Making Things Move: DIY Mechanisms for Inventors, Hobbyists, and Artists - Dustyn Roberts (2010)
Chapter 7. The Guts: Bearings, Couplers, Gears, Screws, and Springs
The guts of a mechanism are everything that happens between the input and output. The input is your energy source, which can range from a hand crank to an electric motor. The output is what you want to happen—does your mechanism crawl, spin, point, or shake? Maybe you need to attach a gear to your motor shaft or figure out how to make something spin with lower friction.
The components we’ll cover in this chapter are integral to being able to work through your ideas and make them into reality. The majority of them can be found through a quick search on McMaster and other suppliers I’ll point out along the way.
Bearings and Bushings
Bearings are components that are used between moving parts and stationary parts for support and reduction of friction. A bearing can be as simple as a drilled hole in a block of wood, or it can be an actual steel ball bearing, as in inline skates or skateboard wheels. You can also find bearings inside motors, where they help to support the motor shaft and keep it running smoothly.
Bearings are categorized by the kind of load they support:
✵ A radial bearing, like the type in your inline skates, supports radial loads. (Recall the illustration of radial and axial loads in Figure 1-26 in Chapter 1.)
✵ A thrust bearing handles the axial loads. You can find this kind of bearing in rotating bar stools and chairs that support your weight but still spin.
✵ A linear bearing, or slide, reduces friction in sliding components that don’t necessarily spin. You can find this type of bearing on the sides of filing cabinets and dresser drawers.
✵ A bushing (also known as a sleeve, plain, plane, or journal bearing) is a type of bearing that doesn’t have rolling elements, but still reduces friction for radial, thrust, or sliding loads. Think of a bushing as a “female” bearing—one without, um, rollers. You can find linear bushings inside machines like MakerBot’s CupCake CNC (see Figure 7-1).
The following sections cover these types of bearings in more detail and go over when and how to use each one.
FIGURE 7-1 Linear bushings on MakerBot’s CupCake CNC (image used with permission from MakerBot Industries)
The purpose of any radial bearing is to support a spinning shaft or rod and keep it running smoothly, even if things like gears and pulleys create radial loads on the supported shaft. Some radial bearings have rolling elements that reduce friction. These are called ball bearings when the rolling element is a ball, or roller bearings when the rolling element is more like a long cylinder or needle (see Figure 7-2).
FIGURE 7-2 Radial ball and roller bearings (credit: McMaster-Carr)
FIGURE 7-3 Radial bushings (credit: McMaster-Carr)
You can also find plastic and metal sleeves that have less friction than a drilled hole in a block of wood does, but aren’t quite as frictionless as ball bearings. We’ll call these radial bushings (see Figure 7-3).
Radial Ball and Roller Bearings
Your basic roller-skate bearing is a radial ball bearing and is by far the most popular type. It’s easier to understand and find bearings for your projects if we go over a bit of bearing anatomy and vocabulary first (see Figure 7-4).
FIGURE 7-4 Bearing anatomy
✵ Outer diameter The outer dimension of the bearing.
✵ Outer race/ring The short cylindrical part outside the rolling elements.
✵ Inner race/ring The shaft you use should fit snugly into the inner diameter of the bearing, so the shaft and inner race rotate together.
✵ Inner diameter Also called bore size, bore diameter, or just for shaft size in reference to the size shaft it is designed to fit over.
✵ Ball/roller The spherical or cylindrical rolling elements, usually made of hardened steel.
✵ Width The thickness of the bearing.
✵ Cage/separator/spacer/retainer (optional) This helps keep balls separate so they don’t run into each other. Bearings without cages where the balls can roll around without constraint are called full-complement bearings.
✵ Seal or shield (optional, not shown) Some bearings are open so you can see all the rolling elements, and some have one or more seals or shields to stop gunk from getting into the bearing.
Here are a few more useful bearing vocabulary terms:
✵ ABEC rating Sometimes bearings are rated with an ABEC number. ABEC stands for Annular Bearing Engineers Committee. The ABEC rating ranges from 1 to 9 (in odd numbers) and is a measure of precision. The higher the ABEC number, the more precise the bearing, and of course, the more expensive it is. More precision generally leads to longer life from less friction and wear, faster spinning, and more reliable performance. For reference, skateboard and Inline skate wheels are normally equivalent to ABEC-3.
✵ Revolutions per minute (rpm) This is how fast you expect your bearing to be spinning. If you can estimate this, you can use the number to narrow down your options on sites like McMaster that ask for an rpm range. Their ranges are generally really high— maybe 15,000 rpm—so will rarely make or break your design. You should always buy bearings that are rated for many more rpms than you need.
✵ Static load and dynamic load You might see options for static load, dynamic load, and dynamic radial load capacity ranges on sites like McMaster and Stock Drive Products (www.sdp-si.com/estore) when you look for bearings. Static load is how much the bearing can handle while not moving, like the bearings in your inline skates if you’re just standing still. This radial load acts perpendicular to the axis on which the bearing rotates. Dynamic load is how much the bearing can handle while moving. For example, you wouldn’t use bearings on your inline skates with a dynamic load rating of 10 lbs if you weigh 200 lbs. Dynamic load ratings are usually more than twice the static load ratings.
NOTE Bearings can handle more load when they’re spinning because more of the rolling elements are sharing the load. When a bearing is not moving, all the load is concentrated on just a few rolling elements, so is more likely to cause wear and dimples in the bearing material.
Ball bearings are the best choice when you have high speeds and light to moderate loads, as in skateboards and inline skates. Each ball only contacts each race (inner and outer) at one point, so there is very little rolling friction. Roller bearings can handle heavier loads, since the weight spreads out over a line along a cylinder and not just a point on a ball, but friction is slightly higher than in ball bearings because of this extra contact. Needle roller bearings have rolling elements that are longer and thinner than cylindrical bearings. They are useful when radial space is limited.1
To use a bearing properly, you want one race of the bearing to stay still while the other one moves. Generally, you install bearings on smooth shafts, but it’s possible to install a bearing on a snug-fitting threaded rod as well. Although unconventional, this does secure the inner race to the rod so they rotate as one. Figure 7-5 shows an example of a bearing installation where the outer race will be held stationary while the inner race spins with the threaded rod.
