What is Hooke’s joint?

Short Answer:

A Hooke’s joint, also called a universal joint, is a type of mechanical coupling used to connect two non-parallel and non-collinear shafts so that power and rotary motion can be transmitted between them. It allows angular movement between the shafts and is especially useful when the shafts are inclined at a small angle to each other.

This joint is commonly used in automobile drive shafts, machine tools, and other mechanisms where the alignment of shafts changes during operation. It provides flexibility in motion transmission while maintaining torque transfer between the rotating shafts.

Detailed Explanation:

Hooke’s Joint

A Hooke’s joint or universal joint is a mechanical device that connects two shafts whose axes are inclined to each other at an angle. It transmits torque and rotary motion from one shaft to another, even when their alignment is not straight. This joint is widely used in automobiles, power transmission systems, and machinery where continuous rotation between misaligned shafts is required.

The Hooke’s joint was invented by Robert Hooke in the 17th century, and it remains a fundamental element of mechanical engineering design due to its simplicity and reliability.

Construction of Hooke’s Joint

A Hooke’s joint consists of the following main parts:

  1. Forks (Yokes): There are two yokes or forks, one attached to each shaft. These forks are positioned at right angles to each other.
  2. Cross or Spider: A central crosspiece connects the two yokes. Each arm of the cross fits into the eyes of the forks using bearings or pins.
  3. Bearings and Pins: These allow free rotation of the forks relative to the cross, enabling angular motion between the connected shafts.
  4. Driving Shaft and Driven Shaft: The driving shaft provides the input rotation, while the driven shaft receives the motion through the joint.

The entire arrangement forms a flexible connection that can transmit power efficiently while compensating for angular displacement between the shafts.

Working Principle

The working of a Hooke’s joint is based on the transmission of rotary motion through an intermediate cross that allows angular movement.

When the driving shaft rotates, its fork drives the cross through a pin connection. The cross, in turn, drives the second fork connected to the driven shaft. As the cross can pivot about two perpendicular axes, it allows the driven shaft to rotate at the same time even though the two shafts are not in a straight line.

However, one important characteristic of a Hooke’s joint is that the angular velocity of the driven shaft is not constant when the shafts are inclined. During each revolution, the driven shaft accelerates and decelerates twice, even though the driving shaft rotates uniformly. This variation depends on the angle between the shafts, known as the angle of inclination.

To maintain uniform motion in practical systems, two Hooke’s joints are often used in series with the forks of the intermediate shaft positioned properly. This setup cancels out the velocity fluctuation and ensures smooth power transmission.

Velocity Ratio

If θ is the inclination between the shafts and φ is the angle turned by the driving shaft, the velocity ratio between the driven and driving shafts can be expressed as:

Where:

  • ω₁ = angular velocity of the driving shaft
  • ω₂ = angular velocity of the driven shaft
  • θ = angle between the shafts

This equation shows that the velocity of the driven shaft varies with the position of the driving shaft.

Applications of Hooke’s Joint

  1. Automobiles: Used in the propeller shaft of rear-wheel-drive vehicles to transmit motion between the gearbox and the differential.
  2. Machine tools: Used in universal shafts of milling or drilling machines to transmit rotary motion to inclined spindles.
  3. Textile and printing machinery: Used to connect shafts at an angle.
  4. Locomotives and ships: Applied in power transmission shafts for smooth motion under angular misalignment.
  5. Aerospace and robotics: Used where flexible rotational connections are needed.

Advantages

  1. Simple design: Easy to construct and assemble.
  2. Transmits power between misaligned shafts: Suitable for non-parallel and non-collinear shafts.
  3. Compact and strong: Can transmit large torque in a small space.
  4. Low maintenance: Requires little lubrication and care.
  5. Versatile: Can be used in both slow-speed and high-torque applications.

Disadvantages

  1. Variable angular velocity: The driven shaft speed fluctuates during rotation.
  2. Vibration and noise: Due to speed variations and angular movement.
  3. Wear and tear: Bearings and pins experience wear due to oscillatory motion.
  4. Limited working angle: Usually effective only up to 15°–20°.
  5. Reduced efficiency at high speeds: Due to joint imbalance and friction.

Double Hooke’s Joint

To overcome the limitation of variable angular velocity, two Hooke’s joints can be connected in series. The forks are arranged such that the speed fluctuations of the first joint are compensated by the second. This arrangement provides uniform motion transmission and is commonly used in automotive drive shafts.

Example in Automobiles

In a rear-wheel-drive vehicle, the engine and gearbox are connected to the rear axle by a long shaft known as the propeller shaft. The engine is mounted at a fixed position, while the rear axle moves up and down with the suspension. The Hooke’s joint allows this up-and-down movement while still transmitting rotation from the gearbox to the axle smoothly.

Conclusion

The Hooke’s joint is an essential mechanical device used to transmit power between two inclined shafts. It provides flexibility in motion transfer and is widely used in automotive and industrial systems. Although it causes velocity variation, this limitation can be eliminated by using a double Hooke’s joint arrangement. Due to its strength, simplicity, and adaptability, it remains one of the most important couplings in modern mechanical engineering.