Machines

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Simple and Compound Machines

From the six simple machines to complex kinematic linkages,

every engineer needs to be familiar with the basics of machinery

movement. If your knowledge base requires refreshment, this fact-

filled, illustrated eBook — Simple and Compound Machines — presents

a colorful and enlightening reminder of how machines do their work. The

following topics are covered: Kinematic linkages, transducers, simple

machines, rotary-to-linear conversion, and drive mechanism basics.

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Simple and Compound Machines table of contents

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4Six simple machines: No matter how complex, all

machines are based on one or more simple machines that

change the direction or magnitude of an applied force.

Simple machines include the lever, wheel and axle, pulley, inclined

plane, wedge, and screw.

6Kinematic linkages: Connecting linkages at joints form

mechanisms, the building blocks of higher systems and

machines. Kinematics, first coined by Andre Marie Ampere

from the Greek word cinematique for motion, is the study of this

motion without regard to forces.

8The ultimate map of transducers: Here we map the

family of motion devices that convert energy to and from

four common forms: Fluidic, mechanical translational,

mechanical rotational, and electrical.

10 Drive mechanisms: There’s more than one way to

drive a load. What’s best depends on what you’re

trying to do.

12Rotary to linear motion: Ballscrews, threaded

shafts, and belts are among the most commonly used

elements to convert rotary motion to linear motion.

Each fits specific application needs for speed, accuracy, life, and

cost — and affects a system’s frequency response.

prised of Massachusetts' Green Egg Robotics Club, Washington's W.A.S.A.B.I. 2 and Ontario, Canada's Simbotics teams.

The Middle School Champion represented an alliance of China teams from Sichuan Chengdu Longjiang Road Primary School and the Shanghai Luwan Teenagers Activity Center.

The College Championship title went to Massey University from New Zealand. In addition, one team from each of the three divisions was pre-sented with an Excellence Award, the highest honor in the VEX Robotics Competition, given to the team with the most well-rounded VEX Robotics Program. Middle School, High School and College Excellence Award winners included, the VEXMEN: NightCrawler team from Downingtown Area Robotics in Downingtown, Pennsylvania, the Cheesy Poofs from Bellarmine College Prep in San Jose, California, and Massey University in New Zealand.



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Wheel and axle This device consists of a wheel attached to an axle where torque applied to the wheel winds a rope or chain onto the axle. It’s a lever in principle, but it can move a load farther than a lever can. In a winch, the rope that carries a load is wrapped around the axle. A light force applied to a crank handle on the side of the wheel creates torque about the axle centerline (the fulcrum) to lift a heavy load.

Inclined plane The inclined plane is a flat object positioned at a slope or incline to aid in lifting. Consider the difficulty in trying to lift a 200-lb load up into the rear of a truck. But placing a 10-ft plank from the truck to the ground lets you slide the load up into the truck easily. The inclined plane principle is used in conveyors.

Lever A lever consists of a bar pivoted on a support or fulcrum, and used to increase an applied force. In a first class lever, such as a crowbar, the fulcrum is between the load and applied force. In a second class lever, such as a wheelbarrow, the load lies between fulcrum and force. In a third class lever, the force is between load and fulcrum.

Wedge The wedge is an adaptation of the inclined plane. It is thick at one end and tapered to a thin edge at the other for insertion in a narrow crevice. It can raise a heavy load over a short distance, tighten an assembly, or split a log when driven by a hammer. The smaller the angle of the thin end, the less force is required to raise a load. Shaft locking devices use the wedge principle.

Pulley Resembling a wheel and axle, a pulley has a rope or belt that passes over it to lift a load. A fixed pulley attached to a support changes the direction of a force. This makes it easier to lift a load by pulling down on a rope and using body weight as an assist. With a movable pulley, a rope

supported at one end wraps around the pulley and is pulled up at the other. Pulling upward lifts the load (and

pulley) with only half the effort -- the support gives the added effort. In another form, pulleys drive a belt or chain.

Screw The screw is an inclined plane cut in a spiral around a cylinder. A jackscrew, used to raise large structures, combines the usefulness of both the screw and lever. The lever turns the screw, and only a small effort is needed to raise a heavy load. Screws also provide linear motion in ball screws and screw conveyors.

Machines consist of elements,

such as gears and bearings, that

work together to transmit force

and produce work. No matter how

complex, all machines are based

on one or more simple machines

that change the direct ion or

magnitude of an applied force.

