Mechatronics · Module 6 of 10
Mechanical Actuation Systems
Motors rarely turn at the speed a task needs. Gears, belts, cams, and leadscrews transform motion: a gear train trades speed for torque, and a leadscrew turns rotation into precise linear travel.
Readiness check
This module transforms motion. Tick only what you can do closed-notes.
- Form a ratio from two tooth counts.
- Recall that power is torque times angular speed.
- Convert revolutions per minute to per second.
- Recall that a screw advances one lead per turn.
- Multiply a rate by a time to get distance.
The core idea
A gear train's ratio is the driven teeth over the driver teeth. It divides the speed and multiplies the torque by that ratio, because power is conserved. A leadscrew converts rotation to linear motion, advancing one lead per revolution, so linear speed is lead times revolutions per second.
ratio G = Nout / Ninωout = ωin/G, Tout = Tin × Gleadscrew v = lead × (rev/s)A motor produces power at some speed and torque, but a task usually needs a different combination, and mechanical transmission is how you convert one to the other. In a gear pair the ratio is set by the tooth counts, G = Nout/Nin. Meshing teeth force the pitch lines to move together, so the larger gear turns slower: the output speed is the input divided by G. Because an ideal gear train neither creates nor destroys power, and power is torque times angular speed, whatever is lost in speed is gained in torque, so the output torque is the input times G. This single trade, speed for torque at constant power, is the reason gearboxes exist. A leadscrew performs a different transformation, rotary to linear: each turn advances the nut by one lead, so the linear speed is the lead times the rotation rate, and the travel is the lead times the number of turns. Belts and chains behave like gears set by pulley or sprocket sizes, while cams and linkages generate shaped motion profiles from steady rotation. Choosing among them sets how a motor's motion reaches the load.
The skills, taught in order
Five skills convert a motor's motion into what a load needs.
6.1 Transmission elements
Gears mesh teeth for exact ratios; belts and chains span a distance with pulleys or sprockets; cams turn rotation into a shaped follower motion; linkages convert and redirect motion. Each suits different distance, precision, and speed needs.
6.2 Gear trains
The ratio G = Nout/Nin divides speed and multiplies torque. With power Tω conserved, ωout = ωin/G and Tout = Tin × G. A compound train multiplies the ratios of its stages, reaching large reductions in a small space.
| Quantity | Through ratio G | Direction |
|---|---|---|
| Speed | ωout = ωin/G | reduced |
| Torque | Tout = Tin × G | increased |
| Power | unchanged (ideal) | conserved |
Speed and torque move oppositely through a gear ratio; their product, the power, stays put.
6.3 Leadscrews and ball screws
A leadscrew advances one lead per revolution, so v = lead × (rev/s) and travel = lead × turns. A ball screw does the same with rolling balls for low friction and high efficiency, common on precision machine axes.
6.4 Cams and linkages
A cam profile programs the follower's displacement against angle, generating dwell, rise, and fall from constant rotation. Linkages such as the four-bar convert rotation to oscillation or shaped paths without electronics.
6.5 The practical drivetrain
Bearings locate and support shafts, couplings join them while tolerating misalignment, and real efficiency is below one, so torque gains are a little less than the ideal ratio. These details decide whether a drive is smooth and lasting.
Engineering connection: a CNC axis pairs a servo motor with a ball screw, converting thousands of rpm into millimetre-per-second travel with the resolution the encoder and screw lead allow.
Worked example 1: a gear reduction
A 20-tooth gear drives a 60-tooth gear. The input runs at 1500 rpm with 2 N·m of torque. Find the ratio, the output speed, and the output torque.
- ProblemFind the ratio, output speed, and output torque for the gear pair in Figure 1.
- Given / findNin = 20, Nout = 60, ωin = 1500 rpm, Tin = 2 N·m. Find G, ωout, Tout.
- AssumptionsIdeal, lossless mesh, so power is conserved.
- ModelG = Nout/Nin; ωout = ωin/G; Tout = Tin × G.
- EquationsG = 60/20 = 3ωout = 1500/3, Tout = 2 × 3
- Solveωout = 500 rpm; Tout = 6 N·m.
