Chapter 8: Frames and Wheels
In the early 1970s an engineer named Bengt Ilon, working at a Swedish company called Mecanum AB, was looking at a problem in a warehouse aisle. Forklifts and pallet trucks ran well enough down a long straight aisle, but they could not step sideways. To shift a load a few centimetres across so that it lined up with a rack, the driver had to reverse, swing the whole machine round, creep forward and try again. Aisles were built wide for one reason only: so that vehicles could turn in them.
Ilon’s answer was an unusual one. He did not redesign the vehicle. He redesigned the wheel. Around the rim of an ordinary wheel he mounted a ring of small free-spinning rollers, each one set at 45° to the wheel’s own axis. Driven forward, a wheel like this still rolls forward — but it also pushes gently to one side. Fit four of them to a single platform and drive them in the right combination, and the sideways pushes add together while the forward pushes cancel out. The machine slides straight across the aisle without turning at all.
None of it works, though, unless those four wheels are held rigidly square to one another. If the platform flexes even slightly under a heavy load, the carefully balanced side forces stop cancelling and the machine crabs off its line. The wheels decide how a robot is able to move. The structure underneath decides whether it actually does.
Photograph
Fig. 8.0-1 – a wheeled robot platform fitted with Mecanum wheels, photographed from a low front-corner angle so that at least two wheels are seen face on; the angled free-spinning rollers around the rim must be clearly visible and individually distinguishable, and the flat chassis plate carrying the wheels must be in frame. Sourcing note: a real mobile robot or industrial platform in a workshop, warehouse or laboratory setting; renderings, exploded computer-generated views, and photographs of a bare wheel alone on a white background are unusable.
This chapter will answer all five of these questions.
8.1 The Frame as the Body of a Robot
Pick up any small robot from a school laboratory and the first thing your hand closes around is not a motor or a sensor. It is a flat board, or a bent metal plate, or a box of laser-cut panels screwed together at the corners. Everything else is attached to it. That board is the robot’s frame, and it is the subject of the first half of this chapter.
A frame is easy to overlook because it does nothing on its own. It draws no current, runs no code and sends no signal. Yet a motor bolted to a frame that twists cannot deliver its torque where it was meant to go, and a distance sensor screwed to a panel that flexes is no longer pointing where the program assumes it is pointing. The frame is the part of the robot that decides whether every other part can do its job.
8.1.1 Two Meanings of the Word Frame
Robotics uses the word frame for two entirely different things, and a student who meets both in the same week has every reason to be confused.
The first meaning is mathematical. A reference frame is a set of axes with an origin, attached to some part of a robot or to the ground, against which a position or an orientation is measured. It has no thickness and no weight. You cannot bolt anything to it, because it exists only on paper and in the controller’s arithmetic. When we say that the tip of an arm is at 300 mm along \(x\) and 150 mm along \(y\), we are speaking about a reference frame.
The second meaning is physical, and it is the one this chapter is about. Here a frame is the structure itself — the metal, wood or plastic that the robot is built from. It has mass, it has stiffness, and it can be drilled, cut and bolted. Fig. 8.1-1 shows the same small mobile robot drawn twice, once with its reference frames marked and once with its structural members shaded, so that the difference is visible at a glance.
Diagram
Fig. 8.1-1 – the same two-wheeled mobile robot drawn twice side by side. Left drawing: reference frames only — a fixed frame on the ground with origin and axes labelled x0 and y0, and a moving frame on the robot body with origin and axes labelled x1 and y1, the robot itself drawn in faint outline. Right drawing: the structural frame only — the chassis plate, the two motor mounting brackets and the corner standoffs drawn solid and shaded, with the wheels, motors and board drawn in faint outline. Caption labels beneath: “reference frames — measured” and “structural frame — built”.
The two are not unrelated, and that is exactly why the same word is used. A reference frame is only useful if the part it is attached to actually stays where it is supposed to be. Fix a base frame to a robot’s base, then let the base rock on a loose mounting, and every position computed from that frame is wrong by however far the base moved. The structural frame is what makes the mathematical frame trustworthy.
In this chapter, the word frame on its own always means the physical structure. Where the mathematical sense is intended, it is written in full as a reference frame.
8.1.2 What a Structural Frame Is
The frame is the load-bearing assembly on which every other subsystem of the robot is mounted. Motors are bolted to it, the controller board is standoff-mounted to it, sensors are bracketed to its edges, the battery is strapped to it, and the wheels or joints hang from it. It holds all of these in a fixed geometric relationship with one another while the robot works.
That last phrase is the important one. A frame is not merely a container. It is what guarantees that the ultrasonic sensor is 120 mm in front of the drive axle and pointing along the direction of travel, this hour and next month, whether the robot is empty or loaded.
Engineers describe this in terms of the workspace — the region of space in which the robot is expected to operate and do useful work. A frame is designed so that positional accuracy is maintained everywhere in that workspace, not just in the one pose in which it was assembled.
The frame of a small wheeled robot is often a single flat plate, sometimes two plates stacked on standoffs. Fig. 8.1-2 shows such an arrangement with each mounted subsystem named, and it is worth noticing how much of the design is simply decisions about where holes go.
Diagram
Fig. 8.1-2 – robot anatomy: a two-level chassis for a small wheeled robot drawn in exploded view. Lower plate labelled as the main frame plate, carrying two labelled motor brackets with drive wheels, one castor wheel at the rear, and a labelled battery position at the centre. Four standoffs labelled, rising to an upper plate carrying the labelled controller board and motor driver module. A labelled ultrasonic sensor bracket fixed to the front edge of the lower plate. Arrows from each component to its mounting holes on the plate.
8.1.3 The Frame and the Skeleton
The most useful way to picture a frame is as a skeleton. Your own bones do exactly this job: they carry your weight, they give muscles something to pull against, and they hold your eyes a fixed distance apart so that your brain can judge depth from what they see.
A robot frame does all three. It carries the weight of the battery and the payload. It gives the motors something to push against, since a motor bolted to nothing would simply spin its own case instead of the wheel. And it holds the sensors in known positions relative to the wheels, which is what allows a measured distance to be turned into a decision about where to drive.
The analogy has one limit worth stating. A skeleton is jointed everywhere and is meant to move. Most robot frames are meant to do the opposite — to stay rigid, so that all the movement happens at the joints and wheels the designer chose, and nowhere else. Unplanned movement in a frame is not flexibility. It is error.
8.2 What a Frame Must Do
A frame is not chosen; it is designed. Before you can say whether a flat sheet of wood or a welded steel box is the right structure for a robot, you have to be clear about what the structure is being asked to do.
Four demands come up in almost every robot, from a classroom line follower to a welding arm on a factory floor. The frame must stay rigid, it must give everything a place to mount, it must carry the loads acting on it, and it must protect what is inside it. This section takes them one at a time, and then looks at what happens when the first of them is not quite met.
8.2.1 Providing Structural Integrity
The first job of a frame is to hold its shape. Engineers call this rigidity — the ability of a structure to resist changing shape when forces are applied to it.
Rigidity matters because a robot’s geometry is written into its program. The controller works out where the gripper is from the lengths of the links and the angles of the joints. It works out where an obstacle is from the position of the sensor on the body. Every one of those calculations assumes the parts are still where the drawing says they are.
When a frame flexes, that assumption quietly fails. A base that twists a fraction of a degree carries the whole arm with it, and the error grows with distance from the base. Joints that were square to one another come out of alignment, bearings take load at an angle they were never meant to, and parts wear out early.
