? C Which gear is the driver (A, B, or C)? A Which gear is the idler (A, B, or C)? B
Direction follower even number of gears: driver & follower turn in opposite directions driver odd number of gears: driver & follower turn in same direction driver follower follower driver
QUESTIONS driver Would the follower gear move clockwise or counterclockwise?
ANSWERS driver Would the follower gear move clockwise or counterclockwise?
QUESTIONS driver Would the follower gear move clockwise or counterclockwise?
ANSWERS driver Would the follower gear move clockwise or counterclockwise?
Geared Up large driver turns small follower increases speed decreases torque (turning force) follower driver driven gear follower gear
Geared Down small driver turns large follower increases torque (turning force) decreases speed driver follower driven gear follower gear
Gears (Spur) Meshing Horizontally 1 2 3 4 5 Possible to mesh at stud lengths of 1 through 5
Spur Gears Most common type of gear, a wheel with teeth. beam axle (put bushings on the back side) Spur gears do three things. 1. Change rot. speed 2. Change torque 3. Change direction 8 tooth gear 40 tooth gear Make sure there isn t too much friction between the gears and the beam. The gears should spin easily.
Gears (Spur) Meshing Vertically 2 4 Using 24 tooth and 8 tooth at distance of 2 stud lengths Using 24 tooth and 40 tooth at distance of 4 stud lengths Mesh at even stud lengths for best results
NOMENCLATURE OF SPUR GEARS See Gears Kinematics Reference for more information
NOMENCLATURE. Pitch surface: The surface of the imaginary rolling cylinder (cone, etc.) that the toothed gear may be considered to replace. Pitch circle: A right section of the pitch surface. Addendum circle: A circle bounding the ends of the teeth, in a right section of the gear. Root (or dedendum) circle: The circle bounding the spaces between the teeth, in a right section of the gear. Addendum: The radial distance between the pitch circle and the addendum circle. Dedendum: The radial distance between the pitch circle and the root circle. Clearance: The difference between the dedendum of one gear and the addendum of the mating gear.
NOMENCLATURE. Face of a tooth: That part of the tooth surface lying outside the pitch surface. Flank of a tooth: The part of the tooth surface lying inside the pitch surface. Circular thickness (also called the tooth thickness): The thickness of the tooth measured on the pitch circle. It is the length of an arc and not the length of a straight line. Tooth space: pitch diameter The distance between adjacent teeth measured on the pitch circle. Backlash: The difference between the circle thickness of one gear and the tooth space of the mating gear. Circular pitch (Pc) : The width of a tooth and a space, measured on the pitch circle.
What happens with improper mesh? When 2 gears are meshed, there is a certain amount of built in play between them called backlash. When 2 gears are not meshed properly i.e. within specification you get too much backlash called slop OR too little backlash and they are jammed together and this creates friction.
Gears (Spur) Meshing Diagonally Slop or friction typically occurs when you make gears mesh diagonally Some Schools of Thought 1. Don t do it as it makes gears out of specification and something may go wrong e.g. gear teeth skipping 2. Do it as it gives you more creativity in meshing gears in different configurations. 3. Do it but within some tolerance e.g. under 1%
What is the best type of gear teeth? Gears need to have teeth that mesh properly otherwise they will not work. Best is a curve on the teeth that provides for constant velocity when gear turning Involute curves modeled on the teeth provides this advantage and is the basis for most modern gears.
Gear Tooth Geometry The involute curve can be generated by wrapping a string around a circle. Ideal Gear Tooth Shape
MESHING OF GEAR TEETH
Gear Ratio In order to determine what a gear will do for us, we must quantify it. Best measure is the gear ratio. Gear Ratio = number of teeth in follower number of teeth in driver G.R. = F t / D t e.g. ⅓ or 1:3 (read as 1 to 3) Interpret above as one turn of driver will turn the follower 3 times.