FIGURE 7-5 Installing a bearing on a threaded rod (images used with permission from MakerBot Industries)
You can also install a bearing so the inner race stays still and the outer race moves. This is how inline skates and skateboard wheels are mounted. The inner races are squished together, while the outer races fit snugly into a plastic wheel, so the wheel and outer race of the bearing rotate together (see Figure 7-6).
FIGURE 7-6 Bearings in inline skates mounted so inner races are clamped while outer races are free to spin
Radial bushings are a better choice for low speeds, light loads, or when precision frictionless movement just isn’t necessary (or in your budget). A radial bushing looks just like a section of a small pipe or straw. These bushings usually come in a variety of plastics, bronze, and sometimes aluminum or steel with a low-friction coating on the inside like Teflon or Frelon. Oilite bushings are a special kind of bronze construction that allows many tiny open pores to be filled with oil and create a very slick surface.
NOTE Teflon is DuPont’s brand name for a slippery plastic with the molecular name of polytetraflourethylene, abbreviated PTFE. So if you see a PTFE on McMaster, it’s the same thing as Teflon.
Three measurements that define radial bushings are outer diameter, inner diameter, and length. Before installing a bushing, make sure it fits on your chosen shaft and spins without being too tight or too loose. To install a bushing, just press or hammer it into a hole the size of its outer diameter. If you have access to an arbor press (like McMaster’s 2444A61), that’s even better. Using some kind of lubricant (like WD-40, 3-IN-ONE, or certain greases) is always a good idea and will decrease friction even more.
Thrust bearings (see Figure 7-7) support axial loads, which are parallel to and ideally in line with a shaft. These can have rolling elements or just be washers made of slippery materials. If you’ve ever been to a restaurant with a rotating center turntable, known as a lazy Susan, you’ve encountered a thrust bearing. This turntable allows a lot of heavy food to be stacked on it while still allowing you to spin it easily. You can also find thrust bearings in rotating bar stools, chairs, and on a smaller scale, in rotating spice racks. See Projects 10-1 and 10-2 in Chapter 10 for examples of how to use these bearings.
Thrust Ball and Roller Bearings
Thrust ball and roller bearings are similar to radial ball and roller bearings with the components reversed to handle axial loads. The vocabulary is mostly the same, with these differences:
✵ Outer diameter The outer diameter on thrust bearings shouldn’t touch anything, so size it accordingly.
✵ Inner diameter Unlike radial bearings, the inner diameter should not be a tight fit on the shaft. There should be clearance between the inner diameter and shaft so they rotate freely relative to each other, but not so much slop that the shaft has room to wiggle around.
✵ Cage Although optional in radial bearings, thrust bearings always have cages to separate and contain the rolling elements.
FIGURE 7-7 Thrust bearings and bushings (credit: McMaster-Carr)
✵ Shield (optional) Some thrust bearings come assembled with thrust washers in a ready-to-use unit with a shielded cover. Shields help stop gunk from getting into the rolling elements.
✵ Thrust load or axial load This load rating describes how much weight the bearing can handle while spinning.
Thrust Washers and Bushings
Thrust bearings with no rolling elements are called thrust bushings or thrust washers. They look just like your average washer, except that they’re made from slippery material and have a higher quality flat surface to support rotating things. They often come in sets with thrust ball and roller bearings to make sure the rolling elements have nice smooth, hard surfaces to interact with. You can use a thrust washer by itself as a thrust bushing to decrease friction if rolling elements aren’t necessary.
Linear Bearings and Slides
Linear bearings allow motion in a straight line, often along a shaft. There are a variety of types with rolling elements in them. The most common are meant to ride on shafts, as shown in Figure 7-8. The cylindrical sleeve has a kind of cage that holds steel balls, as in other bearings, but these allow the bearing to roll along a shaft instead of spin around it. Linear bearings are designed to carry heavy loads on precision, hardened steel shafts, so the system components can get expensive pretty quickly.
Another type of linear bearing is a drawer slide or track roller. You’ve probably seen these on the sides of dresser, kitchen, filing cabinet, or shop drawers. They allow you to pull a drawer out while supporting the weight of the contents in a smooth, relatively frictionless motion. These can be repurposed for many different projects that need smooth, linear motion.
Linear bushings offer an economical alternative when you have light loads and a small bit of friction is okay. Linear bushings, also called linear plain bearings, look a lot like radial bushings. In their simplest form, they are just small, hollow cylinders of a slippery material like plastic or bronze. These are the type used in MakerBot’s CupCake CNC (see Figure 7-1). Higher-end linear bushings have Teflon or other slippery linings on the inside surface. They perform better than linear ball bearings when dirt, water, and vibrations are involved, but have slightly higher friction. Some have grooves that allow dirt and debris to slide right through them.
FIGURE 7-8 Linear ball bearing configurations (credit: McMaster-Carr)
Combination and Specialty Bearings
General-purpose radial ball and roller bearings are not designed to handle axial loads or torques, and thrust bearings are not designed to handle radial loads or torques (see Figure 7-9).
Ball bearings also tend to take up a lot of radial space, so they may not be feasible for use in smaller projects. It can also be hard to align everything in your system perfectly so the bearing functions as intended. Here are a few common bearing alternatives that address these problems:
✵ Angular contact bearings If you try to put an axial load on a radial bearing, it probably won’t work well, and the inner or outer race will likely get damaged. However, in the real world, you rarely have pure axial or radial loads. Angular contact bearings have angled races, so they can handle radial loads as well as axial loads in one direction. Figure 7-10 shows a cross section and the direction of the applied load.
FIGURE 7-9 Right and wrong ways to load radial and thrust bearings
FIGURE 7-10 Angular contact bearings can handle radial and thrust loads.