Consider an industrial arm lifting a heavy casting at full reach. The mass at the tip pulls the whole structure forward. If the base and the links deflect under that pull, the tip lands short of the programmed point — not because the motors turned to the wrong angles, but because the metal between them moved.
8.2.2 Serving as a Mounting Platform
The second job is to be something to bolt things to. Motors, gearboxes, sensors, the controller board, the motor driver and the battery all need a fixed, known place to sit, and the frame provides it.
Mounting is a geometric decision, not a convenience. The distance between the two drive-motor mounts fixes the track width of the robot, which in turn fixes how sharply it can turn. The position of a distance sensor fixes how far ahead of the wheels the robot can see, and therefore how much braking distance it has. Move a mounting hole 20 mm and you have changed the robot’s behaviour, not just its appearance.
Good mounting design also has to allow the robot to be built and rebuilt. Holes must be reachable by a screwdriver, connectors must be accessible without dismantling the machine, and the battery must be removable for charging.
8.2.3 Supporting Loads and Withstanding Forces
The third job is to carry loads. It helps to sort them into three kinds, because they behave very differently.
A static load is a force that is present whether or not the robot is moving. The weight of the battery, the controller and the frame’s own material are static loads. So is the payload — the useful mass the robot is built to carry or handle, such as a tray of components or a box on a warehouse platform.
A dynamic load is a force that appears because the robot is accelerating or decelerating. When a mobile robot starts, stops or turns sharply, everything mounted on it resists the change in motion, and that resistance is delivered to the frame as an extra force. A mast that stands still perfectly well may whip forward when the robot brakes.
An external load is a force applied by the world outside the robot. A gripper closing on a part pushes back on the arm. A drilling or cutting tool feeds a reaction force straight into the structure. A field robot pushing through a crop meets resistance from the plants and the soil.
Fig. 8.2-1 shows all three acting on the same small mobile robot, and it is worth noticing that they do not point the same way.
Diagram
Fig. 8.2-1 – a small two-wheeled mobile robot shown from the side, carrying a box payload on its upper plate, with three sets of labelled force arrows: static load drawn as downward arrows at the battery, the controller board and the payload; dynamic load drawn as a single horizontal arrow at the payload’s centre of mass pointing forward, labelled “inertial force during braking”; external load drawn as a horizontal arrow at the front bumper pointing backward into the robot, labelled “reaction from contact”. Ground line and the two wheel contact points marked with upward reaction arrows.
The static loads on even a small robot are easy to underestimate, so it is worth adding them up once. Table 8.2 lists typical masses for the parts a school-built mobile robot carries; the figures are representative of common components and vary a little between suppliers.
Total mass carried: \[m = (2 \times 40) + 180 + 25 + 30 + 12 + 300 = 627 \text{ g} = 0.627 \text{ kg}\]
Total weight: \[W = mg = 0.627 \text{ kg} \times 9.81 \text{ m/s}^2 = 6.15 \text{ N}\]
Weight of the sensor and its bracket: \[F = 0.012 \text{ kg} \times 9.81 \text{ m/s}^2 = 0.118 \text{ N}\]
Bending moment at the plate edge: \[M = F \times d = 0.118 \text{ N} \times 0.120 \text{ m} = 0.0141 \text{ N·m}\]
Answer: the frame carries about 6.15 N when standing still and loaded, and the sensor bracket applies a bending moment of about 0.014 N·m at the front edge of the plate. Check: 6.15 N is roughly the weight of a 600 g water bottle, which is about right for a robot you can lift with one hand. The moment is small — about what you feel holding a 12 g coin at the end of a 12 cm ruler — which is why a thin bracket is enough for a sensor but would be hopeless for a gripper.
8.2.4 Protecting Internal Components
The fourth job is protection. Control electronics, wiring and delicate sensors sit inside the robot, and the frame is usually shaped to keep the world off them — as panels, covers, or a closed box with the openings placed where nothing can fall in.
Indoors the threats are ordinary: dust settling on a board, a dropped tool, fingers pressing on a connector, a cable snagging as the robot passes a chair leg. Panels and cable routing deal with most of these.
Outdoors and in industry the threats are harsher. A field robot working in an irrigated plot meets water, mud and windblown grit. A welding cell fills with spatter and fumes. Frames for such machines are sealed against water ingress, and in some settings against radiation as well, which turns the frame into an enclosure with gaskets and sealed cable entries rather than an open plate.
Photograph
Fig. 8.2-2 – a field or outdoor mobile robot with a fully sealed enclosure, photographed in its working environment (a farm plot, an industrial yard or similar); the closed body panels, the sealed cable entry points or connector glands, and the wheels or tracks must all be visible, along with the dusty or wet ground it is standing on. Sourcing note: a real deployed machine outdoors, not a studio product shot, not a rendering, and not a robot with its covers removed.
Protection always costs something. A sealed frame is heavier, traps heat around the electronics, and takes longer to open when a fault has to be traced. This is a trade-off, not a free improvement, and it is settled by asking what the robot’s environment will actually do to it.
8.2.5 Deflection, Misalignment and Repeatability
Now put the first demand under a microscope, because this is where frame design meets robot performance.
No structure is perfectly rigid. Every frame bends a little under load, and deflection is the name for how far a point on the structure moves out of position when a force is applied to it. Deflection that disappears the moment the load is removed is elastic, and nothing has broken. It is still a problem.
To see why, think about what the load does. A frame under load deflects; the parts bolted to it are carried out of position with it; and the robot’s geometry is briefly not what the program assumes. Remove the load and everything springs back. Apply it again and everything shifts again.
The consequence shows up as poor repeatability — the ability of a robot to return to the same position over and over again under identical conditions. A robot that runs the same program with a full tray and then an empty one is not working under identical conditions, and a flexible frame will put the gripper in two different places. Fig. 8.2-3 exaggerates the effect so it can be seen.
Diagram
Fig. 8.2-3 – deflection: the same cantilever sensor bracket drawn twice, one above the other. Upper drawing labelled “unloaded” — the bracket straight and horizontal, with a dashed centre line from the sensor running horizontally forward, labelled “beam as programmed”. Lower drawing labelled “loaded” — the same bracket bent downward at an exaggerated angle, the sensor tilted with it, and its dashed centre line now sloping down towards the floor, labelled “beam as it actually points”; the vertical gap between the two sensor positions marked and labelled “deflection”.
Two practical points follow. First, stiffness matters more than raw strength for precision work: a frame that is strong enough never to break may still be far too springy to be accurate. Second, deflection is predictable, which means it can be designed out — by choosing a stiffer material, by making the section deeper, by adding a brace across a corner, or simply by shortening the distance between a load and its support.
8.3 Materials for Robotic Frames
Two robots can have identical motors, identical sensors and identical programs, and still behave quite differently — because one is built on a sheet of wood and the other on a plate of steel. The material a frame is made from settles how heavy the robot is, how much it flexes, how long it survives its surroundings, and how quickly a student can cut a new one during a lunch break.
Four materials cover almost everything a school or a workshop will build: MDF, acrylic, aluminum and steel. Each is genuinely the right answer for some robots and genuinely the wrong answer for others, and this section is about telling those cases apart.
8.3.1 What Makes a Material Suitable
Before naming any material, it helps to name the properties that decide the choice.
Strength is the load a material can carry before it permanently deforms or breaks. Rigidity, which you met in the last section, is different — it is how far the material moves before that point. A material can be strong and springy, or stiff and brittle, and a frame usually needs stiffness more than it needs raw strength.