Simple machines include the lever,

wheel and axle, pulley, inclined

plane, wedge, and screw.


UpBrushing

Six simple machines



Fourbars are so prevalent because of their simple elegance; they

contain the fewest parts while still returning a degree of freedom.

Capable of many types of motion, possible forms include the sliders,

cranks, and rockers.

Spring-loaded structure

StructureRoller mechanism

Fourbar mechanism

Cam

Geneva mechanism

Crank

Helical joint

Dx

Du

Du

Pin joint Roll or slide joint

Slider joint

Fourbar family

Du

0 degrees of freedom 1 degree of freedom

Exchanging actuators for linkage constraints is common

practice when building robots with multiple degrees of freedom.

The resulting motion is more complex but comes at a cost.

Fivebar mechanism

Spherical joint

Dx

Pin-slot joint

Cylindric joint

Du

Dy

Planar joint

Du

Du

Du

DcDf

Joints with two degrees of freedom are also known as half-joints.

Dx

Dx

2 degrees of freedom 3 degrees of freedom

Connecting linkages at joints form mechanisms, the

building blocks of higher systems and machines. The

mobility of any mechanism can be quantified by its

degrees of freedom, which is defined as the number of

inputs needed to fully control output motion.

Any link floating in a plane has three degrees of freedom. Adding linkages to a system tends to increase degrees of freedom, while engaging or

grounding their joints tends to have the opposite effect. Considering links in three-dimensional space is more cumbersome and less common; a

link floating in space will have six degrees of freedom.

The Kutzbach modification determines a system’s degrees of freedom as Greubler’s equation does, but makes working with grounded links and half-joints easier:

M = 3(L-1) - 2F - Hwhere M is the degrees of freedom, L is the number of links, F is the number of full links, and H is the number of half links.

The Grashof condition determines whether a fourbar contains a link capable of full revolution or only partial rotation:

S + L ≤ X + Ywhere S is the shortest link’s length, L is the longest link’s length, and X and Y are the remaining links’ lengths. When the condition is met with both sides equal, full linkage revolution will be possible, but at two positions the output will be indeterminate.

Let freedom ring

Sometimes a set of links can be connected into different

isomers to give different motion. For an isomer to be

valid, the degrees of freedom cannot be concentrated in a

subchain.Stevenson’s sixbar

Watt’s sixbar

Kinematics, first coined by Andre Marie Ampere from the Greek word cinematique for motion, is the study of this motion without regard to forces. Because every input requires an actuator and must be coordinated with other inputs, keeping system complexity and degrees of freedom as low as possible helps keep cost low too.


Freedom FightersgreublerKutzbachgrashoF

Kinematics



Electrical

MechanicalrotationalCouplings

Brakes and clutches

Solenoids

Sprockets, chains, belts,and pulleys

Ballscrews, lead screws,and screw jacks

Gears

Air motors

Rack and pinion sets

Cylinders

Bearings and bushingsSeals

Shafts

Rings and springs

Motors

Gear lubes

Fluidic

Bushings, or journal bearings, are sleeves that transmit load by sliding on an oil film. In anti-friction bearings rolling, load-carrying elements carry axial and radial loads on a shaft. Application considerations: Though negligible compared to that of bushings, roller bearing starting friction is still twice running friction.

Rings and springs hold components on shafts or in a housing. Under constant loading, both can also act as spacers to compensate for radial and axial dimensional variation and to isolate vibration. Application considerations: Rings and springs increase precision and predictability of load-deflection curves. By taking up additional clearance in bearings andother components, springs also decrease wear and increase life. Other uses include oil dam and oil slinger ring.

Couplings connect shafts to transmit torque and angular velocity while allowing for some misalignment. Application considerations: Couplings can be used to tweak system dynamics. Metallics are torsionally stiff and impart high natural frequencies to systems, while elastomeric servo-insert couplings have natural frequencies below operating points to absorb motor excitation. Windup varies from about 0.05 with bellows, up to 5 with beam couplings.

Coil current produces a magnetic field that draws a plunger into an iron C-shaped stack, which further intensifies magnetic flux and solenoid force. Cutting current lets the plunger retract; a spring usually helps this along. Application considerations: To stem noise and increase holding power, sometimes additional windings, or shading coils atop the C-shaped stack, magnetically latch onto the plunger. Cycling too quickly can cause detrimental heat buildup; insulating steel laminations help here.

