Title: Gear train
Content:  The simplest example of a gear train has two gears. The "input gear" (also known as drive gear) transmits power to the "output gear" (also known as driven gear). The input gear will typically be connected to a power source, such as a motor or engine. In such an example, the output of torque and rotational speed from the output (driven) gear depend on the ratio of the dimensions of the two gears.
Title: Gear train
Content: The ratio of the pitch circles of mating gears defines the speed ratio and the mechanical advantage of the gear set. ; A planetary gear train provides high gear reduction in a compact package. ; It is possible to design gear teeth for gears that are non-circular, yet still transmit torque smoothly. ; The speed ratios of chain and belt drives are computed in the same way as gear ratios. See bicycle gearing. A gear train is a mechanical system formed by mounting gears on a frame so the teeth of the gears engage. Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission of rotation from one gear to the next. Features of gears and gear trains include:   The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and the south-pointing chariot of China. Illustrations by the Renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio.
Title: Transmission (mechanics)
Content:  The simplest transmissions, often called gearboxes to reflect their simplicity (although complex systems are also called gearboxes in the vernacular), provide gear reduction (or, more rarely, an increase in speed), sometimes in conjunction with a right-angle change in direction of the shaft (typically in helicopters, see picture). These are often used on PTO-powered agricultural equipment, since the axial PTO shaft is at odds with the usual need for the driven shaft, which is either vertical (as with rotary mowers), or horizontally extending from one side of the implement to another (as with manure spreaders, flail mowers, and forage wagons). More complex equipment, such as silage 
Title: Gear
Content:   A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called cogs), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic principle behind the operation of gears is analogous to the basic principle of levers. A gear may also be known informally as a cog. Geared devices can change the speed, torque, and direction of a power source. Gears of different sizes produce a change in torque, creating a mechanical advantage, through their gear ratio, and thus may be considered a simple machine. The rotational speeds, and the torques, of two meshing gears differ in proportion to their diameters. The teeth on the two meshing gears all 
Title: Machine
Content: The ratio of the pitch circles of mating gears defines the speed ratio and the mechanical advantage of the gear set. ; A planetary gear train provides high gear reduction in a compact package. ; It is possible to design gear teeth for gears that are non-circular, yet still transmit torque smoothly. ; The speed ratios of chain and belt drives are computed in the same way as gear ratios. See bicycle gearing. The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and the south-pointing chariot of China. Illustrations by the renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio. Some important features of gears and gear trains are:
Title: Gear
Content:  the same shape. Two or more meshing gears, working in a sequence, are called a gear train or a transmission. The gears in a transmission are analogous to the wheels in a crossed, belt pulley system. An advantage of gears is that the teeth of a gear prevent slippage. In transmissions with multiple gear ratios—such as bicycles, motorcycles, and cars—the term "gear" (e.g., "first gear") refers to a gear ratio rather than an actual physical gear. The term describes similar devices, even when the gear ratio is continuous rather than discrete, or when the device does not actually contain gears, as in a continuously variable transmission. Furthermore, a gear can mesh with a linear toothed part, called a rack, producing translation instead of rotation.
Title: Virtual work
Content:  A gear train is formed by mounting gears on a frame so that the teeth of the gears engage. Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, this provides a smooth transmission of rotation from one gear to the next. For this analysis, we consider a gear train that has one degree-of-freedom, which means the angular rotation of all the gears in the gear train are defined by the angle of the input gear. The size of the gears and the sequence in which they engage define the ratio of the angular velocity ωA of the input gear to the angular velocity ωB of the output gear, known as the speed ratio, or gear ratio, of the gear train. Let R be the speed ratio, then Thus, the speed ratio of a gear train also defines its mechanical advantage. This shows that if the input gear rotates faster than the output gear, then the gear train amplifies the input torque. And, if the input gear rotates slower than the output gear, then the gear train reduces the input torque.
Title: Gear train
Content:  If a simple gear train has three gears, such that the input gear GA meshes with an intermediate gear GI which in turn meshes with the output gear GB, then the pitch circle of the intermediate gear rolls without slipping on both the pitch circles of the input and output gears. This yields the two relations Notice that this gear ratio is exactly the same as for the case when the gears GA and GB engage directly. The intermediate gear provides spacing but does not affect the gear ratio. For this reason it is called an idler gear. The same gear ratio is obtained for a sequence of idler gears and hence an idler gear is used to provide the same direction to rotate the driver and driven gear. If the driver gear moves in the clockwise direction, then the driven gear also moves in the clockwise direction with the help of the idler gear. 
Title: Mechanism (engineering)
Content: The ratio of the pitch circles of mating gears defines the speed ratio and the mechanical advantage of the gear set. ; A planetary gear train provides high gear reduction in a compact package. ; It is possible to design gear teeth for gears that are non-circular, yet still transmit torque smoothly. ; The speed ratios of chain and belt drives are computed in the same way as gear ratios.  The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and the south-pointing chariot of China. Illustrations by the Renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio. Some important features of gears and gear trains are:
Title: Pinion
Content: the typically smaller gear in a gear drive train (although in the first commercially successful steam locomotive—the Salamanca—the pinion was rather large). In many cases, such as remote controlled toys, the pinion is also the drive gear for a reduction in speed, since electric motors operate at higher speed and lower torque than desirable at the wheels. However the reverse is true in watches, where gear trains commence with a high-torque, low-speed spring and terminate in the fast-and-weak escapement. ; the smaller gear that drives in a 90-degree angle towards a crown gear in a differential drive. ; the small front sprocket on a chain driven motorcycle. ; the clutch bell gear when paired with a centrifugal clutch, in radio-controlled cars with an engine (e.g., nitro). Drivetrains usually feature a gear known as the pinion, which may vary in different systems, including 

Question: where is a simple gear train used in real life?
Answer: Automobile drivetrains.