✵ Spherical bearings Spherical bearings have a spherical-shaped outer race that increases surface contact with the housing and boosts load capacity while accommodating misalignment. They handle radial and thrust loads, so are often used when these loads are present in combination with some misalignment, as on the gym equipment in Figure 7-11.
✵ Combination bushings Flanged bushings (see Figure 7-12) handle both radial and axial loads. You can install these just like radial bushings, and then use the flange as a thrust washer and/or spacer.
FIGURE 7-11 Spherical bearings are used on gym equipment to accommodate misalignment in the cable pull direction.
Bearing Installation Tips and Tricks
There are two main ways to work with bearings: build them into your structure or use mounted bearings (pillow blocks). We’ve already talked a bit about building them into your structure, such as installing bushings by pressing them into a hole just bigger than their outer diameter. For radial bearings or bushings, if you’re working with wood, you should drill a small hole first, and then drill progressively larger holes until you get the right fit. You can also use counterbore bits (also known as Forstner bits), as shown in Figure 7-13, to create a recess for a bearing to sit in.
FIGURE 7-12 A flanged bushing can handle radial and thrust loads.
FIGURE 7-13 Counterbore bits can be used to create recesses for bearings (credit: McMaster-Carr).
If you’re working with metal like aluminum, you can use the same method of drilling progressively larger holes until you reach the correct outer diameter to hold your bearing snugly. You can also create counterbores the same way as in wood, but most of the counterbore bits that can handle metal are not designed to work with portable handheld tools.
The best way to create holes for bearings in metal is to use a drill press or a milling machine. A drill press is basically what you get when you mount a portable drill on a stable structure with a base. A milling machine is a fancier version of a drill press that allows the base to move in the x, y, and z axes so you can do more than just drill straight down (see Figure 9-4 in Chapter 9). You can use a counterbore drill bit in a drill press. The best tool to create a counterbore on a milling machine is called an endmill. An endmill looks like a drill bit with the tip cut off, so it can create holes with flat bottoms.
FIGURE 7-14 Common bearing mount configurations
There are many ways to mount bearings and bushings. The important considerations with ball bearings are to mount them so the shaft fits snugly to the inner race and the outer race fits snugly to some sort of housing. Figure 7-14shows common configurations used to mount a long shaft. Variations on this scheme include using bearings with flanges built into their outer races, using washers or nuts in place of the shoulders on the housing, or using retaining rings or shaft collars to keep the shaft from shifting inside the bearing.
Another way to work with bearings and avoid using fancy tools and bits is to use mounted bearings, or pillow blocks. Pillow blocks are just bearings mounted in their own case. The case provides mounting holes or slots so you can adjust the alignment before tightening down the mounting screws (see Figure 7-15). You pay for the convenience, but with a starting price of around $3, you might be willing to spend the extra dollar or two and save yourself a lot of time.
FIGURE 7-15 Pillow blocks allow you to easily mount bearings to support rotating shafts (credit: McMaster-Carr).
A coupler, or coupling, is anything that joins two rotating things to transfer torque from one to the other. Attaching, or coupling, something to your motor’s shaft can be the first and biggest challenge you face when building your mechanism. Information about how do to this is rarely rounded up in the same reference. The methods depend on the motor type and shaft shape. The following sections summarize recommendations from different sources and years of experience, so you can easily see your options for extending a motor shaft, attaching it to an existing shaft, connecting it to a gear, and so on.
Working with Hobby Servos
Hobby servos make connecting anything to them very easy because they come with a spline (a little gear-shaped thing) already fixed to the motor shaft (see Figure 7-16). All the hardware designed to interface with servos has the female indent of the spline already in the part, so it just slides on, and then is usually secured with a screw into the motor shaft itself.
FIGURE 7-16 Servo motor with spline on motor shaft and extra attachments
In the Servos & Accessories section, ServoCity (www.servocity.com/html/servo_ shafts___couplers.html) has at least six different couplers you can use to extend the shaft, attach other parts, or attach another shaft. ServoCity also offers all kinds of arms, pulley wheels, gears, and sprockets (for chains) that attach directly to the spline on the shaft. If you can use hardware ready-made to interface with a servo, definitely do it.
Even if you don’t use one of the ready-made servo accessories, you can still take advantage of the fact that the motor shaft is threaded and use a screw to attach something to it. You can also glue the flimsy plastic servo arms that come with most hobby servos to something more durable. Many hobby servo suppliers will sell you a small amount of screws that work with your motor, so you don’t need to figure out what size they are and buy a box of 100 from McMaster. Screw size 4-40 (screw sizes are covered in Chapter 3) is common to standard servos, but it’s worth checking to confirm before you try a random screw and ruin the threads.
Working with Other Types of Motors
Common shaft sizes for other motors you might work with (DC, DC gearhead, and stepper) range from as small as 1/16 in to around 3/8 in for larger motors. The problem here is that most gears and other components have inner diameters that are larger than the motor shafts. You also might want to attach your motor shaft to a smaller or larger shaft, and if you don’t get it perfectly centered, the whole thing will wobble.
When you attach something to a motor shaft, you are really asking for all the motor torque to go from the motor into what you are attaching (gear, pulley, coupler, and so on) without slipping. Hobby servos solve this problem for you by using a spline that can bite into the mating piece to transfer torque. On the other hand, a smooth, metal, circular shaft inserted into something with a smooth metal inner diameter is just about the worst possible way to transfer torque, yet is often what we’re stuck with when dealing with all motors other than hobby servos. Let’s look at these common problems and how to solve them.
Using D-Shaped or Flatted Motor Shafts
An important rule of thumb is that any shape transfers torque better than a circle ! Many motors come with a D-shaped or flatted shaft (a circle with a flat on one side; see Figure 7-17) or a shaft that’s flatted on both sides. Find and use these as often as possible.
FIGURE 7-17 A gearhead motor with a flatted shaft makes it easier to attach components with set screw hubs (credit: ServoCity).