Belts and chains pass around pulleys and sprockets to transmit rotation or traverse loads. Application considerations: Belts offer the highest operating speeds, but low repeatability and positioning accuracy. They dampen shocks and convert more than 90% of motor energy to thrust, but tensile strength limits thrust and increases backdriving. Though louder than belts and restricted to one plane, chains stretch less and typically operate longer.

Compressed air pushes pistons, vanes, gerotors, or turbines for continuous rotary power. Application considerations: Useful in volatile atmospheres, they have higher power densities than electric counterparts, but at higher operating costs due to the need for compressed air.

A driving gear engages another with infinite radius to advance a load. Application considerations: Most error comes from racks. Though rugged and efficient, they induce backlash,require brakes for vertical mounting, and are limited in speed by mass and length. Rack and pinion benefits include economical, light open-loop actuation for accurate drives.

Pressurized fluid floods a barrel, causing a piston and attached rod (or load) to advance or retract. Fluid pressure and flow is converted into force and velocity. Application considerations: Drawbacks of complex installation and possible leakage are offset by cylinders’ high force linear motion (to 20,000 psi stress at rated system pressures).

Gaskets fill space between two clamped components, while elastomeric static seals rest in grooves on one component or the other ensure tight mating. Mechanical packing, contacting radial lip,as well as non-contacting labyrinth and visco seals are dynamic seals that keep lubricants in and foreign particles out. Placed between components that move relative to one another, they are subject to wear and dynamic forces. Application considerations: Special textures and helices on dynamic seals can actually pump lubricants back to their origin. Nitrile seals are low in cost; neoprene is weather-resistant; and ethylene propylene resists even powerful acids and alkalis. However, excessive heat causes most synthetics to dry, crack, and fail.

A moving magnetic field produced in the coils (stator) of a electromagnetic machine opposes a current or magnet-induced field surrounding a moving element (rotor) — causing it to turn. Servo-driven ac and dc motors provide self-correcting closed-loop control, using work as the controlled variable. A stepper-driven motor doesn’t operate continuously; rather, it pulses in a "meter as you go" (usually) open-loop motion. Application considerations: All dc motorsride smoothly down to zero, and even when switching directions. Generally speaking, ac induction motors are powerful constant-speed motors suitable for industrial use. Common dc brush motors (and their expensive, more reliable brushless cousins) are suited for closed-loop servo use.

Oil or grease coats gears to prevent tooth-to-tooth contact. Application considerations: Only a small amount keeps gears lubricated, but larger volumes are needed for heat removal. Most commonly used greases can break down into oil and thickener components when temperatures run too high.

Clutches engage and disengage an output shaft to transfer torque from an input shaft. Brakes stop and hold loads. Both can be electrically, fluidically, mechanically, or self-actuated. Application considerations: Electric brakes are more conveniently controlled and can cycle quickly: up to 1,600 cpm in some cases. Air-actuated, the most common brake and clutch type, produce little heat and maintain grip with minimal power. Disc, drum, and cone friction brakes are good emergency brakes because of their failsafe holding.

Threaded nut or ball circuits travel a threadedscrew. Application considerations: Ballscrews convert more than 90% of motor torque to thrust, allowing use of small gears, clutches, and drive motors. Maximum speed depends on critical screw speed and ball recirculation speed. Jack screws have lower efficiency, converting 30 to 50% of motor torque to thrust. Remaining energy dissipates as heat, with duty cycles up to 50%. On the other hand, jack screws are locking, quiet, and have a high tolerance for shock loads.

Axles support rotating members; shafts accept and drive gears, pulleys, and sprockets. Application considerations: Overly ductile shafts can deflect andmisalign. Operation at critical speed induces resonance and allows centrifugal forces to exaggerate eccentricity, possibly to failure. When rates beyond critical speed are required, quickly moving through it helps. Stepped geometries to accommodate gears and pulleys (and restrict axial displacement) are local stress intensifiers and potential fatiguing trouble spots.

Mechanicaltranslational

Gears on input shafts engage variously sized gears to change direction, torque and speed — usually for slower, more forceful motion. Application considerations: Spur, helical, and bevel gears average about 98% efficiency, while worm gear efficiency can dip to 50%. Bending fatigue in tooth root fillets and contact fatigue on tooth surfaces limit life. Though gear drives are rugged, they require lubrication and can induce backlash.