What is the gear ratio? 84 tooth driver 60 tooth follower
What is the gear ratio? Show Videos driver follower 5 to 7 or 5:7 follower teeth 60 teeth gear ratio = = = driver teeth 84 teeth 5 7
Idler Gears An idler gear is a gear that is inserted between 2 other gears. idler gear 8 tooth gear to the right of the 40 tooth gear. How many turns of the 8 tooth gear on the left does it take to make 1 turn of the new 8 tooth gear on the right?
Idler Gears Answer: 1! It s as if the 8 tooth gears are meshed together. Idler gears DO NOT change the gear ratio. Idler gears DO make both 8 tooth gears rotate in the same direction, add spacing between gears.
Long Gear Trains The gear attached to the motor is the driver. The gear doing work is the follower. All in-between gears are idlers. Ignore the idler gears! Driver Follower Gear Ratio = 24 / 40 = 3 / 5 3 turns of the 40 tooth gear will turn the 24 tooth gear 5 times. Idlers
Compound Gears (Multiple Gears on One Axle) 1. Pair up drivers and followers 2. Start a new driver/follower pair if an axle has a second gear attached. 3. Multiply the gear ratios of all the driver/follower pairs. D 2 Gear 1 = 12 teeth Gear 3 = 12 teeth Gear 2 = 36 teeth Gear 4 = 60 teeth
Compound Gears (Multiple Gears on One Axle) 1. Pair up drivers and followers 2. Start a new driver/follower pair if an axle has a second gear attached. 3. Multiply the gear ratios of all the driver/follower pairs. Gear 1 & Gear 2: follower driver = 36 12 = 3 1 D 2 Gear 1 = 12 teeth Gear 3 = 12 teeth Gear 2 = 36 teeth Gear 4 = 60 teeth
1. Pair up drivers and followers Compound Gears (Multiple Gears on One Axle) 2. Start a new driver/follower pair if an axle has a second gear attached. 3. Multiply the gear ratios of all the driver/follower pairs. Gear 1 & Gear 2: follower driver = 36 12 = 3 1 Gear 1 = 12 teeth Gear 3 = 12 teeth D 2 Gear 2 = 36 teeth Gear 4 = 60 teeth Gear 3 & Gear 4: follower 60 = = driver 12 3 1 x 5 1 = 15 1 5 1 Multiply the gear ratios:
1. Pair up drivers and followers Compound Gears (Multiple Gears on One Axle) 2.Start a new driver/follower pair if an axle has a second gear attached. 1. Multiply the gear ratios of all the driver/follower pairs. Gear 1 & Gear 2: follower driver = 36 12 = 3 1 Gear 1 = 12 teeth Gear 3 = 12 teeth D 2 Gear 2 = 36 teeth Gear 4 = 60 teeth Gear 3 & Gear 4: follower 60 = = driver 12 3 1 5 1 = 15 1 5 1 Multiply the gear ratios: 15:1
Calculate the Gear Ratio (Assume the last axle does the useful work) 60t 36t 12t 12t 12t 36t 1 2 3 4
Calculate the Gear Ratio (Assume the last axle does the useful work) Pair 1: 12t 36t 12t 60t follower driver = 36 12 = 3 1 12t 36t 1 2 3 4
Calculate the Gear Ratio (Assume the last axle does the useful work) 12t 12t 36t 12t 36t 1 2 60t 3 4 follower driver = 36 12 Pair 2: follower 36 = = driver 12 Pair 1: 3 = 1 3 1
Calculate the Gear Ratio (Assume the last axle does the useful work) 12t 12t 36t 12t 36t 1 2 60t 3 4 follower driver = 36 12 = Pair 2: follower 36 = = driver 12 Pair 3: follower 60 = = driver 12 Pair 1: 3 1 3 1 5 1
Calculate the Gear Ratio (Assume the last axle does the useful work) 12t 36t 12t 60t follower driver Pair 2: 36 = 12 Pair 1: 3 = 1 12t 36t 1 2 3 4 follower = driver Pair 3: 36 12 = 3 1 follower driver = 60 12 = 5 1 Multiply the gear ratios: 3 1 3 1 5 1 = 45 1 45:1
Clever 2-Speed Transmission!