Density is the mass of a material per unit volume, measured in kg/m³. It decides what a given plate weighs, and therefore how much torque the motors must produce, how fast the battery drains, and how hard the robot is to stop. Table 8.3 gives typical values for the four materials.
Put those two properties together and you get the figure engineers actually argue about: the strength-to-weight ratio, which is how much load a material can carry for each unit of its own mass. A material that is enormously strong is of little use in a flying or fast-moving robot if most of its strength is spent carrying itself.
Machinability is how easily a material can be cut, drilled, shaped and joined with the tools available. This is not a minor practical detail. A material that needs a welding set and a milling machine cannot be used by a class that has a hand drill and a coping saw, however good its properties are on paper.
Two more properties complete the list. Resistance to the environment covers moisture, chemicals and corrosion, which is the gradual chemical attack of a material by its surroundings — rusting is the familiar example. And cost, including both the material itself and the equipment needed to work it, decides what a school or a start-up can actually build.
Volume of the plate: \[V = 0.200 \text{ m} \times 0.150 \text{ m} \times 0.003 \text{ m} = 9.0 \times 10^{-5} \text{ m}^3\]
Mass in each material: \[m_{\text{MDF}} = 750 \text{ kg/m}^3 \times 9.0 \times 10^{-5} \text{ m}^3 = 0.0675 \text{ kg} = 67.5 \text{ g}\] \[m_{\text{acrylic}} = 1180 \times 9.0 \times 10^{-5} = 0.106 \text{ kg} = 106 \text{ g}\] \[m_{\text{aluminum}} = 2700 \times 9.0 \times 10^{-5} = 0.243 \text{ kg} = 243 \text{ g}\] \[m_{\text{steel}} = 7850 \times 9.0 \times 10^{-5} = 0.707 \text{ kg} = 707 \text{ g}\]
Answer: about 68 g in MDF, 106 g in acrylic, 243 g in aluminum and 707 g in steel. Check: the steel plate alone weighs more than the entire 627 g load the same robot was carrying in the previous section, which is a useful warning. The ratios follow the densities exactly, as they must, since the geometry is identical in every case.
That last calculation is worth holding on to. Choosing steel over MDF for a small mobile robot does not add a little weight; it multiplies the plate’s mass by ten, and every gram of it has to be accelerated, carried and braked by the same motors and the same battery.
8.3.2 MDF
Medium-density fibreboard (MDF) is an engineered wood product. Wood fibres from hardwood or softwood are broken down, mixed with wax and a resin binder, and pressed under heat into a dense board with no grain and no knots.
That absence of grain is the point. Natural timber splits along its grain and behaves differently in different directions; MDF is uniform throughout, so it can be cut, routed and drilled anywhere on the sheet with the same predictable result. Its surface is smooth enough to take paint and adhesives directly, and it is among the cheapest materials on the list. Fig. 8.3-1 shows a typical school robot built on an MDF base.
Photograph
Fig. 8.3-1 – a small wheeled school robot built on a plain MDF base plate, photographed at a shallow angle on a workbench; the cut edge of the board must be visible so its uniform fibrous cross-section can be seen, along with the drilled mounting holes and at least one bracket screwed directly into the board. Sourcing note: a real student-built or kit-built robot on untreated MDF; painted or laminated boards that hide the material, and renderings, are unusable.
Against that, MDF is heavy for the strength it offers, and its load-bearing capacity is modest beside any metal. It is brittle under concentrated stress, so a screw driven too enthusiastically near an edge will split it. Its most serious weakness is water: MDF absorbs moisture, swells and loses its structural integrity, and a swollen board never recovers its shape.
MDF therefore belongs where mechanical stress is low, the surroundings are dry, and the ability to make a new part in twenty minutes matters more than durability — classroom robot chassis, prototype platforms built to test a layout before committing to metal, enclosures for controllers and power modules, and test rigs that hold components steady during an experiment.
8.3.3 Acrylic
Acrylic is a transparent thermoplastic, sold under trade names such as Plexiglas and Perspex. In robotics it is used as flat sheet, typically 3 mm to 6 mm thick, cut to shape and bolted together with standoffs.
Its appeal is a combination that no other material on this list offers. It is light — about a seventh the density of steel — it can be laser cut into intricate shapes with clean edges and precise holes, and it is transparent, so the wiring and boards mounted behind it stay visible. In a classroom that last property is genuinely useful: a fault can often be traced without taking the robot apart, and a student can see what the machine is made of. Fig. 8.3-2 shows a laser-cut acrylic chassis with its electronics visible through the plate.
Photograph
Fig. 8.3-2 – a small robot built on a clear laser-cut acrylic chassis, photographed from above and slightly to one side so that the controller board, battery and wiring are visible through the transparent plate; the laser-cut slots and mounting holes and the polished cut edges must be distinguishable. Sourcing note: a real assembled robot with clear (not tinted or opaque) acrylic; renderings and bare uncut sheets are unusable.
Acrylic’s weakness is that it is brittle. It does not bend and recover the way a metal or a tougher plastic does; past a certain stress it cracks, and a crack once started tends to run. Sudden impact is its enemy, which is why an acrylic robot that falls off a bench often lands in two pieces. It also scratches easily, and it softens and warps if it is left in strong sunlight or near a hot component.
Acrylic suits educational robots such as line followers and maze solvers, early prototypes built to test a layout before moving to metal, and transparent enclosures for electronics. It does not suit heavy-duty machines or industrial environments.
8.3.4 Aluminum
Aluminum is the metal that most working mobile robots are built from. It is used as an alloy — a metal mixed with small amounts of other elements to improve its properties — because pure aluminum is too soft to be useful as a structure.
Its defining property is a high strength-to-weight ratio. At 2700 kg/m³ it is roughly a third the density of steel, yet a well-chosen alloy carries enough load for most robots below industrial scale. A machine framed in aluminum accelerates faster, runs longer on the same battery and is easier to lift onto a bench than the same machine in steel.
Aluminum also protects itself. Exposed to air, its surface forms a thin, tightly bound oxide layer that stops the attack going any deeper, so it does not rust the way untreated steel does. For an outdoor or field robot this matters as much as the weight saving.
It is straightforward to work with ordinary workshop tools — it can be sawn, drilled and tapped without special equipment — and it is widely sold as extrusion, which is aluminum pushed through a shaped die to give a long section of constant profile. Slotted extrusion profiles let a frame be bolted together, taken apart and rearranged without a single new hole being drilled, which is why so many laboratory and teaching platforms are built from them. Fig. 8.3-3 shows such a frame.
Photograph
Fig. 8.3-3 – a robot or test platform frame built from slotted aluminum extrusion profiles, photographed at a three-quarter angle; the T-slots along the length of the profiles, at least two corner brackets with their bolts, and the joint between two profiles must be clearly visible. Sourcing note: a real assembled extrusion frame in a workshop or laboratory; catalogue photographs of loose profiles, and renderings, are unusable.
The limitations are real but narrow. Aluminum is less stiff than steel, so under very heavy or sustained load it deflects further; alloying improves this but does not close the gap. It costs more than MDF or acrylic. And it expands and contracts noticeably with temperature, which can matter in a machine holding tight tolerances across a hot working day.
Aluminum is therefore the usual choice for mobile robots, for drones and other aerial robots where every gram limits flight time, for the moving links of lighter robotic arms, for collaborative robots that work beside people and must not be heavier than necessary, and for the modular teaching and research platforms just described.
8.3.5 Steel
Steel is the material of choice when a frame must not move at all. It is an iron-based alloy, used for robot frames as mild steel or as an alloy steel, and fabricated by welding, bolting or machining.