If the motor you need does not have a flat section to the shaft, you can always file in a small patch with a metal file. Others have grooves (called keyways) cut out of the motor shaft and mate with a component with a matching key cutout. Some motors even come with a tapped hole in the shaft so you can screw components directly into them. At the very least, you should take a file or sandpaper to a circular motor shaft to give it some texture to better enable components to hold onto it.
Attaching Components to Motor Shafts
If you’re really lucky, you can find a motor that has a wheel or other component that matches the shape of your motor’s output shaft. For example, Solarbotics sells a great little DC gearhead motor kit (www.solarbotics.com/products/gmpw_deal/) that includes a motor with a shaft that’s flatted on both sides, a wheel with a matching profile, and a mounting screw to keep the wheel in place.
If you’re not that lucky, make your life easier by searching for components (gears, pulleys, sprockets, and so on) that come with a hub. A hub slides onto your motor shaft and is secured with a set screw or clamp (see Figure 7-18). Some components come with hubs but without a set screw or clamp to secure them. The term for this is plain bore. If the fit is too loose, you can always drill and tap your own hole for a set screw. (See Chapter 3 for details on how to drill and tap holes.)
FIGURE 7-18 Components with set screw hubs, like this gear from ServoCity, are easy to attach to motors (credit: ServoCity).
If you’re not lucky enough to find a component with a convenient hub, you can always press fit a component to your motor shaft. This is when the hole in your component is so close to the size of your motor shaft that you need to push it really hard to slide it on, and it will hold that position because of the stress of the fit. Figure 7-19 shows a gear that ServoCity has designed to press onto the shaft of small DC motors.
CAUTION A press fit is one of the weaker methods we’ve talked about for attaching components to a motor and is tricky to get just right. The act of pressing on the gear or other component can also damage the radial bearings in some motors because you are putting an axial load on the shaft when you press something onto it. You should use this method only after you’ve run out of other options.
Another way to attach components is by using a clamp hub, also called a flanged coupling or mounting flange, like the one shown in Figure 7-20. This attachment allows you to grip onto circular motor shafts with the clamp and then use the mounting holes for gears, pulleys, wheels, or whatever you want. For larger diameter motor shafts, McMaster sells a mounting flange (9684T1) that does the same job.
FIGURE 7-19 Press-on gear from ServoCity
FIGURE 7-20 Clamp-style hubs offer strength and flexibility.
WM Berg (www.wmberg.com) is another good place to find hubs, shaft adapters, and other components in convenient sizes. (The product search on the WM Berg site doesn’t have pictures at the time of this printing, so it may be easier to order the company’s free print catalog.)
Increasing Shaft Size
Since motor shafts are often smaller than the components you need to attach to them, there are a few handy tricks you can use to fill the gap. One way is to use a shim. Shim is a general term for a thin thing that fills a gap, and can be made of wood, metal, or plastic. If you’ve ever tried wrapping duct tape around a shaft to make it fit tightly to a component, you were shimming the shaft. You can certainly stick with duct tape if that works, but a more professional approach is to get a roll of shim stock—basically thick tin foil—and cut a piece that wraps around your motor shaft.
You can find shim stock sheets and rolls at most hardware stores (and McMaster, of course). Soda and beer cans are also readily available sources of metal shims if you have some tin snips to cut off the ends. Shim stock comes as thin as 0.001 in, so if your component fits on your motor just a little too loosely, you can jam some layers of shim stock in that gap until you get a snug fit.
You can also use aluminum or brass tubes as a kind of shim to create a new uniform surface on the motor shaft. These are available from McMaster and most hardware and craft stores, and they come in many diameters. The walls can be almost as thin as plastic drinking straws, so you can layer one size on top of another if necessary.
Attaching the Motor Shaft to Another Shaft
Sometimes you need to extend a motor shaft to reach a wheel or rotate a long shaft. For example, if you are trying to automate your window shades, you might want to connect your motor to a rod that runs the width of your window and rolls up the window shade when you turn on the motor. There are three main options here, depending on the relative sizes of the shafts:
✵ Insert a smaller shaft into a bigger shaft Make a hole in the bigger shaft, stick the smaller one into it, and secure it with a set screw if necessary. See Project 9-2 in Chapter 9 for an example of how to drill a hole in the center of something without a lathe.
✵ Use a rigid shaft coupling Some types of couplers can join shafts of different sizes (see Figure 7-21). The inner diameter of the coupling is a tight fit to the shaft, and the set screws bite into the shaft a little to help transfer torque. Rigid shaft couplers come in a variety of styles, including clamped hubs (see Figure 7-22). Clamped hubs give you a tighter grip on both shafts, so they transfer torque better, but are not well suited to high-speed applications since the weight of the clamp hub is off center and can make the system wobbly.
NOTE As you can probably tell from the pictures in Figures 7-21 and 7-22, these set screw shaft couplers are relatively easy to make yourself in a pinch. Just take a short length of aluminum or plastic rod, drill a hole through the center the size of your motor shaft (it doesn’t need to be perfectly centered), drill and tap two holes for whatever size screw you have lying around (see Chapter 3), and you’re done. It’s best to use a small vise, like McMasters 5312A2, to hold the material while you drill. If one shaft is bigger than the other, use a bigger drill bit to drill back through half of the coupling. The bigger drill bit will naturally center itself on the existing hole.
✵ Use a flexible shaft coupling Flexible couplings compensate for a certain amount of misalignment of the shafts (parallel, angular, or axial) by giving a little if they aren’t perfectly aligned. These are highly recommended because the coupling takes the stresses induced by poor alignment instead of making the motor work harder to turn something that’s not on center.
If you go with flexible shaft coupling, rubber tubing is by far the simplest (but weakest) option. If you’re lucky enough to find rubber tubing that has an inner diameter that fits the motor and shaft you want to join, all you need to do is cut a short piece of it, and then push your motor shaft into one side and the shaft you want to connect into the other. If you want a tighter fit, you can put small hose clamps (like McMaster 5388K14) on each end of the tube to secure your coupler.2 Search for “tubing” on McMaster for a dizzying array of options in every material and dimension you can think of.
