A universal joint, often called a U-joint, is a mechanical coupling that transmits rotation between two shafts that meet at an angle. In robotics, it can route torque through tight spaces where a straight shaft would not fit. The basic parts are an input yoke, an output yoke, and a central cross or spider with four bearing caps.
This simple geometry makes U-joints useful in drivetrains, steering linkages, robot arms, and test fixtures.
Key Facts
- A U-joint connects two rotating shafts whose axes intersect at an angle.
- Main parts are input shaft, input yoke, cross or spider, bearing caps, output yoke, and output shaft.
- For a single U-joint at angle beta, output angular speed is not constant even when input speed is constant.
- Velocity ratio for a single U-joint: omega_out / omega_in = cos(beta) / (1 - sin^2(beta) cos^2(theta)).
- At beta = 0 degrees, a U-joint behaves like a straight coupling with omega_out = omega_in.
- A double U-joint with equal joint angles and correctly phased yokes can cancel speed fluctuation.
Vocabulary
- Universal joint
- A mechanical coupling that transmits torque and rotation between two shafts whose axes are at an angle.
- Yoke
- A fork-shaped part attached to a shaft that holds two opposite ends of the cross or spider.
- Cross
- The four-armed central member of a U-joint that pivots inside the yokes and transfers motion between them.
- Bearing cap
- A small bearing assembly at each end of the cross that lets the joint pivot with reduced friction.
- Phasing
- The angular alignment of yokes in a multi-joint shaft, which determines whether speed fluctuations add or cancel.
Common Mistakes to Avoid
- Assuming a single U-joint gives constant output speed at any angle is wrong because the output shaft speeds up and slows down twice per revolution when the joint angle is not zero.
- Ignoring joint angle limits is wrong because larger angles increase velocity fluctuation, bearing load, vibration, and wear.
- Misaligning the yokes in a double U-joint is wrong because incorrect phasing prevents cancellation of speed fluctuation and can create strong vibration.
- Treating a U-joint like a constant velocity joint is wrong because a standard single U-joint transmits average speed, but not instantaneous speed, uniformly at an angle.
Practice Questions
- 1 A robot shaft uses a single U-joint at beta = 0 degrees. If the input shaft spins at 120 rpm, what is the output shaft speed?
- 2 A single U-joint has beta = 30 degrees. Using omega_out / omega_in = cos(beta) / (1 - sin^2(beta) cos^2(theta)), find the velocity ratio at theta = 0 degrees and at theta = 90 degrees. Use cos(30 degrees) = 0.866 and sin(30 degrees) = 0.5.
- 3 A mobile robot drivetrain uses two U-joints in series. Explain why the two joint angles should be equal and the yokes correctly phased.