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Examples of rope and pulley systems illustrating mechanical advantage. Consider lifting a weight with rope and pulleys. A rope looped through a pulley attached to a fixed spot, e.g. a barn roof rafter, and attached to the weight is called a single pulley. It has a mechanical advantage (MA) = 1 (assuming frictionless bearings in the pulley ...
The ideal Atwood machine consists of two objects of mass m 1 and m 2, connected by an inextensible massless string over an ideal massless pulley. [1] Both masses experience uniform acceleration. When m 1 = m 2, the machine is in neutral equilibrium regardless of the position of the weights.
where is the angle (in radians) between the two flat sides of the pulley that the v-belt presses against. [5] A flat belt has an effective angle of α = π {\displaystyle \alpha =\pi } . The material of a V-belt or multi-V serpentine belt tends to wedge into the mating groove in a pulley as the load increases, improving torque transmission.
The rope is threaded through the pulleys to provide mechanical advantage that amplifies the force applied to the rope. [4] Hero of Alexandria described cranes formed from assemblies of pulleys in the first century. Illustrated versions of Hero's Mechanica (a book on raising heavy weights) show early block and tackle systems. [5]
The mechanical belt drive, using a pulley machine, was first mentioned in the text of the Dictionary of Local Expressions by the Han Dynasty philosopher, poet, and politician Yang Xiong (53–18 BC) in 15 BC, used for a quilling machine that wound silk fibres onto bobbins for weavers' shuttles. [1]
The fixed pulley on the upper shaft is driven at constant speed by a belt from the power source. The loose pulley ('idler') allows the machine to be stopped in isolation – necessary for changing speed. The stepped pulleys (left) provide three drive speeds for the machine tool (not shown), depending on which pair of pulleys is connected by the ...
The belt problem. The belt problem is a mathematics problem which requires finding the length of a crossed belt that connects two circular pulleys with radius r 1 and r 2 whose centers are separated by a distance P. The solution of the belt problem requires trigonometry and the concepts of the bitangent line, the vertical angle, and congruent ...
The application of mechanical engineering can be seen in the archives of various ancient societies. The pulley appeared in Mesopotamia in 1,500 BC, improving water transportation. German Archaeologist Robert Koldewey found that the Hanging Gardens likely used a mechanical pump powered by these pulleys to transport water to the roof gardens. [11]