FIGURE 7-21 Rigid shaft couplers, set screw style
FIGURE 7-22 Rigid shaft couplers, clamp style
FIGURE 7-23 U-joints (credit: ServoCity)
For flexible coupling of two shafts in different planes, you need to use a universal joint (U-joint) (see Figure 7-23). These come in many different sizes and shapes, and sweep through a variety of angles. They can also be used to join shafts of different sizes. Many other flexible coupling options are available. Just search for flexible shaft couplings on McMaster (or any other components supplier website), and you’ll find a wide array of options with funny names like spider, Oldham, and bellows couplings that accommodate different kinds of misalignment.
Attaching Gears and Other Components to Shafts
The options for attaching components to shafts are basically the same as for attaching components to a motor shaft, with a few additions:
✵ Press it It’s easier to press fit components at the ends of shafts. If you need to locate a component in the middle of a shaft, this is probably not the way to go.
✵ Glue it If your component will slide onto the shaft, you can try using a strong super glue or epoxy to hold it on. If both components are wood, wood glue is a good choice.
✵ Pin it If your component is wide enough to drill a small hole through its side or hub, you can match drill the component and shaft, and use a nail or dowel pin (wooden or metal) to hold them together (see Figure 7-24, left and middle images). Match drilling refers to lining up two things and drilling through them both at once to make sure they are perfectly aligned.
FIGURE 7-24 Attaching components to shafts
✵ Screw it If your component has a set screw hub, this is easy. If it has a plain bore with a hub, you can drill and tap a hole for a set screw. If it has no hub at all, you can make your own, or use an off-the-shelf mounting hub like the one shown earlier in Figure 7-20.
✵ Screw and pin it If you can drill a hole radially through your shaft, and you can drill a hole anywhere on the face of your component, you can probably connect them with a stiff wire or pin. This is displayed in the right image of Figure 7-24.
✵ Pinch-clamp it Use a shaft collar on either side of a flat gear or other component to hold it in place. If you squish the shaft collar together while you tighten their clamps or set screws, you can pinch the component as well. This method is used in Project 10-2 in Chapter 10 to secure the wind turbine parts that hold the blades.
✵ Hold-and-stick it Use epoxy putty to glue a shaft collar onto a flat component (and/or the shaft) to create your own hub. This method is used twice in Project 10-2 to secure the laser-cut gears to the wind turbine shaft and motor shaft.
A clutch is a special type of coupling designed to connect or disconnect the driven part (shaft) from the driving part (motor), usually as a safety mechanism or to allow motion in only one direction. Some clutches, like part MSCB-4 from SmallParts (www.smallparts.com/), let you set the limit between where they slip or grip (see Figure 7-25).
FIGURE 7-25 Common spiral claw/rachet type clutch (credit: SmallParts.com)
An example of a ratchet type clutch is seen in bicycles.3 It engages the rear sprocket with the rear wheel when the pedals are moving forward, and lets the rear wheel move freely when the pedals are stopped or moving backward.
Shaft collars, also called lock collars, are like one half of a rigid shaft coupling. You can use them as mechanical stops or to limit movement on a shaft. They can also be used as spacers between gears or other components.
As shown in Figure 7-26, shaft collars come in set screw and clamp types, and can be made of metal or plastic.
FIGURE 7-26 Shaft collars (credit: McMaster-Carr)
Gears are easy to use if you know the vocabulary (introduced in Chapter 1) and can space them apart at the correct distance. One nice thing about gears is that if you know any two things about them, such as outer diameter and number of teeth, you can use some simple equations to find everything else you need to know, including the correct center distance between them.
Before we talk about the types of gears, let’s review the anatomy of a spur gear drive train in Figure 7-27 and the related vocabulary.
✵ Number of teeth (N) The total number of teeth around the outside of the gear.
✵ Pitch diameter (D) The circle on which two gears effectively mesh, about halfway through the tooth. The pitch diameters of two gears will be tangent when the centers are spaced correctly.
✵ Diametral pitch (P) The number of teeth per inch of the circumference of the pitch diameter. Think of it as the density of teeth—the higher the number, the smaller and more closely spaced the teeth. Common diametral pitches for hobby size projects are 24, 32, and 48.
FIGURE 7-27 Spur gear anatomy
NOTE Remember that the diametral pitch and circular pitch of all meshing gears must be the same.
✵ Circular pitch (p) = π / P The length of the arc between the center of one tooth and the center of a tooth next to it. This is just pi (π = 3.1416) divided by the diametral pitch (P). Although rarely used to identify off-the-shelf gears, you may need this parameter when modeling gears in 2D and 3D software (see Project 7-1).
✵ Outside diameter (DO) The biggest circle that touches the edges of the gear teeth. You can measure this using a caliper like SparkFun’s TOL-00067.
NOTE Gears with an even number of teeth are easiest to measure, since each tooth has another tooth directly across the gear. On a gear with an odd number of teeth, if you draw a line from the center of one tooth straight through the center across the gear, the line will fall between two teeth. So, just be careful using outside diameter in your calculations if you estimated it from a gear with an odd number of teeth.
✵ Center distance (C) Half the pitch diameter of the first gear plus half the pitch diameter of the second gear will equal the correct center distance. This spacing is critical for creating smooth-running gears.
✵ Pressure angle The angle between the line of action (how the contact point between gear teeth travels as they rotate) and the line tangent to the pitch circle. Standard pressure angles are, for some reason, 14.5° and 20°. A pressure angle of 20° is better for small gears, but it doesn’t make much difference. It’s not important to understand this parameter, just to know that the pressure angle of all meshing gears must be the same.
All of these gear parameters relate to each other with simple equations. The equations in Table 7-1 come from the excellent (and free) design guide published by Boston Gear (www.bostongear.com/pdf/gear_theory.pdf).
Table 7-1 Gear Equations
Project 7-1: Make Your Own Gears
In this project, we’ll design and fabricate spur gears using free software and an online store, Ponoko, that does custom laser cutting at affordable prices.4 If you have access to a laser cutter at a local school or hacker space, even better! You can also print out the template and fix it to cardboard or wood to cut the gears by hand.