Calculate This: 60 tooth 36 tooth 60 tooth 36 tooth 60 tooth 60 tooth Is this transmission currently geared up or down? geared down What is the current gear ratio of this transmission? 60:36 = 5:3 What is the gear ratio of the other set of gears? 60:60 = 1:1
Calculate This: 60 tooth 36 tooth 60 tooth 36 tooth 60 tooth 60 tooth Is this transmission currently geared up or down? geared down What is the current gear ratio of this transmission? 60:36 = 5:3 What is the gear ratio of the other set of gears? 60:60 = 1:1
Bevel Gears Bevel gears are spur gears that mesh at a 90 degree angle. The gear ratio rules remain the same, but the axles are perpendicular to one another. These 12 tooth bevel gears can only mesh with them-selves.
Where Can You Find a Bevel Gear? Hand drill Car differential Shaft-driven bicycle The bevel gear is used to change rotational motion at a 90 angle. Using gears with differing numbers of teeth will change the speed and torque.
Worm Gears 1x6 beam 1 #6 axle 2 3 2 1x4 plates half bushing 4 24 tooth gear 1x4 beam 5 worm gear full bushing #10 axle
Worm Gears Worm gears have some special properties. 1: The axles are perpendicular, like bevel gears. 2: How many rotations of the worm gear does it take for 1 rotation of the spur gear? ANSWER: 24! The worm gear acts like a gear with 1 tooth! This gives very large gear ratios.
Worm Gears Worm gears are not back-driveable. You can turn the worm gear s axle, but you can t turn the spur gear s axle. This property is used as a locking mechanism.
Gear Analysis To analyze any gear train you need to: 1. Locate the driver gear (see force applied) 2. Locate the follower gear (see where useful work done) 3. Figure out if it is geared up or geared down (big circle turning small circle geared up) 4. Calculate the Gear Ratio using F t /D t. Use the following 3 rules for gear ratio calculation.
Rule 1 Pair up gears In the case of 2 gears, it is easy. The driver is the one driven by the motor or applied force. The follower is the one doing work. Driver Follower Gear Ratio = 8 / 24 = 1 / 3 One turn of the 24 tooth will turn the 8 tooth 3 times based on GR=F/D
Rule 2 - Long Gear Trains For many gears on different axles, driver is one connected to applied force, follower is the last one in the gear train. All others idlers. Driver Follower Gear Ratio = 24 / 40 = 3 / 5 3 turns of the 40 tooth will turn the 24 tooth 5 times based on GR=F/D Idlers
Rule 3 Compound Gears Pair up as many drivers and followers and label them D1, F1, D2, F2, etc. as needed. Note every time you follow an axle and it has a second gear attached, start a new driver. Multiply the gear ratios of all pairs of driver-follower. Based on GR=F/D D2 F2 Gear Ratio = 24 / 40 X 24 / 40 = 3 / 5 X 3 / 5 F1 = 9 / 25 D1
Speed Change The change in RPM from the input gear to the output gear is directly proportional to the gear ratio Example: 3:1 gear ratio Input gear turns at 900 RPM Output gear turns at 300 RPM
Torque Multiplication The change in torque from the input gear to the output gear is directly proportional to the gear ratio Example: 3:1 gear ratio Motor turns input gear at 900 RPM with 50 lb/ft of force Output gear turns driveshaft at 300 RPM with 150 lb/ft of force ** this is what you want in robotics, slower RPMs with more torque
Gear Types Spur gears Helical gears Bevel gears Differential gears Worm gears Planetary Gears Harmonic Drive gears
Simple Gear Train with Idler Input and Output Shafts parallel IDLER GEAR Speed is decreased Torque is increased Ratio 4:1 Flow of Power reversible Input and Output Gears same direction Without Idler Gear different direction
Where Do You Find a Simple Gear Train with Idler? Two meshed gears will rotate in opposite directions. An Idler Gear allows the drive and driven gears to rotate in the same direction. Paper Transport Rollers
90 Angle Worm and Wheel Speed is decreased Torque is increased Gear Ratio 20:1 Flow of Power NOT reversible Direction of Travel reversible
Where Do You Find a Worm and Wheel? Tuning mechanism on string instruments Electric winch A worm is used to reduce speed and increase torque. The motion is not reversible; a gear cannot drive a worm.l Allows for small precise incremental adjustments
Motor-load connection through a gear Increasing torque by using gears -
Planetary Gear Train (Epicyclic Gear Train)
Planetary Gear Train In this train, the blue gear has six times the diameter of the yellow gear The size of the red gear is not important because it is just there to reverse the direction of rotation In this gear system, the yellow gear (the sun) engages all three red gears (the planets) simultaneously All three are attached to a plate (the planet carrier), and they engage the inside of the blue gear (the ring) instead of the outside.
