Gear and Power Transmission
The gear is a symbol of engineering. Dating back to 100 B.C., the Greeks already had a good understanding of the gear (Wikipedia 2002 ). The gears are used to transmit motion and power. There are many kinds of gears: spur gears, helical gears, bevel gears
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Gear and Power Transmission
6.1 A Historical Review of the Gear Train in Mechanical Movements The gear is a symbol of engineering. Dating back to 100 B.C., the Greeks already had a good understanding of the gear (Wikipedia 2002). The gears are used to transmit motion and power. There are many kinds of gears: spur gears, helical gears, bevel gears, hypoid gears, crown gears, worm gears, non-circular gears, gear racks, sun and planet gears, harmonic gears, etc. The teeth of a gear may follow different profiles, such as involute, cycloidal, spline, etc. We assume that the reader has basic knowledge of gears and understands the terms, such as module, pitch circle, etc. The reader may also refresh his/her memory by reading reference books, such as (Litvin and Fuentes 2004). For mechanical watch movements, gears play an essential role. A typical mechanical watch movement has approximately 30 gears carrying out different functions such as winding, setting, etc. The most important ones are those in the main gear train which transfers the kinetic energy from the mainspring (stored in the barrel) to the escapement, as shown in Fig. 6.1. The main gear train has a couple of distinct features. First, it is constantly moving and must move precisely. Second, it is small (typically the wheels are about 1 mm in thickness and the pinions are about 1 mm in diameter) and has a large transmission ratio (e.g., 110/ 16). As a result, even a small error may jeopardize timekeeping accuracy. In this chapter, we focus on the main gear train. The gears in the main gear train of the mechanical watch movement are spur gears. Their tooth profile is not the usual involute but cycloid (Litvin and Fuentes 2004). It is not clear who started to use cycloid gears. Compare to the involute gear, the cycloidal gear has two advantages. First, it can accommodate large gear ratio without tooth interference. Second, it can have a small number of teeth. Under the same conditions, the involute gear would become radically undercut,
R. Du and L. Xie, The Mechanics of Mechanical Watches and Clocks, History of Mechanism and Machine Science 21, DOI: 10.1007/978-3-642-29308-5_6, Ó Springer-Verlag Berlin Heidelberg 2013
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6 Gear and Power Transmission Fourth wheel Escape pinion
Barrel gear Third wheel
Escape wheel
Center pinion Third pinion Center wheel
Fig. 6.1 The main gear train in a mechanical watch movement
making it easy to break and difficult to manufacture. Still, owing to their small sizes, cycloid gears are sensitive to manufacturing and/or misalignment errors. Even a small error may cause significant deterioration in performance. Therefore, detailed analysis is helpful. The gear problem is a complex problem. Before detailed analysis can be carried out, the solid model of the gear pair should be established first. According to the literatures, much effort has been made to construct the gear model. In the late 1980s, the 2D model of an involute spur gear was constructed to study the static contact problem (Varangan and Ganesan 1994). Later,
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