We’ll use Inkscape, a free, open source vector-based drawing program similar to Adobe Illustrator. It plays well with most modern Windows, Mac, and Linux operating systems (check the Inkscape FAQ at http://wiki.inkscape.org/wiki/index.php/FAQ for details). In Inkscape, you can draw gears with a built-in tool. One glitch is that the circular pitch is given in pixels, not inches, as in the equations in Table 7-1. You can get different gear ratios by just choosing a circular pitch that looks good and varying the teeth number, but if you want to make gears that interface with off-the-shelf gears, you need to pay a little more attention.
In Inkscape, there are 90 pixels (px) in 1 in by default. So if you set circular pitch to 24px in the Gear tool, that rounds to 0.267 in (24/90 = 0.2666…). Since diametral pitch (P) = π / circular pitch (p), the diametral pitch (P) in inches is =π / 0.267 = 11.781. You will not find any off-the-shelf gears with a diametral pitch of 11.781. As mentioned earlier, common diametral pitches are 24, 32, and 48. So if you plan to make gears to play nice with off-the-shelf gears, start with the diametral pitch of your off-the-shelf gear and use the equations in Table 7-1 to work backward to what your circular pitch should be in pixels in Inkscape.
✵ 1/4 in wooden dowel
✵ Hobby knife
1. Download and install Inkscape from www.inkscape.org.
2. Download the Inkscape starter kit from www.ponoko.com/make-and-sell/ downloads. This will give you a making guide (a PDF file) and three templates that relate to the sizes of materials Ponoko stocks. Unzip the file and save it to somewhere you’ll remember.
3. Open a new file in Inkscape. Choose File | Document Properties from the menu bar to open the Document Properties window. Change the default units in the upper-right corner to inches. Back in the main window, change the rulers from pixels to inches in the toolbar. Your screen should look like Figure 7-28. Close the Document Properties window.
4. Choose Extensions | Render | Gear from the menu bar. You’ll see a small Gear window that gives you three options: Number of teeth; Circular pitch, px; and Pressure angle. Leave the Pressure angle setting at 20.0, since 20° is standard for off-the-shelf gears and a good place to start. Set the other options as desired for your gear. In Figure 7-29, you can see that I chose 28 teeth with a circular pitch of 24. Click Apply, and then click Close.
5. Since gears are no fun by themselves, repeat steps 3 and 4 to make at least one more gear. I created a second gear with 14 teeth.
FIGURE 7-28 Changing document settings in new Inkscape file
FIGURE 7-29 Using the Gear tool in Inkscape
NOTE Remember that the pressure angle and circular pitch must be the same for the gears to mesh; change only the number of teeth!
6. Use the Circle tool and hold down the CTRL key (on a PC) to draw a circle inside the big gear. The default circle is filled with black. Zoom in if you need to. Make sure the arrow selector is active and click the circle. Make sure inches is selected in the toolbar and the Lock button on the toolbar looks locked. Type 0.250 in the W box in the toolbar, press ENTER, and watch the H box change automatically. Your circle will resize to a diameter of 0.250 in, and your screen should look like Figure 7-30.
FIGURE 7-30 Resizing the circle
7. Click and drag a box around the big gear, small gear, and circle shape to select them all. From the menu bar, choose Object | Fill and Stroke. You will see the Fill and Stroke window, as shown in Figure 7-31.
a. In the Fill tab, click the X button for no paint.
b. In the Stroke paint tab, click the button next to the X for flat color. Leave the default color (black) for now.
c. In the Stroke style tab, change the width to 0.030mm and hit ENTER. This is what Ponoko wants the line thickness to be for laser cuts. Adjust as necessary if you’re using a different laser cutter. Close the window.
FIGURE 7-31 Fill and Stroke window
8. You need to get this circle in the exact center of the gear. Make sure the arrow selector is active. Click and drag a box around the big gear and the circle to select them. From the menu bar, select Object | Align and Distribute. Click the Center objects horizontally button (highlighted in Figure 7-32). Then click the button directly below it, which is Center objects vertically. Now you have a gear with a hole perfectly centered! Copy and paste this circle, and repeat this step to center a circle in the other gear.
FIGURE 7-32 Centering the circle within the gear
9. Now that you have your gears, you’ll create a base with holes spaced the correct distance apart so you can mount the gears with 1/4 in wooden dowels and make them spin.
a. Calculate the center distance (CD) of your gears using the equations from Table 7-1. Both gears have a circular pitch of 24 pixels and a pressure angle of 20°. The big gear has 28 teeth, and the small one has 14. As explained in the project’s introduction, you convert the circular pitch in pixels to a diametral pitch in inches of 11.781. If you look at Table 7-1, all you need is that number and the numbers of teeth on the two meshing gears to find the center distance (CD). Use the equation CD = (N1 + N2)/2 P, and you’ll find that CD = 1.783.
FIGURE 7-33 Placing circles for the gear base
b. Copy one of the circles inside the gears, and paste two of them about 2 in apart on the lower part of the template. Select the one farthest to the left, change the x coordinate in the toolbar to 3 in, and then press ENTER. Your screen should look like Figure 7-33.
c. Use the same procedure to place the second circle to the right of the first with an x coordinate of 4.783. This is the center distance you calculated (1.783) added to the x coordinate of the first circle (3.000).
d. Draw a rectangle around the two circles to complete the base. Align the rectangle with the two circles, as shown in Figure 7-34.
FIGURE 7-34 Gears and base ready to transfer to Ponoko template
10. Now you need to prepare the file to be uploaded and ordered on the Ponoko site.
a. Ponoko uses colors to indicate how to treat the files. A blue 0.030mm line means cut it all the way through. Select everything you’ve drawn so far, go to the color swatches at the bottom of the screen, and hold down the SHIFTkey while you click blue.
b. Open the P1.svg template you downloaded earlier. Select everything you have drawn so far, and copy and paste it into this template, as shown in Figure 7-35. Don’t worry about the orange border and words; Ponoko knows to cut only the blue outlines. Save the file.