Planetary Gear Train Because there are three red gears instead of one, this gear train is extremely rugged. Planetary gear sets can produce different gear ratios depending on which gear you use as the input, which gear you use as the output They have higher gear ratios. Because you have an idler gear the direction is the same
Planetary Gear Train They are popular for automatic transmissions in automobiles. They are also used in bicycles for controlling power of pedaling automatically or manually. They are also used for power train between internal combustion engine and an electric motor Used to achieve large speed reductions in compact space Can achieve different reduction ratios by holding different combinations of gears fixed
Calculating Planetary Gear Ratios Direct Drive = 1:1 Carrier is output # of sun gear teeth + #of ring gear teeth # of teeth on the driving member = Ratio
Example: Electric drill includes an integrated planetary gearbox with either a 15:1 or 4.25:1 ratio. A massive 9mm thick steel ring gear supports the steel planet gears riding on hardened 5mm steel pins.
Gear Transmissions Output Shaft Two Stage, parallel shaft, helical gearset - from the SKIL electric drill Ball Bearing Bushing Input Pinion
A variant of a planetary gear Carrier 71
Planetary gears in automotive transmission 72 Planetary gears
Gear box Stick shift Synchronizers 73 The gear box is in first gear, second gear
AndyMark Toughbox 12.75:1 Ratio Options for 6:1 and 8.5:1 Long shaft option 2.5 lbs $98
AndyMark Gen 2 Shifter 11:1 & 4:1 Ratios 3.6 lbs Servo or pneumatic shifting Two chain paths Encoder included $350
AndyMark SuperShifter 24:1 & 9:1 standard ratios + options Made for direct drive of wheels 4.6 lbs Servo or pneumatic shifting Direct Drive Shaft Includes encoder $360
Instantaneous Motor Torque Stall Torque Motor Torque = - ( ) * Motor RPM + Stall Torque Free Speed When Motor RPM = 0, Output Torque = Stall Torque (stopped) When Motor RPM = free speed Output Torque = 0 (in theory) Accelerati on = Acceleration Force - Friction Resistance Robot Mass Stall Current - Free Current Current Draw = * Torque Load + Free Current Stall Torque
Where Do You Find a Crown and Pinion? Watches Carousel DVD player How many crown and pinion gears do you see in this pendulum clock?
Rack and Pinion Input Movement rotary Output Movement Linear (prismatic) Distance is 2 in. With a Larger Pinion Gear - the rack will move a longer distance Flow of Power reversible Direction of Travel reversible
Lead Screw Input Movement rotary Output Movement linear 6 Revolutions = 1 in. Flow of Power NOT reversible Force is Increased Direction of Travel reversible
Where Do You Find a Lead Screw? Jack Vice Changes rotary movement into linear movement Significantly increases force A person can put a little force into turning the handle to move a heavy car.
Cam and Follower Input Movement rotary FOLLOWER CAM Output Movement reciprocating Follower moves up and down 1 time for every revolution of the crank Flow of Power Not reversible Direction of Travel reversible
Belts & Pulleys Belts & pulleys are related to gears. They change speed and torque, but with a few differences... Pulleys transfer their force by the friction of the belts, rather than direct contact with the teeth of gears. Unlike gears, the pulleys rotate in the same direction. This can cause the belts to slip.
Belts & Pulleys Belts can transfer force across long distances. Like gears, however, belts and pulleys do have a gear ratio. It is the ratio of the diameters of the pulleys.
