Power Transmission
Thesis
Belts, chains, and gears are the three families of mechanical power transmission, and the selection among them is not a matter of "which is best" but of which failure mode you can tolerate. Belts slip gracefully and quietly, but they slip — power is lost and, under shock, transmitted torque is capped by friction. Chains carry high torque at modest speed without slipping. They are noisy, need lubrication, and fail violently. Gears are precise, compact, and expensive. They demand tight shaft alignment. Every transmission choice is a vote for a particular bundle of advantages and a particular failure mode, and the honest selection logic begins by asking which failure the rest of the system can survive.[fn::The classical selection literature frames this as a cost-or-efficiency optimization, but in practice the binding constraint is usually the failure mode. A timing belt that strips its teeth under shock leaves you coasting; a chain that breaks at speed can flail and damage adjacent structure; a gear tooth that pits can shed metal into the lubricant and propagate damage through the train. The question "which is cheapest?" is almost never the question that matters; the question is "which fails the way I can afford?"]
Belts, Chains, Sprockets and Gears
A robot must transmit motor power to wheels or mechanisms. Speed and torque often need altering. Belts, chains, sprockets, and gears accomplish this. This module provides insights into mechanical techniques for transmitting mechanical power as well as how to calculate gear (and sprocket) ratios:
Belt Types
Belts transmit power by friction (flat, V) or positive engagement (timing/synchronous). This distinction governs most design decisions.
- Flat belts are the oldest form: a leather, rubber, or polyurethane band on flat or crowned pulleys. They run at high speed (up to ~80–100 m/s surface speed) and are quiet, but their power capacity is limited by the coefficient of friction and the wrap angle — the classic Euler \(T_1/T_2 = e^{\mu\theta}\) relationship. They slip before they break, which is a feature for overload protection and a bug for precision. Crowned pulleys keep the belt tracking center by the same physics that keeps a ball on a saddle: the belt climbs to the high point.
- V-belts wedge into a grooved sheave, multiplying the normal force and thus the friction for a given tension. A standard V-belt carries an order of magnitude more power per unit width than a flat belt and is the default for industrial drives up to ~100 kW. The wedge action means belt tension, not just friction, sets the capacity; overtensioning flexes the cord and kills the belt, undertensioning lets it slip and burn. Multi-rib (poly-V) belts stack many small V's and approach timing-belt compactness while retaining the slip-overload-protection of the V.
- Timing (synchronous) belts have teeth that engage a matching pulley — positive drive, no slip, no creep, and the ability to index position. They are the choice when the input and output must stay in phase (camshafts, 3D printers, CNC axes). The penalty is that they transmit shock directly — a locked output strips the belt teeth instead of slipping — and they are noisier than V-belts at high speed. HTD (high-torque drive) and GT-style profiles improved on the older trapezoidal tooth by using a rounded curvilinear form that reduces stress concentration and raises power density roughly 2–3×.[fn::The HTD tooth profile was developed by Gates in the 1970s specifically to allow timing belts to carry the torques previously reserved for roller chain in industrial drives. The curvilinear tooth engages more belt material per tooth than the trapezoidal form, dropping peak tooth stress. Most modern 3D printers and light-CNC use 3M/5M/15M HTD or GT-series belts, and the older trapezoidal (T-series, MXL) is now a legacy choice retained for compatibility.]
Power capacity scales with belt width, cord tensile strength, and speed; speed limits come from centrifugal tension (the belt's own mass pulls it off the pulley as speed rises) and from flex fatigue at the pulley entry. A typical timing belt tops out around 30–50 m/s surface speed; flat belts can exceed this because they flex more easily over small pulleys.
Chain Types
- Roller chain (the bicycle and motorcycle chain) is the workhorse: a pin-bush-roller-link assembly that engages sprocket teeth with rolling rather than sliding contact. It carries high torque (a #40 chain handles ~1–2 kW at moderate speed; #50 and #60 scale up proportionally), does not slip, and is more compact than a belt of equivalent capacity. The failure modes are elongation (pin and bush wear increases pitch over time — the classic "stretched chain" that ruins sprockets by riding on the tooth tips) and catastrophic break. Roller chain requires lubrication, and unlubricated chain in a dusty environment wears fast and abrasively.
- Silent chain (inverted-tooth) uses stacked toothed links that engage the sprocket like a timing belt's teeth but in metal. Quieter than roller chain, higher speed, more expensive, and rarer. Used where roller chain's noise is unacceptable and a timing belt's temperature or durability is inadequate — timing drives in some engines, for example.
Chain speed limits come from the polygon effect. Sprockets are not circles, so the chain rides up and down each tooth. This produces velocity ripple inversely proportional to tooth count. Impact at engagement also limits speed. High-tooth-count sprockets reduce both. A sprocket with 12 teeth produces roughly 3× the speed ripple of one with 36 teeth, and small sprockets are the usual culprit when a chain drive is noisy or short-lived.[fn::The polygon effect is why drives almost never use sprockets below ~17 teeth if they can avoid it, and why the old "hunting tooth" rule exists: choose sprocket and chain tooth counts with no common factor so that the same chain link does not hit the same sprocket tooth every revolution, distributing wear. A 17:25 ratio hunts; a 16:32 ratio does not and wears the same teeth into early failure.]