FIGURE 7-35 Transferring gears and base to the Ponoko template
c. Go to www.ponoko.com/ and set up a free account. Then upload your file, pick a material, and arrange to have it shipped. I chose blonde bamboo, as shown in Figure 7-36, and the total cost was just $4.13 (plus shipping).
NOTE Once you open your free account, go to My Accounts | Preferences to set your shipping hub to Ponoko - United States (or the location closest to you). Mine was set to New Zealand by default, so my shipping charges were curiously high until I figured this out.
FIGURE 7-36 Ordering gears on Ponoko.com
11. While you’re waiting for your Ponoko order, get out your 1/4 in wooden dowel and cut off two 2 in sections with a hobby knife. File down any splintery ends.
12. The gears will come in the square template with a sticky paper protector on each side. Peel off the paper, pop out the gears, and position the two gears over the holes in the base. Insert your wooden dowels, and voila! Figure 7-37 shows my gears.
FIGURE 7-37 Final laser-cut gear assembly
When you have two gears that mesh, they both turn in opposite directions when they spin. If you want to make two gears spin in the same direction, you can space them out with another gear between them. This is called an idler gear. It doesn’t change the gear ratio of the system. It just allows you to get the input and output gears moving in the same direction (see Figure 7-38).
Idler gears are also handy when your input and output gear shafts are far apart. They don’t need to form a straight line between your input and output gears, but can be offset, which allows you to vary your input and output shaft distance almost infinitely.
Compound gears are formed when you have more than one gear on the same axle (see Figure 7-39). A compound gear system has multiple gear pairs. Each pair has its own gear ratio, but since a shared axle connects the pairs to each other, you multiply the gear ratios together to get the gear ratio of the system.
Compound gears are a very efficient way to gear up a weak motor to increase torque and decrease speed.
FIGURE 7-38 Idler gears change the direction of rotation without changing the gear ratio.
FIGURE 7-39 Compound gear system
Pulleys and Sprockets, Belts and Chains
Belt or chain drives are often preferred over gears when torque needs to be transferred over long distances. Imagine how funny a bicycle would look with a bunch of gears between the pedals and the back wheel. They are also more forgiving about misalignment than gear systems are.
Sprockets, like the ones on your bicycle, are used with chains. Pulleys are used with belts, and can be flat or V-shaped with matching belts or grooved pulleys with matching toothed belts. We covered the latter type, called a timing belt pulley system, in Chapter 1. The pulleys and sprockets that come with hubs and set screws are mounted on shafts and motors to do the work. Remember that you have a mechanical advantage only if the input pulley is smaller than the output pulley, and the advantage is just the ratio of their sizes. For example, if your input pulley is half the diameter of the output, your mechanical advantage is 2:1.
It’s common to include one or more tensioners in a pulley system (see Figure 7-40). Tensioner is the common name for a pulley that’s spring-loaded and/or adjustably mounted in a slot to keep the belt tight while the mechanism runs. Tensioners are often tightened after the belt is installed, which makes installation much easier than needing to stretch the belt over pulleys that are already in position. Tensioners are similar to idler gears in that they don’t change the mechanical advantage of the system; they just alter the behavior. In fact, they’re often called idler pulleys, and commonly have bearings or bushings as hubs to allow for smooth rotation.
FIGURE 7-40 MakerBot timing belt pulley system with tensioners (image used with permission from MakerBot Industries)
Two good sources for all these kinds of pulleys and belts are McMaster and Stock Drive Products. ServoCity is a good source for smaller sprockets and chains, especially if you’re working with servo motors or the ServoCity DC motors.
Standard Pulleys and Belts
Standard pulleys provide a friction drive, so they are very sensitive to getting the belt stretched just enough to transfer motion between pulleys, but not so much that the tension causes friction or structural problems. Two pulleys connected by a belt will rotate in the same direction. To get them to rotate in opposite directions, put a half twist in the belt to create a figure 8.
Pulleys can be totally flat on the perimeter or have grooves that accommodate round or V-shaped belts. Some belts are very stiff and need a lot of tension to make them work properly, which will not bode well if you have a cardboard-and-popsicle-stick construction. So before committing to a belt, make sure you have the rest of the structure in place. There’s no really good way to estimate the stiffness of a belt before you buy it, but in general, the thinner and skinnier it is, the more flexible it will be.
Timing Pulleys and Belts
Timing belts provide positive drive since the belt teeth mesh with the grooves in the timing belt pulley. You can find these in cars (see Figure 1-10 in Chapter 1), and also on a smaller scale in printers, copiers, and in the CupCake CNC (see Figure 7-40).
There are a dozen different series of sizes with names like MXL and HTD, but the series name is less important than just making sure your pulley and belt are the same series, and that your pulley is wide enough to accommodate your belt. The timing belt pulley and belt should be the same pitch, similar to meshing gears.
Sprockets and Chains
Sprockets and chains provide a positive drive similar to gears because the sprocket teeth and chain mesh together. Standard bicycle chain is 3/8 in, and you can find smaller metal chains and even plastic chains with snap-together links. Figure 7-41 shows an aluminum sprocket and 14 in chain mounted to a servo motor.
FIGURE 7-41 An aluminum sprocket and 1/4 in chain mounted to a servo motor (credit: ServoCity)
We talked about using screws as simple machines in Chapter 1, and screws as fasteners in Chapter 3. Power screws get their name from their intended use. Their geometry allows them to lift heavy loads, as well as precisely position anything riding on them.
There are a couple kinds of power screws: threaded rods and ball screws. You may have encountered common threaded rods, sometimes referred to as all-thread. These are designed for fastening things that are thick or far apart, and look just like longer versions of fastening screws. Although not designed to be used as power screws, they do the job well in MakerBot’s CupCake CNC, where high precision and heavy lifting are not the main concerns. Acme threaded rods use a special geometry thread designed to lift heavy loads more efficiently.