- CheckInput power ∝ 2 × 1500 = 3000; output ∝ 6 × 500 = 3000, equal, confirming conservation.
- ConclusionThe reduction trades speed for torque threefold, exactly what a motor needs to drive a slow, heavy load.
Worked example 2: a leadscrew drive
A leadscrew of 4 mm lead is turned at 900 rpm. Find the linear speed and the time to travel 120 mm.
- ProblemFind the linear speed and the 120 mm travel time for the leadscrew in Figure 2.
- Given / findlead = 4 mm, speed 900 rpm, distance 120 mm. Find v and t.
- AssumptionsNo backlash or slip; the nut is prevented from rotating.
- Modelv = lead × (rev/s); t = distance / v.
- Equationsrev/s = 900/60 = 15v = 4 × 15, t = 120/v
- Solvev = 4 × 15 = 60 mm/s; t = 120/60 = 2 s (30 turns).
- Check120 mm at 4 mm per turn is 30 turns; at 15 turns per second that is 2 s, matching.
- ConclusionThe leadscrew converts 900 rpm into a controlled 60 mm/s linear feed, the basis of a machine axis.
Misconceptions and diagnostics
| Mistake | Symptom | Diagnostic question | Correction |
|---|---|---|---|
| Speed and torque both up | Power seems created | "Is Tω conserved?" | One rises as the other falls; power is constant. |
| Ratio inverted | Reduction acts as an overdrive | "Is G driven over driver?" | G = Nout/Nin for a reduction above one. |
| Ignoring efficiency | Predicted torque never reached | "Did I assume lossless?" | Real torque gain is a little below the ideal ratio. |
| Lead confused with pitch | Travel per turn wrong on multi-start screws | "Lead or thread pitch?" | Travel per turn is the lead, not the pitch. |
Practice ladder
A 15-tooth gear drives a 45-tooth gear at an input of 3000 rpm. Find the ratio and the output speed.
Show answer
G = 45/15 = 3; output = 3000/3 = 1000 rpm.
A gear train has ratio 4. The input is 1200 rpm at 5 N·m. Find the output speed and torque (ideal).
Show answer
Output speed = 1200/4 = 300 rpm; output torque = 5 × 4 = 20 N·m.
A leadscrew of 5 mm lead turns at 600 rpm. Find the linear speed and the time to move 200 mm.
Show answer
v = 5 × (600/60) = 50 mm/s; t = 200/50 = 4 s.
A motor runs at 3000 rpm and a stage must move at about 100 mm/s. Choose a leadscrew lead and any gearing to achieve it.
What good work looks like
At 3000 rpm (50 rev/s) a 2 mm lead gives 100 mm/s directly; or reduce to 1500 rpm (25 rev/s) with a 2:1 gear and use a 4 mm lead, again 100 mm/s, trading speed for torque and resolution.
Working with AI, and proving it yourself
Use AI as an examiner, not a solver
Portfolio task
Design a drivetrain from a chosen motor to a load: pick a gear ratio and, if linear, a leadscrew lead, and predict speed and torque.
Retrieval and spaced review
Closed notes. Answer out loud, then reveal.
1. Write the gear ratio.
G = Nout/Nin, the driven teeth over the driver teeth.
2. How do speed and torque change through G?
Speed divides by G, torque multiplies by G, power unchanged.
3. Write the leadscrew speed.
v = lead × revolutions per second.
4. Why is real torque below the ideal?
Efficiency is less than one, so some power is lost to friction.
5. What does a cam do?
Programs a shaped follower motion from steady rotation.
Textbook mapping
This module follows William Bolton, Mechatronics, 6th edition. Use these references to read further.
| Topic in this module | Where to read more |
|---|---|
| Gear trains and ratios | Bolton, Chapter 8, Gears |
| Belts, chains, cams, and linkages | Bolton, Chapter 8, Mechanical aspects |
| Leadscrews and bearings | Bolton, Chapter 8, Bearings and screws |
Chapter numbers refer to Bolton's Mechatronics, 6th edition. Any edition with the same chapter titles is equivalent for study.