Its strength is stiffness. Steel deflects far less than aluminum under the same load, which is exactly what an industrial arm needs when it swings a heavy casting at full reach and must still put the tool within a fraction of a millimetre of the programmed point. Steel also damps and resists vibration well, so a machine standing on a factory floor beside presses and conveyors keeps working smoothly. And it is cheap for what it does, widely available and easily repaired or modified by any workshop. Fig. 8.3-4 shows a steel-framed arm bolted to its foundation.
Photograph
Fig. 8.3-4 – the base and lower links of a heavy industrial robotic arm, photographed from ground level so that the massive steel base casting, the bolts fixing it to the floor, and the welded or machined joints of the lower structure are clearly visible. Sourcing note: a real installed industrial arm on a factory floor, with no person inside the working area; close-ups of the gripper alone, and renderings, are unusable.
The drawback is weight, and it is decisive. A steel frame makes the whole robot heavier, which means larger motors, a larger battery and more energy for every movement — which is why steel is rare on mobile robots and normal on machines that are bolted down. Untreated steel also corrodes when it meets moisture or chemicals, so it has to be painted, plated or specified as stainless steel where the environment is damp.
Steel suits fixed-base industrial robots such as welding, cutting and machining arms; material-handling robots that lift heavy loads repeatedly; assembly-line robots working continuously to tight tolerances; and the test rigs and support structures where long-term durability and vibration resistance matter far more than mobility.
8.3.6 Comparing the Four Materials
Set side by side, the four materials form a clear progression. Table 8.4 draws the comparison feature by feature.
Reading the table across, the pattern is a trade of weight against stiffness, with workability and cost cutting across both. MDF and acrylic buy speed and cheapness at the cost of load capacity. Aluminum buys a genuine structural material at a modest weight penalty. Steel buys precision under heavy load, and pays for it in mass.
That is why the selection question is never “which material is best”. It is “what does this robot actually have to survive”. A prototype that will be redesigned twice next week is best made in the material that can be recut fastest. A machine that will lift 50 kg for ten years is best made in the material that will not have moved a millimetre at the end of it.
Other materials exist, and a professional designer will meet them — titanium for space and underwater work, carbon fibre composites for racing drones, tougher engineering plastics for impact-prone service robots. They are chosen by exactly the same reasoning applied here, against the same properties.
8.4 Wheels in Robotic Systems
The frame decides what a robot can carry. The wheels decide where it can take it.
A motor, left to itself, does only one thing: it turns a shaft. Everything a mobile robot does — crossing a workshop floor, following a line, backing out of a dead end — begins with the problem of converting that turning into travel across the ground. Wheels are the usual answer, and this section is about how they do it and what a designer gains and loses by using them.
8.4.1 Turning Rotation into Travel
Put a wheel on a motor shaft and stand the robot on the floor, and something quietly clever happens. The motor turns the wheel; the rim of the wheel presses against the floor and cannot slide; so instead of the rim sliding backwards, the whole robot is pushed forwards. Rotation at the shaft has become locomotion — movement of the machine as a whole from one place to another.
The word cannot slide is doing the real work in that sentence, and it points to the property everything depends on. Traction is the grip between a wheel and the surface it runs on, produced by friction at the small patch where the two touch. Without traction the motor turns, the wheel spins and the robot stays exactly where it was.
How far the robot travels follows from the geometry of the wheel. In one complete revolution, a wheel that is rolling without slipping lays its entire rim along the ground once, so the axle advances by the wheel’s circumference: \[s = \pi d\] where \(d\) is the wheel diameter in m and \(s\) is the distance travelled in one revolution, also in m. Fig. 8.4-1 shows this for a single revolution, and it is the relation the whole of section 8.6 is built on.
Diagram
Fig. 8.4-1 – a single wheel of diameter d shown rolling from left to right along a ground line, drawn in three positions: start, quarter turn and one full turn. A marked point on the rim is shown at each position to make the rotation visible. The horizontal distance between the axle at the start and the axle after one full turn is dimensioned and labelled with the circumference. At the contact point of the middle wheel, two labelled arrows: the friction force from the ground acting forward on the wheel, and the wheel’s push acting backward on the ground.
Three things follow from that single relation, and they are worth noticing now. A larger wheel covers more ground per revolution, so the same motor speed gives a faster robot. A larger wheel also needs more torque to drive, because the ground pushes back further from the axle. And the whole calculation assumes there is no slipping — which is exactly the assumption traction is there to protect.
8.4.2 Why Wheels Rather than Legs
A robot could walk. Legs cross broken ground, climb steps and step over obstacles in ways no wheel manages. Yet almost every robot in a warehouse, a hospital corridor or a school laboratory rolls. It is worth being clear about why.
Wheels are efficient. A rolling wheel loses very little energy to friction on a hard flat surface, while a leg must be lifted, swung and set down against gravity at every step. For the same battery, a wheeled robot travels considerably further.
Wheels are simple. Two motors and two wheels make a working drive system. A walking machine needs several joints per leg, each with its own actuator, and a control program that keeps the whole body balanced while some of the legs are off the ground. Fewer moving parts also means fewer things to fail.
Wheels are stable and carry load well. A platform standing on three or four wheels distributes its weight through fixed contact points and does not have to balance, which is what makes wheeled machines the natural choice for service robots, industrial automated guided vehicles (AGVs) and mobile platforms used in teaching and research.
The cost of all this is terrain. Wheels need a surface that is reasonably flat, firm and continuous. A step taller than about a third of the wheel’s radius will stop an ordinary wheel; soft mud and loose sand rob it of traction; a gap in the floor swallows it. Where the ground is broken, designers turn to tracks or legs and accept the extra complexity and power that go with them.
8.4.3 Driven Wheels, Supporting Wheels and Drive Arrangements
Not every wheel on a robot has a motor behind it, and the distinction matters.
A driven wheel is connected to a motor and produces the force that moves the robot. An idler wheel — a supporting or free-running wheel — has no motor at all. It turns because the robot is moving, and its job is to hold part of the machine’s weight and keep it stable.
The pairing of the two is what makes small mobile robots so simple. Fig. 8.4-2 shows the three arrangements you will meet most often, drawn from above.
Diagram
Fig. 8.4-2 – three drive arrangements drawn as top views of a rectangular chassis, side by side and labelled. (a) Differential drive: two driven wheels on a common axis at the middle of the chassis, each with its own motor drawn as a labelled block, and one free-swivelling supporting wheel at the rear; a curved arrow showing the robot pivoting when the two driven wheels turn at different speeds. (b) Four-wheel drive: four driven wheels, one at each corner, each with a labelled motor. (c) Steered drive: two driven wheels at the rear on a common axle, and two front wheels linked by a labelled steering mechanism, with a curved arrow showing the front pair swivelling together. Under each, a label naming the arrangement.
The first arrangement is called differential drive, and it is the one most school robots use. Two driven wheels sit on a common axis, one on each side of the robot, and each is controlled independently. Turn both at the same speed and the robot runs straight. Turn one faster than the other and it curves towards the slower side. Turn them at the same speed in opposite directions and it spins on the spot without going anywhere.
What makes this elegant is that it needs no steering mechanism at all. There is no linkage, no steering motor and no extra joint — the same two motors that drive the robot also steer it. The price is that the robot needs a third point of support, since two wheels on one axis would simply topple forward or backward, and that support has to be free to follow wherever the robot turns.
That third point is almost always a swivelling supporting wheel, and the next section begins with the family it belongs to.
