Planetary gearbox
A planetary gearbox, also known as a planetary gear set or epicyclic gear train, is a type of gearbox that uses a system of gears called planet gears that rotate around a central, or sun, gear. The planet gears are held in place by an outer ring gear, also known as an annulus gear. This type of gearbox is often used in automatic transmissions for vehicles as well as in industrial equipment.

Dual-clutch transmission (DCT)
A dual-clutch transmission (DCT) is a type of semi-automatic transmission that uses two separate gear sets and two clutch plates, allowing for lightning-fast gear changes without the need for a clutch pedal. Instead of a traditional torque converter, a DCT uses two wet multi-plate clutches to engage and disengage gears. This type of gearbox is most commonly found in high-performance cars and is known for its smooth and quick gear changes.

Continuously variable transmission (CVT)
A continuously variable transmission (CVT) is a type of automatic transmission that uses a belt or chain system to continuously vary the gear ratio between the engine and the wheels. Unlike traditional automatic transmissions that use a set of fixed gears, a CVT can smoothly change the gear ratio as the vehicle’s speed changes. This allows for a more efficient use of engine power and a more consistent driving experience. CVT’s are commonly found in smaller cars, hybrid cars, and high-efficiency vehicles.

Their Pros and Cons
In terms of efficiency, the CVT transmission is considered to be the most efficient among the three types of gearboxes. It allows for an infinite number of gear ratios, which means that the engine can always operate at its most efficient RPM. This results in better fuel economy and lower emissions. The Planetary gearbox, on the other hand, is less efficient than CVT and it is typically found in heavy-duty vehicles and industrial equipment due to its ability to handle high torque loads. The DCT is known for its quick and smooth gear shifts which makes it popular among sports and high-performance cars.
In terms of durability, the Planetary gearbox is known to be the most durable among the three types of gearboxes. It is designed to handle high torque loads, which makes it suitable for heavy-duty vehicles and industrial equipment. The CVT and DCT are less durable than the Planetary gearbox. CVT’s are known to have problems with belt wear and slippage, while the wet clutches used in a DCT can wear out over time.
In terms of cost, the Planetary gearbox is the most expensive among the three types of gearboxes. This is because of its high durability and ability to handle high torque loads. The DCT and CVT are less expensive than the Planetary gearbox. However, the cost of maintenance and repair for a CVT or DCT can be higher than that of a Planetary gearbox.
Brief summary
In conclusion, each type of gearbox has its own set of advantages and disadvantages. The Planetary gearbox is known for its durability and ability to handle high torque loads, making it suitable for heavy-duty vehicles and industrial equipment. The DCT is known for its quick and smooth gear shifts, making it popular among sports and high-performance cars. The CVT is known for its efficiency and smoothness but is less durable and less expensive. Ultimately, the type of gearbox that is best for a particular application will depend on the specific requirements of that application.