Efficiency Comparisons
The literature reports wide ranges; representative numbers under typical, well-maintained conditions:
| Drive type | Efficiency (typical) | Notes |
|---|---|---|
| Timing belt, well-tensioned | 96–98% | drops with small pulleys, high speed |
| V-belt, properly tensioned | 93–97% | flex losses dominate; slip if under-tensioned |
| Flat belt | 95–99% | best of the belts; low flex, high speed |
| Roller chain, lubricated | 96–98% | unlubricated drops to ~90% fast |
| Spur gear, oil-bath | 98–99% | per mesh; a train multiplies losses |
| Worm gear | 50–90% | high ratio, low efficiency; self-locking often a feature |
The steelman of the belt against the gear: at the same ratio and power, a belt drive is cheaper, isolates shock, tolerates shaft misalignment, and is often more efficient than a multi-stage gear train because it does the ratio in one step. The steelman of the gear: it is compact, handles reversible and bidirectional loads cleanly, and has the best efficiency per unit size at high reduction. Belts win on cost and forgiveness; gears win on density and precision; chains sit in the middle, carrying torque like a gear but running like a belt.
Tensioning
Belt and chain drives both need controlled slack-side tension to engage the teeth (timing belt) or maintain wrap and prevent skipping (V-belt, chain).
- Belts: fixed-center (design the center distance to pre-tension the belt by elastic elongation on assembly — common in 3D printers), spring-loaded idler (cheap, self-adjusting as the belt stretches), or automatic tensioner (a damped spring arm, standard in automotive serpentine systems).
- Chains: an adjustable idler sprocket on the slack side, or a spring-loaded slipper/tensioner (especially in engines). Over-tensioning a chain is as bad as under-tensioning: it loads the shaft bearings and accelerates pin wear.
The rule: a belt or chain that is "just right" today will be loose in 100 hours as it beds in and stretches. Design for retensioning, not for a set-and-forget assembly — unless you have chosen a center distance that takes up the initial stretch elastically (which is what fixed-center printer builds do, at the cost of a stiffer frame requirement).
Shaft Alignment
Power transmission assumes the input and output shafts are where the design put them. In practice they are not — tolerances, frame flex, thermal growth, and assembly error all conspire. The consequences differ by drive type:
- Belts tolerate the most misalignment: a few degrees of angular offset and a few mm of parallel offset are absorbed by the belt's flexure, though at a cost in wear and edge-tracking. Timing belts are less tolerant than V-belts because misaligned teeth load one edge and strip.
- Chains tolerate some parallel offset (the sprocket face guides the chain) but little angular offset; a misaligned chain sprocket wears the chain's side plates and the sprocket's tooth flanks asymmetrically.
- Gears tolerate almost none. Spur and helical gears are sensitive to both angular and parallel misalignment; bevel and hypoid gears more so. Misalignment shifts the contact pattern to the tooth edge, concentrating load on a small area, and the failure is pitting and tooth breakage at the edge — the classic misalignment failure mode.
The alignment discipline scales with the precision of the drive: a V-belt drive verified with a straightedge is fine; a gear drive demands dial-indicator or laser alignment, and a high-speed gear train demands it under hot and loaded conditions because the cold, static alignment is not the operating alignment.[fn::Thermal growth is the silent alignment killer. A steel gearbox case grows ~12 µm per meter per °C; a 50 °C temperature rise across a 1 m center distance shifts the shaft by 0.6 mm — enough to destroy a precision gear mesh. The cure is to either align hot (run, shut down, re-align immediately) or to compute the expected growth and pre-offset the cold alignment. Most industrial alignment standards (ANSI/ASA) now specify hot-alignment checks as a separate procedure.]
Selection Logic
A rough decision sequence, with the caveat that every rule below has exceptions driven by specific constraints (space, cost, environment, duty cycle):
1. Is position synchrony required? Yes → timing belt or gear. No → V-belt or chain. 2. Is the reduction ratio high (>~8:1)? Single-stage gear is hard above 8:1 for spur; worm or multi-stage gear or belt-chain combo. Chain and V-belt single-stage ratios typically top out around 6:1 for reasonable sprocket sizes. 3. Center distance? Large center distance favors belts and chains (the length is cheap); short center distance favors gears. A 2 m center-distance gear train is absurd; a 2 m timing belt is routine. 4. Shock or reversal? Belts slip (good for shock, bad for precision); chains and gears transmit it. If the load reverses, timing belts and gears are bidirectional; V-belts and flat belts are not (slip on reversal). 5. Environment? Heat, oil, abrasion favor chain or gear (metal survives) over belts (polymer degrades). Clean, dry, quiet favors timing belt. 6. Cost? For equivalent power, generally belt < chain < gear, though gear cost is dominated by the gear itself while belt/chain cost is dominated by the sprockets and the tensioning hardware.
Lifting Mechanisms
Robotics competitions often involve lifting objects, which is a power-transmission problem: converting motor torque into vertical force via screw jacks, winches, or linkages. Merged from the former Lifting Mechanisms note.
Lifting is the high-torque, low-speed corner of the power-transmission space, and the selection logic inverts: here the screw jack (high ratio, self-locking, slow) and the winch (chain or cable on a drum) dominate, and the belt's slip is a liability (a slipping belt under load drops the load) rather than a protective feature. The governing tradeoff in lifting is not efficiency but holding — does the mechanism hold the load with power off? A worm gear or a self-locking screw does; a timing-belt drive does not, and a brake must be added, which is itself a failure-prone component.
Related
- Gears — the teeth that carry the torque; the gear-specific companion to this note.
- Screws — linear power transmission; lead screws and ball screws for the lifting-mechanism case.
- Bearings — supporting the shafts; alignment and load paths pass through these.
- Journal Bearings — the sliding variant; relevant to the idler and tensioner supports.
- Locomotion — the application context; belts and chains drive the wheels.
- Lifting Mechanisms — the merged source; high-ratio low-speed transmission.
- Tribology — chain wear and gear pitting are tribological failure modes.
- Fasteners — shaft couplings, keyways, and the joints that hold it all together.