8.5 Types of Wheels
A wheel looks like a solved problem. It is round, it turns, and it has been doing so for several thousand years. Yet a robot that has to reverse into a narrow aisle, or slide sideways to line up with a shelf, or hold itself steady while two driven wheels spin it round, asks things of a wheel that a cart never asked.
Robotics answers with four types: standard, castor, Mecanum and Omni. The first two are ordinary wheels used in particular roles. The last two are wheels with moving parts on their own rims, and they change what a robot is able to do.
8.5.1 Standard Wheels
A standard wheel — sometimes called a fixed wheel — is the plain wheel of everyday life: a circular rim on a hub, mounted on an axle whose direction is fixed relative to the robot’s body. It rotates about that one axis and nothing else, which means it can roll forward or backward and cannot do anything sideways at all. Fig. 8.5-1 shows a typical example.
Photograph
Fig. 8.5-1 – a standard robot drive wheel of the kind used in school kits, photographed at a three-quarter angle against a plain background; the rubber tyre with its tread pattern, the plastic or metal hub, and the shaft opening at the centre must all be clearly visible. Sourcing note: a real wheel, unmounted or on a motor shaft; renderings and cross-sectional drawings are unusable.
This restriction is not a defect. It is the reason standard wheels grip so well: the whole width of the tyre presses against the floor and none of it is free to slide, so almost all of the motor’s effort goes into moving the robot forward. Because a standard wheel cannot go sideways, a robot using them changes direction by turning its whole body — which, in a differential drive arrangement, it can do on the spot without any steering mechanism at all.
8.5.2 Castor Wheels
A castor wheel is a small free-rotating wheel mounted on a vertical pivot, so that it can swivel to face whatever direction it is being dragged in. You have met one on every shopping trolley and office chair you have used.
Castors are not motorised. They contribute nothing to propulsion. Their job is to hold up part of the robot’s weight and to let it change direction without fighting the floor — which is exactly what the third support point of a differential drive robot needs to do.
The mechanism that makes this work is a small geometric trick, shown in Fig. 8.5-2. The wheel’s axle is set a short distance behind the pivot axis rather than directly under it. When the robot moves, the drag at the contact patch pulls the wheel round the pivot until it trails straight behind — automatically, with no motor and no instruction.
Diagram
Fig. 8.5-2 – castor wheel drawn as a side view and a top view side by side. Side view: mounting plate at the top, vertical pivot axis drawn as a dashed line down through the swivel bearing, the wheel below with its horizontal axle marked; the horizontal offset between the pivot axis and the wheel axle dimensioned and labelled “offset”. Top view: the same castor shown in three positions as the robot’s direction of travel reverses — trailing straight, mid-swivel, and trailing straight the other way — with a curved arrow through the pivot showing the swivel and a straight arrow showing the robot’s direction of travel at each stage.
That automatic alignment is also the castor’s weakness. Because nothing controls it, its behaviour during the swivel is not fully predictable: for a moment it drags sideways and pushes the robot slightly off its line. At speed a castor can begin to shimmy, oscillating from side to side, and on rough ground the small wheel snags in gaps that a driven wheel would roll over.
8.5.3 Mecanum Wheels
Everything so far has assumed a wheel can only push along the direction it rolls. A Mecanum wheel breaks that assumption.
Around the rim, in place of a continuous tyre, sits a ring of small barrel-shaped rollers, each free to spin on its own axis, and each mounted at 45° to the wheel’s axis. Drive the wheel and the rim still pushes against the floor — but because the roller in contact can spin freely along its own length, the push does not come out along the robot’s forward line. It comes out at 45° to it, as a force with both a forward part and a sideways part.
One such wheel on its own is not much use; it simply skids off at an angle. Four of them, mounted in matched left-hand and right-hand pairs, are transformative. Each wheel contributes a 45° push, and by choosing which wheels turn forward and which turn backward, the designer chooses which of those pushes survive and which cancel out. Fig. 8.5-3 shows the arrangement with the force from each wheel drawn in.
Diagram
Fig. 8.5-3 – top view of a rectangular robot chassis with four Mecanum wheels, one at each corner, labelled front-left, front-right, rear-left and rear-right. On each wheel the roller direction is drawn as a set of short parallel lines at 45°, arranged so that the four sets form an X pattern across the chassis. At each wheel’s contact point, an arrow at 45° shows the force produced when that wheel is driven forward. To the right of the chassis, three small repeat drawings labelled “forward”, “sideways” and “rotate on the spot”, each showing the four wheel rotation directions as F or B beside each wheel and a large resultant arrow for the robot’s motion.
The combinations follow a clear pattern, set out in Table 8.5. Notice which one produces sideways travel: it is not one side forward and the other backward — that spins the robot, exactly as it would on ordinary wheels. Sideways travel comes from driving one diagonal pair forward and the other diagonal pair backward.
Which physical direction the sideways rows produce depends on how the particular set of wheels is handed and mounted, so the sensible practice is to test each combination on the bench before trusting it in a program.
8.5.4 Omni Wheels
An Omni wheel uses the same idea as a Mecanum wheel with one change: its rollers are set at 90° to the wheel’s main rotation rather than at 45°. The central wheel still rolls normally; the rollers let it slide freely straight sideways with very little resistance. Fig. 8.5-4 shows the arrangement.
Photograph
Fig. 8.5-4 – a single Omni wheel photographed face on and slightly angled, against a plain background; the individual free-spinning rollers around the circumference and their perpendicular mounting must be clearly visible, along with the central hub and shaft opening. Sourcing note: a real wheel, mounted or unmounted; renderings, and photographs where the rollers are obscured by a tyre or guard, are unusable.
The consequence of that 90° setting is worth thinking through. A Mecanum wheel pushes at 45° and slides at 45°. An Omni wheel pushes straight along its rolling direction, like an ordinary wheel, and is simply free to be pushed sideways by whatever else is happening. That makes each wheel behave more simply, but it means the wheels have to be arranged at angles to one another for the robot to go anywhere but straight — most often three wheels at 120° apart, or four at 90°.
Both wheel types deliver what is called holonomic motion — motion in which a robot can travel in any direction on the plane, and rotate, without first having to turn to face where it is going. A holonomic robot in a corridor can move straight across to the far wall; a robot on standard wheels must turn, drive and turn back.
8.5.5 Comparing the Four Wheel Types
Table 8.6 sets the four side by side on the features that decide a design.
Read down the table and one trade-off runs through everything: freedom of movement is bought with traction, efficiency, cost and control effort. A standard wheel does one thing supremely well. A Mecanum or Omni wheel does everything moderately well, and needs four motors and a careful program to do it.
The choice therefore follows the task rather than the specification sheet. A robot running a fixed route down a clear corridor gains nothing from holonomic motion and loses grip and battery life paying for it. A robot that must slide into a gap barely wider than itself cannot manage without it.
8.6 Matching the Structure to the Task
The frame and the wheels have been treated separately so far, and in a real design they cannot be. The frame decides where the weight sits; where the weight sits decides whether the wheels grip; and what the wheels can do decides what shape the frame has to be.
This section brings the two together, first through the physics that links them, then through the arithmetic that turns a wheel size into a speed, and finally through the questions a designer actually asks before cutting anything.
8.6.1 Weight, Traction and Load Distribution
A wheel can only push the robot as hard as friction at its contact patch allows. That limit depends on two things: how firmly the wheel is pressed against the floor, and how grippy the pairing of tyre and surface is.