A ball screw has a semicircular groove that spirals up the screw and allows little steel balls (housed in a ball nut) to ride up and down it. Ball screw and nut assemblies are much more expensive than other types of power screws because of their efficiency. Because the friction is so low, more of the input energy is transferred to useful work.
Regardless of the type of screw chosen, all power screws do one thing well: give tremendous mechanical advantage. As you saw from the 600:1 ratio in the car jack example in Chapter 1, this is pretty crucial in applications when you need to lift heavy loads with a low input force. Power screws have been used in this capacity for many years, and sometimes in reverse. The wooden ones in Figure 7-42 were actually hand-driven and used to squish grapes in wineries before mechanical presses were invented.
FIGURE 7-42 A diorama in a winery museum shows wooden power screws that were used to press the grapes.
McMaster and Nook Industries (www.nookindustries.com) are two good sources for power screws.
Springs can be very useful components in your mechanisms. They can keep lids closed, return solenoids to their original position, create latches and ratchets, and more. Springs can store energy, as mentioned in Chapter 5, and are often components in the mechanical toys we’ll talk about in Chapter 8. Here, we’ll cover the different kinds of springs and how they can be used.
When most people hear “spring,” the compression spring is the type that comes to mind. You can find tiny ones inside mechanical pens and pencils, and larger ones in the shocks on mountain bikes. First, let’s go over some vocabulary so you’ll know what all the words mean when you shop for springs. Figure 7-43 shows how these terms apply to a compression spring.
✵ Inner diameter The diameter of the biggest rod that will fit inside the spring.
✵ Outer diameter The diameter of the outer edge of the spring.
✵ Wire diameter The diameter of the wire that is wound to make the spring.
✵ Free length The length of the spring before you do anything to it.
✵ Solid height The height of the spring when completely squished.
✵ Spring rate or stiffness The k in Hooke’s law (in units of force/length), which tells you how much the spring will squish under a given weight:
Force (F) = Stiffness (k) × Distance (x)
FIGURE 7-43 Anatomy of a compression spring
Compression springs are used as shock absorbers, return springs for solenoids, projectile launchers, belt tensioners, and return springs for jack-in-the-box latches (see Figure 7-44). It’s easiest to work with compression springs that have ground ends or that are designed to sit flat. It’s also a good idea to either surround the spring with a housing or mount it on a shaft to prevent it from buckling out to the side.
Tension springs (also called extension springs) are the opposite of compression springs, but we can use most of the same vocabulary to describe them. These springs start out completely squished, and then resist as you pull them longer and longer (see Figure 7-45). You can stretch them only so far before they stay like that forever, so the maximum safe stretch distance is often specified as maximum extended length.
FIGURE 7-44 A compression spring returns the latch in a jack-in-the-box.
Most of us have a tension spring on our desk at all times—check inside your stapler. The tension spring inside keeps consistent force on the little staples so the next one is always ready and waiting to go.
You can also use tension springs for many of the same functions as compression springs, just mounted differently. They are generally easier to design for, since you don’t need to worry about a hole or shaft to act as a guide. Instead of resting on a surface, these springs are often hung from something, as in fish scales and grocery store scales. You’ll also see them in garage door mechanisms and around the edges of trampolines.
FIGURE 7-45 Extension springs (credit: McMaster-Carr)
Torsion springs exert a torque or rotary force that’s usually used to keep something shut. You’ve probably seen them in hair clips, mousetraps, clothespins, and clipboards. They also live inside doorknobs, allowing them to return to their original resting position after you open the door.
Torsion springs are a bit trickier to understand and buy, and there are a few different kinds. Torsion springs are categorized by the angle the legs stick out from the center spiral and the range of motion you can expect from those legs (see Figure 7-46).
Spring listings will usually give you torque only as a means of determining the strength of the spring. This is the torque at maximum deflection (closed). However, this torque changes as you go from fully closed to fully open. Here is the equation that relates torque to how far apart the legs are:
FIGURE 7-46 Shapes of torsion springs (credit: McMaster-Carr)
Torque (T) = Stiffness (k) × Angle (in radians)
NOTE Remember that degrees × (π /180) = radians.
To find the torque at an intermediate location, first figure out the stiffness (k) by using the equation and maximum angle deflection of your spring. Then you can use the stiffness multiplied by any angle and find the torque. You can also use a direct proportion. For example, if the listing says 1 in-lb at 90°, then it will have 0.5 in-lb of torque at 45°. If you want to experiment with torsion springs, revisit Project 5-1 in Chapter 5, and you’ll have a new appreciation for the simplicity of a mousetrap.
Spring-lock washers, sometimes called disc washers, were mentioned back in Chapter 3 when we talked about putting them in bolted joints to help keep the joints from coming loose. This is the most common use of spring-lock washers. They act like little compression springs with just one revolution.
A diving board is an example of a leaf spring that probably everyone has seen and most have used. When you jump on the end of the board, the springiness of it cushions your landing and moves down, and then helps push you back up and propel you into the air. This same cushioning effect is used in leaf springs in mechanisms and car and truck suspensions.
As mentioned in Chapter 5, spiral, or clock, springs are often used in wind-up toys to store energy that is converted to motion when the winding stops. Another version of a spiral spring, called a constant-force spring, is used in tape measures. These springs constantly want to return to their rolled-up state, and will provide a consistent pull force in that direction. You can find constant-force springs on McMaster.
1. Richard G. Budynas, J. Keith Nisbett, and Joseph Edward Shigley, Shigley’s Mechanical Engineering Design (Boston: McGraw-Hill, 2008).
2. Dennis Clark, Building Robot Drive Trains, ed. Michael Owings (New York: McGraw-Hill, 2003).
3. U.S. Bureau of Naval Personnel, Basic Machines and How They Work (New York: Dover Publications, 1971).
4. Lesley Flanigan, “Making Basic Gears: Tutorial,” ITP Mechanisms and Things That Move Archives (http://itp.nyu.edu/~laf333/itp_blog/mechanisms_and_ things_that_move/).