Pulley and Belt Input and Output Shaft parallel Speed is increased Torque is decreased Ratio 1:2.5 Flow of Power is reversible Open Belt wheels turn in same direction Crossed Belt wheels turn in opposite direction
BELTS AND CHAINS FLAT BELT DRIVES WITH PARALLEL SHAFTS
BELTS AND CHAINS FLAT BELT DRIVES WITH PERPENDICULAR SHAFTS
A. Non-slip Panther drive (Standard on H-frame style) Ideal for robot arms, in between each joint! Extremely efficient Best for operation in rain and snow Uses synchronous gearbelts and sprockets B. V-belt drive - Conventional Frame Only Very smooth and almost silent Economical 4L belts are widely available
ROLLER CHAIN TERMINOLOGY BELTS, CHAINS, AND GEARS
BELTS, CHAINS, AND GEARS SPROCKETS Notes: Set screws, shaft locking pin
Useful for arm links
BELTS, CHAINS, AND GEARS CHAIN DRIVE WITH LONG CENTER DISTANCE
REFERENCES http://www.societyofrobots.com/mechanics_dynamics.shtml http://www.societyofrobots.com/mechanics_gears.shtml
Wheels
Wheels are a Compromise (Like everything else) Coefficient of friction You can have too much traction! Weight Diameter Bigger equals better climbing and grip but also potentially higher center of gravity, weight, and larger sprockets. Forward vs lateral friction
Wheel Types Conveyor belt covered Solid Plastic Pneumatic Omniwheels
Innovation FIRST
Two Wheels - Casters Pros: Simple Light Turns easily Cheap Cons: Easily pushed Driving less predictable Limited traction Some weight will always be over nondrive wheels If robot is lifted or tipped even less dive wheel surface makes contact.
4 Standard Wheels Pros: Simpler than 6 wheel Lighter than 6 wheels Cheaper than 6 wheels All weight supported by drive wheels Resistant to being pushed Cons Turning! (keep wheel base short) Can high center during climbs Bigger wheels = higher COG
4 Wheels With Omni Wheels Pros: Same as basic four wheel Turns like a dream but not around the robot center Cons: Vulnerable to being pushed on the side when bumping into objects Traction may not be as high as 4 standard wheels
6 Wheels Pros: Great traction under most circumstances Smaller wheels Smaller sprockets = weight savings Turns around robot center Can t be easily high centered Resistant to being pushed Cons: Weight More complex chain paths Chain tensioning can be fun More expensive
Six Wheel Variants
Mecanum Pros: Highly maneuverable Might reduce complexity elsewhere in robot Simple Chain Paths (or no chain) Redundancy Turns around robot center Cons: Lower traction Can high center Not great for climbing or pushing Software complexity Drift dependant on weight distribution Shifting transmissions impractical Autonomous challenging More driver practice necessary Expensive
Holonomic Drive
Treads Pros: Great traction Turns around robot center Super at climbing Resistant to being pushed Looks awesome! Cons Not as energy efficient High mechanical complexity Difficult for student-built teams to make Needs a machine shop or buy them Turns can tear the tread off and/or stall motors
Swerve/Crab Wheels steer independently or as a set More traction than Mecanum Mechanically Complex! Adds weight
Bearings Two Common Types Bushings - simple, cheap, limited life, porous material such as Oilite which holds oil like a sponge Rolling Element support axial or radial loading, long life, grease or oil-filled, various types of seals, readily available from standard product catalogs, ex. ball bearings
Roller Bearings Needle Roller Tapered Roller Spherical Roller
Rolling Element Bearing Parts Outer Race Inner Race The parts and nomenclature for a Ball Bearing Bore Ball Cage or Separator
Bearings -continued Hydrodynamic or Sleeve - oil filled, no wear, radial or thrust, common in automobile engines (e.g., crankshaft bearings) Rotating Shaft Sleeve Bearing Shaft Rides On Oil Wedge Oil Filled Cavity A typical radial clearance is on the order of.010
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