The force pressing the wheel down is the normal force — the share of the robot’s weight carried by that wheel, measured in N. The grippiness is captured by the coefficient of friction, written \(\mu\), a number with no unit that depends on both surfaces: rubber on clean concrete is high, hard plastic on polished tile is low, anything on wet or dusty tile is lower still. The largest force the wheel can deliver before it slips is \[F = \mu N\]
Read that relation carefully, because it settles a question students often get wrong. Traction does not come from the motor. A more powerful motor cannot push harder than \(\mu N\) — past that point it only spins the wheel faster. Grip is bought by pressing the wheel down harder, or by changing the surfaces.
This is where the frame re-enters. The centre of mass of a robot is the single point at which its whole weight can be taken to act, and its position depends entirely on where the frame puts the heavy components. Move the battery and you move the centre of mass; move the centre of mass and you change how the robot’s weight is shared between the driven wheels and the supporting castor. Fig. 8.6-1 shows the same robot with the battery in two positions and the very different results.
Diagram
Fig. 8.6-1 – two side views of the same differential drive robot, one above the other, each showing the chassis, the driven wheel at the front-centre and the castor at the rear. Upper drawing labelled “battery over the drive axle”: the battery block drawn directly above the driven wheel, the centre of mass marked with a labelled dot close to the drive axle, and reaction arrows at the two contact points drawn with a long arrow at the driven wheel and a short one at the castor. Lower drawing labelled “battery over the castor”: the battery block drawn at the rear, the centre of mass marked well back, and the reaction arrows reversed — short at the driven wheel, long at the castor. A note line beside each pair of arrows reading “share of weight carried”.
A robot whose battery sits over the castor has moved most of its weight onto a wheel that produces no force at all. The driven wheels are lightly loaded, \(N\) is small, and \(\mu N\) with it — so the robot slips on a smooth floor, struggles on a gentle slope, and accelerates poorly. Nothing is wrong with the motors or the wheels. The weight is in the wrong place.
The working rule that follows is simple: put the heavy items over or close to the driven wheels, and keep them low. Low helps for a second reason — a high centre of mass makes a robot lean when it accelerates or turns, shifting weight off the wheels that need it and, in the worst case, tipping the machine over.
8.6.2 Wheel Diameter, Distance Travelled and Speed
Section 8.4 established that a wheel rolling without slipping advances by its circumference, \(\pi d\), in each revolution. Everything a designer needs to know about how fast a robot goes, and how far, follows from that one line.
The motor contributes the other half. A geared motor is rated in revolutions per minute (rpm), and if the wheel is mounted directly on its output shaft, wheel speed and motor speed are the same. Distance per revolution multiplied by revolutions per second gives speed.
Distance travelled in one revolution: \[s = \pi d = \pi \times 0.065 \text{ m} = 0.204 \text{ m}\]
Revolutions needed for 2.0 m: \[n = \frac{2.0 \text{ m}}{0.204 \text{ m}} = 9.8 \text{ revolutions}\]
Wheel speed in revolutions per second: \[\frac{100}{60} = 1.67 \text{ rev/s}\]
Straight-line speed: \[v = 0.204 \text{ m} \times 1.67 \text{ rev/s} = 0.34 \text{ m/s}\]
Answer: about 0.204 m per revolution, about 9.8 revolutions to cover 2.0 m, and a speed of about 0.34 m/s. Check: 0.34 m/s is roughly a quarter of an adult’s walking pace, which is about right for a small classroom robot — fast enough to cross a table in a couple of seconds, slow enough to stop before it reaches the edge. A result of 3.4 m/s or 0.034 m/s would have signalled a factor-of-ten slip in the unit conversion.
Applying the same method to the other wheel sizes found in a school laboratory gives Table 8.7, and the pattern is worth reading rather than just checking.
The relationship is proportional: going from a 65 mm wheel to a 90 mm wheel, an increase of about 38%, raises the speed by about 38% too, with no change of motor. That looks like a free gift, and it is not.
The catch is torque. The ground pushes back at the rim, a distance \(r\) from the axle, so the turning effort the motor must supply for a given driving force is \(\tau = F \times r\). A larger wheel means a longer lever arm against the motor, so the same motor delivers less force at the contact patch. The robot goes faster on flat ground and struggles more on a slope, over a threshold or when starting with a load.
There is a third consequence, and it concerns accuracy. Odometry is the technique of estimating how far a robot has travelled by counting wheel revolutions and multiplying by the circumference. Because the multiplier is \(\pi d\), any error in \(d\) — a tyre that has worn down, a wheel measured to the outside of the rubber rather than to the rolling surface, or a tyre squashed flat under load — is multiplied into every distance the robot believes it has covered.
8.6.3 Selecting a Frame and Wheels for a Given Robot
Design decisions in this chapter are rarely made one at a time. A designer works through a short list of questions, and the answers narrow the choices together.
What must the robot carry, and how heavy is it in total? The payload plus the fixed components gives the static load, and the material must be stiff enough to carry it without the deflection that costs repeatability.
Where will it work? A dry classroom floor, a wet corridor, a dusty yard and an oily workshop rule different materials in and out — moisture alone eliminates MDF and untreated steel.
How much space does it have to move in? An open floor and a fixed route need nothing more than standard wheels and a castor. An aisle barely wider than the robot is where Mecanum or Omni wheels earn their cost.
How precisely must it position itself? Tight positioning demands a stiff frame, since flexing under load is what turns a correct calculation into a wrong result, and it demands wheels that do not slip unpredictably.
How often will the design change? A machine that will be rebuilt three times this term should be built in something that can be recut in an afternoon.
What can actually be made with the tools available? A design that needs welding is not a design for a laboratory with a hand drill.
Work those through for a school line-following robot and the answers converge quickly: a light payload, a dry indoor floor, an open track, modest precision, frequent rebuilding, hand tools only. MDF or acrylic for the frame, two standard wheels driven differentially, one castor at the rear, and the battery mounted low and over the drive axle.
Work them through for a warehouse pallet mover and they converge somewhere else entirely: hundreds of kilograms of payload, a hard concrete floor, aisles with no room to turn, tight positioning against a rack, a design that will not change for years, and a factory that can weld. A steel frame, and Mecanum wheels so the machine can slide sideways into position rather than manoeuvring for it.
Neither robot is better engineered than the other. Each is the honest answer to a different set of six questions, and that habit — deciding from the task rather than from the catalogue — is the one worth carrying out of this chapter.
8.7 Summary
Frames
- Robotics uses the word frame in two senses. A reference frame is a set of axes and an origin used to measure position and orientation; it has no mass and exists only in calculation. A structural frame is the physical assembly the robot is built from. This chapter uses frame for the second sense throughout.
- The two are linked: a reference frame is only trustworthy while the structure it is attached to holds its position. If the structure moves, every position computed from that frame is wrong.
- A frame is the primary structural assembly of a robot. It supports, aligns and integrates the mechanical, electrical and control components, carries the loads acting on the robot, and maintains positional accuracy throughout the robot’s intended workspace.
- A frame has four jobs: providing structural integrity, serving as a mounting platform, supporting loads and withstanding forces, and protecting internal components.
- Rigidity is the ability of a structure to resist changing shape under load. It matters because a robot’s geometry is written into its program — the controller assumes every part is exactly where the drawing places it.
- Mounting is a geometric decision, not a convenience. Motor mounts fix the track width and therefore the turning behaviour; a sensor’s position fixes how far ahead the robot can see.
- Three kinds of load act on a frame. A static load is present whether or not the robot moves, and includes the payload — the useful mass the robot is built to carry. A dynamic load appears when the robot accelerates or decelerates. An external load is applied by the world outside, such as a gripper’s reaction or resistance from a crop.