The ultimate map of motion transducers




Direct drive

Cam drive

Screw drive

Load Load

Load

Motor

Coupling

Motor

Motor

Gear drive

Load

Drive

Motor

Pros & cons3 High reduction ratio3 Rugged7 Backlash7 Lubrication needs

Belt or chain drive

Load

DriveMotor

Pros & consBelt drive3 No lubrication3 Low cost7 Belts slip and stretch7 Lubrication needs

Pros & consChain drive3 Rugged3 No slipping or stretching7 Noisy7 Low speed

Pros & cons3 Simplicity3 Speed and precision7 Low inertia7 Mounting limitations

Pros & cons3 Speed and precision3 Rugged7 Must be customized7 Short travel

Drive

Drive

Pros & cons3 Rugged3 Low cost7 Low efficiency7 Backlash

The following illustrations are a reminder that there’s more than one way

to drive a load. You can use gears, belts, cams, screws, or even a rack-

and-pinion. What’s best depends on what you’re trying to do. If you

want to achieve, say, a complex cyclic motion in a nasty environment,

you might consider using a cam. If simplicity is the goal and you have a

relatively low-inertia load, direct drive may be the answer to your needs.

Rack-and-pinion

Load

Motor

Pros & cons3 Rugged3 Efficient7 Backlash7 Needs brakes for vertical mounting

Drive


Drive mechanisms



Rotary to linear motionBallscrews, threaded shafts, and belts are among the most commonly

used elements to convert rotary motion to linear motion. Each fits

specific application needs for speed, accuracy, life, and cost. Also,

each affects a system’s frequency response through backlash or

torsional and axial stiffness.

Operation: A toothed belt attached to a carriage passes around a pulley in each end of an actuator. A carriage, joined to the belt and supported by a linear bearing system, is pulled back and forth along the length of travel. Application considerations: Offers highest operating speeds, but low repeatability and positioning accuracy. Converts more than 90% of motor energy to thrust. However, tensile strength of transport belt limits thrust capability, and it backdrives easily.

Timing belt

Operation: One or more circuits of recirculating balls roll between the ballnut and threaded screw. Application considerations: Converts more

than 90% of motor torque to thrust, allowing use of small gears, clutches, and drive motors. High positioning accuracy and repeatability, with duty cycle to 100%. Maximum operating speed depends on screw’s critical speed and ball

recirculation speed. There’s a tendency to backdrive, so you may need a brake or holding device. Plus, they can be noisy and they have a low tolerance for shock loads.

Ballscrews

In-line reciprocator

Operation: In a simple reciprocating device, the input and output shafts are in line with each other. Rotating the input crank causes the second link to oscillate, resulting in the output shaft moving back and forth in linear motion.

Rolling-ring device

Operation: Two or more rings, suspended through ball bearings, are held at non-ninety degree angles on a smooth shaft. The shaft rotates the bearings in the rings, resulting in the rings moving linearly along the shaft.Application considerations: Low friction and noise. Some models backdrive easily, but a third ring can be used to control this. Very high speed, can double that of ballscrew systems. Converts about 90% of energy into motion.

More on




Acme screws

Operation: Threaded plastic or bronze solid nut slides along thread-ed screw. Application considerations: Con-verts 30 to 50% of motor torque to thrust. Remaining energy dissipated through heat and friction. Duty cycle can be up to 50%. Plus, these devic-es are self-locking, quiet, and have a high tolerance for shock loads.

Cycloid gear mechanism

Adjusting handle

Worm gear

Ring gear

Planet gear

Connecting rodOperation: Adjustable ring gear meshes with worm gear for infinitely variable stroke length. Rotating inside the ring gear is a planet gear that is half the ring gear’s diameter. One end of the connecting rod is pinned to the planet and moves back and forth as the gear rotates in the ring.

Pin


Have you seen the newest products launched by AutomationDirect? Now you can watch short videos with product descriptions, features and tips. Our new “KICKSTART” video program can be found on our Learn site. Check out these short two-minute videos on products such as our new compact air cylinders, coiled air hoses, compact fuse switches and more.

Visit http://learn.automationdirect.com and look for the Kickstart tab along the top.





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