A universal joint passes turning power around a bend, but not smoothly. When the joint is bent, the output shaft speeds up and slows down twice every turn, even if the input turns perfectly steadily. At its fastest it turns 1 ÷ cos(angle) times the input speed, and at its slowest cos(angle) times. It still makes exactly one turn per input turn. The chart below gives the numbers for the angles builders use, and the lab shows why two joints can cancel the wobble.
The chart
Each row is one joint bent by that angle, with the input turning steadily. Fast and slow are the output’s top and bottom speeds compared with the input, in percent; the gap is the difference between them. “Off by” is the most the output gets ahead of or behind where a steady shaft would point.
| Angle | Fast % | Slow % | Gap % | Off by |
|---|---|---|---|---|
| 5° | +0.4 | −0.4 | 0.8 | 0.1° |
| 10° | +1.5 | −1.5 | 3.1 | 0.4° |
| 15° | +3.5 | −3.4 | 6.9 | 1.0° |
| 20° | +6.4 | −6.0 | 12.4 | 1.8° |
| 25° | +10.3 | −9.4 | 19.7 | 2.8° |
| 30° | +15.5 | −13.4 | 28.9 | 4.1° |
| 35° | +22.1 | −18.1 | 40.2 | 5.7° |
| 40° | +30.5 | −23.4 | 53.9 | 7.6° |
| 45° | +41.4 | −29.3 | 70.7 | 9.9° |
The numbers come from the ideal joint used in the lab, and its test checks the fastest and slowest speeds against 1 ÷ cos and cos for several angles. The gap grows quickly: doubling the angle from 15° to 30° roughly quadruples it. Real joints add play and friction on top.
Where a real build bends its joint
The AWD with Central Diff (level 5, about 90 minutes) has one universal joint. Its front shaft runs from the centre differential through a 5-long axle, the joint and a 2-long axle to a 12-tooth corner gear that drives the front axle. The whole front axle swings on a turntable steered by a Servo, and the joint sits right under that turntable, so it bends at the same point the axle swings about. The build’s animation swings the axle 20°, and a step note says the joint doesn’t like more than about 30°.
So when this car drives round a full-lock corner, the chart says its front shaft swings between about 6% faster and 6% slower than the shaft behind the joint, twice a turn. The corner gears change the speed but not that percentage. Driving straight, the joint is unbent and there is no wobble at all. The four-wheel drive FAQ explains what the centre differential does in the same car.
Predict it, then check it
Start the challenges, pick your answer, and only then see the dials and the speed chart. The dashed pointer shows where a steady shaft would be, so you can watch the output run ahead and fall behind.
Interactive: Universal joint lab. Bend a universal joint and watch the output shaft run ahead and fall behind a steady input twice a turn, then add a second joint and line up its forks to cancel the wobble, or twist them a quarter-turn and double it. Six challenges.
Why does it happen?
The joint is two forks joined by a cross. The input fork swings the cross round in a circle that stays square to the input shaft. The output fork has to follow the cross in a circle square to the output shaft, and when the shafts are bent those two circles are tilted against each other. Seen from the output, the cross’s steady circle looks like a squashed one, and a point moving steadily round a squashed circle seems to speed up across the narrow parts and slow down across the wide parts. There are two narrow parts per turn, so there are two speed-ups. The universal joint idea page has the simple version.
How do you cancel the wobble?
Use two joints at equal angles, with the two forks on the middle shaft lined up. The second joint then speeds up exactly when the first slows down, and the end shaft turns steadily. The middle shaft still wobbles, so keep it light. Twist those middle forks a quarter-turn apart and the two wobbles add up instead: at 30° each, the end shaft peaks about 33% fast. The lab lets you try both.
Builders on the Eurobricks forum reported that lining up the joints on each axle “almost completely eliminated the wiggles” in a driveshaft, and one pointed out that with three or five joints in a row you can’t cancel it completely. Pairs cancel; an odd joint is left over. Robert Hooke, who named the universal joint in 1676, proposed the cancelling pair in 1683. Earlier, in 1664, Gaspar Schott had wrongly described the single joint as constant-speed.
Rules of thumb for your own drivetrain
- Keep a single joint’s angle small: under about 15° the gap stays under 7%.
- For steering or suspension, put the joint’s centre exactly on the pivot, as the AWD with Central Diff does.
- If a shaft must bend a lot, use two joints at equal angles with the middle forks lined up.
- Watch slow parts as well as fast ones: a pointer or turret driven through a bent joint can be off by the chart’s last column.
For other ways round a corner, the bevel gears worksheet covers fixed 90° turns, and the Driveshaft 4×4 Pusher shows a straight driveshaft with corner gears at each end.
The AWD with Central Diff is in the Gearbox & Drivetrain Cars booklet pack, and its booklet is free on the build page.
Interactive: Check yourself. A few quick questions on the ideas in this guide, each with an explanation.
- A universal joint is bent and the input turns steadily. What does the output do?
- At about what joint angle does the output speed swing by about 29% between fastest and slowest?
- Two joints at equal angles. What cancels the wobble?
- In the AWD with Central Diff, why does the universal joint sit right under the steering turntable?