- Protection covers dust, moisture, impact and, in harsh settings, sealing against water ingress or radiation. It is a trade-off: a sealed frame is heavier, traps heat and is slower to open for repair.
- Deflection is how far a point on a structure moves out of position under load. Elastic deflection breaks nothing, but it makes the robot’s geometry depend on how heavily it is loaded, which shows up as poor repeatability — the ability to return to the same position under identical conditions. For precision work, stiffness matters more than raw strength.
Materials
- A frame material is judged on strength, density, strength-to-weight ratio, machinability, resistance to moisture and corrosion, and cost — including the cost of the equipment needed to work it.
- The mass of a plate follows \(m = \rho V\). For the same 200 mm × 150 mm × 3 mm plate, MDF gives about 68 g, acrylic 106 g, aluminum 243 g and steel 707 g. Choosing steel over MDF multiplies the plate’s mass roughly tenfold.
- The four materials named for robotic frames are MDF, acrylic, aluminum and steel.
- MDF is an engineered wood board of uniform density, cheap and workable with hand tools, used for classroom chassis, prototypes and enclosures. It is heavy for its strength, brittle at edges, and swells irreversibly when it absorbs moisture.
- Acrylic is a light, transparent thermoplastic that laser cuts cleanly, used for educational robots, prototype chassis and clear enclosures. It is brittle, cracks under impact, scratches easily and softens with heat.
- Aluminum has a high strength-to-weight ratio, resists corrosion through its own oxide layer, works with ordinary workshop tools, and is sold as slotted extrusion for modular frames. It is used for mobile robots, drones, light arms, cobots and teaching platforms. It is less stiff than steel, costs more than MDF or acrylic, and expands noticeably with temperature.
- Steel is the stiffest of the four and resists vibration well, which is why fixed industrial arms, material-handling robots and test rigs are built from it. Its weight makes it unsuitable for most mobile robots, and untreated steel corrodes.
- The selection question is never which material is best, but what the robot has to survive.
Wheels
- A wheel converts a motor’s rotation into locomotion. Traction — the friction available at the contact patch — is what allows the rotation to push the robot rather than spin uselessly.
- A wheel rolling without slipping advances by its circumference in each revolution, \(s = \pi d\). Wheel rotation equals distance travelled only while there is no slip, which is why odometry drifts on smooth or loose surfaces.
- Wheels are preferred to legs because they are efficient, mechanically simple and stable under load. They need a surface that is reasonably flat, firm and continuous; broken ground calls for tracks or legs.
- A driven wheel is connected to a motor and produces the driving force; an idler or supporting wheel is free-running and only carries weight. In differential drive, two independently controlled wheels on a common axis both drive and steer the robot, with no steering mechanism at all, and a third free support point is needed.
- The four wheel types named for robotic systems are standard, castor, Mecanum and Omni.
- A standard wheel rotates about a single fixed axle axis. It is simple, efficient, grippy, cheap and durable, but cannot move sideways, so the robot must turn to change direction.
- A castor wheel is an unpowered wheel on a swivel pivot, with its axle offset behind the pivot axis so drag makes it trail automatically in the direction of travel. It gives stability and easy turning but no propulsion, and it can shimmy at speed and snag on rough ground.
- A Mecanum wheel carries free-spinning rollers set at 45° to the wheel axis, so each driven wheel pushes at 45° to its rolling direction. With four wheels in matched left-hand and right-hand pairs, sideways travel comes from driving one diagonal pair forward and the other diagonal pair backward; driving one side forward and the other backward rotates the robot on the spot.
- An Omni wheel carries rollers set at 90° to the main rotation, so it drives along its rolling direction while sliding almost freely sideways. Several such wheels, mounted at angles to one another, give motion in any direction.
- Both Mecanum and Omni wheels deliver holonomic motion — movement in any direction on a plane, and rotation, without first turning to face the direction of travel. The ability is paid for in traction, efficiency, cost and control complexity.
Putting them together
- The largest force a wheel can deliver before slipping is \(F = \mu N\), where \(N\) is the share of the robot’s weight carried by that wheel and \(\mu\) is the coefficient of friction between wheel and surface. Grip comes from load and surface, never from a more powerful motor.
- The centre of mass is the point at which the robot’s whole weight can be taken to act, and the frame layout decides where it sits. Heavy items belong low and over the driven wheels; weight placed over a castor is weight that produces no traction at all.
- Wheel diameter trades speed against force. A larger wheel covers more ground per revolution and so runs faster at the same motor speed, but gives the ground a longer lever arm against the motor, so less force reaches the contact patch and the robot climbs and starts less well. Because \(\tau = F \times r\), this trade cannot be avoided by any change of wheel alone.
- Frame and wheels are selected together, from the task: what the robot must carry, where it will work, how much room it has to move in, how precisely it must position itself, how often the design will change, and what the available tools can actually make.
8.8 Key Terms
- Acrylic — a light, transparent thermoplastic sheet material, easily laser cut, used for prototype and educational robot frames.
- AGV — automated guided vehicle; a wheeled mobile robot that carries loads along routes in a factory or warehouse.
- Alloy — a metal mixed with small amounts of other elements to improve properties such as strength, stiffness or corrosion resistance.
- Aluminum — a light metal, used in alloy form for robot frames where a high strength-to-weight ratio and corrosion resistance are needed.
- Castor wheel — an unpowered wheel on a swivel pivot, with its axle offset behind the pivot axis, so that it trails automatically in the direction of travel.
- Centre of mass — the single point at which the whole weight of a body can be taken to act.
- Coefficient of friction — a number, written \(\mu\) and having no unit, describing how much frictional force two surfaces can develop between them.
- Corrosion — the gradual chemical attack of a material by its surroundings, of which the rusting of untreated steel is the familiar example.
- Deflection — the distance a point on a structure moves out of position when a force is applied to it.
- Density — the mass of a material per unit volume, measured in kg/m³.
- Differential drive — a drive arrangement in which two independently controlled wheels on a common axis, one on each side of the robot, both propel and steer it.
- Driven wheel — a wheel connected to a motor, which produces the force that moves the robot.
- Dynamic load — a force on a structure that arises because the machine is accelerating or decelerating.
- External load — a force applied to a robot by the world outside it, such as the reaction from a gripper, a tool or the ground.
- Extrusion — a length of material of constant cross-section, formed by pushing it through a shaped die; slotted aluminum extrusion is widely used for modular robot frames.
- Frame — the primary structural assembly of a robot, which supports, aligns and integrates its components, carries the loads on it, and maintains positional accuracy throughout its workspace.
- Holonomic motion — motion in which a robot can travel in any direction on a plane, and rotate, without first turning to face the direction of travel.
- Idler wheel — a free-running, unpowered wheel that carries part of a robot’s weight but produces no driving force.
- Locomotion — the movement of a machine as a whole from one place to another.
- Machinability — how easily a material can be cut, drilled, shaped and joined with the tools available.
- MDF — medium-density fibreboard; an engineered wood board of uniform density, made from wood fibres bonded with wax and resin under heat.
- Mecanum wheel — a wheel carrying free-spinning rollers set at 45° to its axis, so that driving it produces a force at 45° to its rolling direction.
- Normal force — the force pressing two surfaces together, here the share of a robot’s weight carried by one wheel, measured in N.
- Odometry — estimating how far a robot has travelled by counting wheel revolutions and multiplying by the wheel circumference.
- Omni wheel — a wheel carrying free-spinning rollers set at 90° to its main rotation, so that it drives normally along its rolling direction while sliding almost freely sideways.
- Payload — the useful mass a robot is built to carry, handle or transport, excluding its own structure and components.
- Reference frame — a set of axes with an origin, attached to a part of a robot or to the ground, against which a position or orientation is measured.
- Repeatability — the ability of a robot to return to the same position over and over again under identical conditions.
- Rigidity — the ability of a structure to resist changing shape when forces are applied to it.
- Standard wheel — a rigid wheel that rotates about a single fixed axle axis, able to roll forward and backward only.
- Static load — a force on a structure that is present whether or not the machine is moving, such as the weight of its components and payload.
- Steel — an iron-based alloy, the stiffest of the four named frame materials, used where a structure must not deflect under heavy load.
- Strength — the load a material can carry before it permanently deforms or breaks.
- Strength-to-weight ratio — how much load a material can carry for each unit of its own mass.
- Traction — the frictional force available at the contact patch between a wheel and the ground, which lets the wheel’s rotation push the robot along.
- Workspace — the region of space in which a robot is expected to operate and do useful work.
8.9 Objective Questions
- Which of the four named frame materials swells and permanently loses its structural integrity after absorbing moisture?
- Acrylic
- MDF
- Aluminum
- Steel
- A wheel carries free-spinning rollers mounted at 45° to its own axis. The wheel is a
- standard wheel
- castor wheel
- Mecanum wheel
- Omni wheel
State the full form of each of the following abbreviations used in this chapter: MDF, AGV.
Fill in the blanks.
- A wheel rolling without slipping advances by a distance equal to its ____________ in one complete revolution.
- The point at which the whole weight of a robot can be taken to act is called its ____________.
- A force on a robot’s frame that appears only because the robot is accelerating or braking is called a ____________ load.
- State whether each statement is true or false.
- A castor wheel contributes to a robot’s propulsion as well as to its support.
- A frame that deflects elastically under load has not broken, but it can still make a robot less repeatable.
- Fitting a more powerful motor increases the traction available at a wheel’s contact patch.
- Steel is stiffer than aluminum but roughly three times as dense.
- Match each item in Column A with the correct description in Column B.
| Column A | Column B |
|---|---|
| a. Standard wheel | i. Rollers set at 90° to the main rotation |
| b. Castor wheel | ii. Unpowered, with its axle offset behind a swivel pivot |
| c. Mecanum wheel | iii. Rotates about a single fixed axle axis |
| d. Omni wheel | iv. Rollers set at 45° to the wheel axis |
- A four-wheel Mecanum platform is commanded to drive its two left-hand wheels forward and its two right-hand wheels backward. In one line, predict the motion of the platform.
8.10 Check Your Concepts
Define traction, and state one condition under which a wheel loses it even though the motor is working correctly.
The word frame is used in robotics in two senses. Name both, and give one example of a sentence in which each sense would be intended.
Differentiate between static, dynamic and external loads acting on the frame of a mobile robot, giving one example of each from the same robot.
Explain why a frame that bends elastically under load, and springs back completely when the load is removed, still reduces a robot’s repeatability. Support your answer with reasons.
A geared motor rated at 120 rpm drives a wheel of diameter 70 mm mounted directly on its output shaft. Assuming the wheel rolls without slipping, find the distance travelled in one revolution, the robot’s straight-line speed in m/s, and the number of revolutions needed to cover 1.5 m. Then state, with a reason, what happens to the speed and to the force available at the contact patch if the same motor is fitted with a 90 mm wheel instead.
A robotics laboratory is choosing a frame material for the moving links of a light robotic arm that will lift 500 g parts, run continuously through a hot summer, and be rebuilt several times as the design is refined. Compare aluminum, steel and acrylic against the criteria of stiffness, mass, ease of working and behaviour with temperature, and recommend one material. Justify your recommendation and state one limitation the school must plan around.
8.11 Diagram, Circuit & Output Reading
- A four-wheel Mecanum platform is drawn as a top view, with its wheels labelled front-left, front-right, rear-left and rear-right. The following rotation directions are commanded, where F means driven forward and B means driven backward.
| Front-left | Front-right | Rear-left | Rear-right |
|---|---|---|---|
| F | B | B | F |
- Name the motion the platform will perform.
- Explain how the four 45° forces produced by the wheels combine to give that motion.
- A team’s robot has a chassis plate 240 mm long. Its two driven wheels are mounted on a common axis near the front of the plate, a castor supports the rear, and the battery pack — the heaviest single item on the robot — is strapped to the plate directly above the castor. On a level floor the robot runs well, but on a gentle ramp the wheels spin and the robot makes no progress.
- Identify the single fault in this arrangement.
- Explain, using the relation between normal force and available traction, why the fault produces exactly this symptom.
- State the change you would make, and where you would move the item concerned.
- A robot’s program was written for wheels of diameter 65 mm and computes the number of wheel revolutions needed for any commanded distance. Without changing the program, a team fits wheels of diameter 90 mm and commands the robot to travel 1.0 m in a straight line on a surface where no slipping occurs.
- Calculate the distance the robot will actually travel.
- State whether the robot overshoots or falls short, and by how much.
- Name the technique whose accuracy has been affected, and state what must be corrected in the program.
- The table below gives four candidate plates, all of the same size and thickness, offered to a team building a small aerial robot in which every gram limits flight time. The plate must also survive occasional knocks on landing.
| Plate | Material | Mass (g) | Behaviour under sudden impact |
|---|---|---|---|
| P | MDF | 68 | Splits at the edges |
| Q | Acrylic | 106 | Cracks suddenly |
| R | Aluminum | 243 | Bends and stays bent |
| S | Steel | 707 | Almost unaffected |
- Which two plates would you rule out first, and on which single criterion?
- Choose between the two that remain, giving the reason that decides it for this particular robot.
- State one disadvantage the team must accept as a result of your choice.
8.12 Case-Based Questions
- A Class XI group is building a line-following robot for a school competition. The rules allow a maximum robot mass of 1.2 kg. The track is a printed sheet laid on a dry indoor floor, and it includes several sharp bends but no slopes and no obstacles. The team has a hand drill, a coping saw and a screwdriver set, and expects to redesign the chassis at least twice during the term. The components to be mounted are listed below.
| Item | Mass (g) |
|---|---|
| Two geared motors with brackets | 40 each |
| Lithium polymer battery pack | 180 |
| Controller board and motor driver module | 55 |
| Two infrared line sensors with brackets | 10 each |
- Recommend a frame material from the four named in this chapter, and justify your choice against at least three of the team’s constraints.
- Recommend a wheel arrangement, naming the wheel types used and the number of each, and explain how the robot will take the sharp bends.
- State where on the chassis the battery pack should be mounted and give the engineering reason. Calculate the total mass of the mounted items listed above, and state how much of the 1.2 kg allowance is left for the frame itself.
- A warehouse is replacing its manual pallet trucks with mobile robots. The aisles are 1.2 m wide and the robot is 0.8 m wide, so there is not enough room for it to turn round; it must be able to move straight across the aisle to line up with a rack. Each robot carries pallets of up to 60 kg on a concrete floor, works two shifts a day, and will not be redesigned for several years. The warehouse has a workshop equipped for welding.
- Recommend a wheel type from the four named in this chapter, and explain how it solves the aisle problem that a standard wheel cannot.
- Recommend a frame material, justifying it against the payload, the working life and the equipment available.
- Your wheel choice brings at least two disadvantages compared with standard wheels. Name them, and for one of them describe a practical step the warehouse could take to reduce its effect.