In a Power Transmission the Work is the source of the change in energy, and thus: The corresponding definition of work for rotational motion is given by: Work = Force X Motion (where the force and motion are parallel to each other) For translational motion work is given by: In a mechanism energy is transferred by mechanical work. Power is defined as the change in energy divided by the change in time. With this assumption we can set the power in to equal to the power out. Ω => angular speed (in radians per second)įor basic analysis of Gear Ratios we initially neglect frictional losses, and then incorporate their effect separately. Θ => angle of rotational motion (in radians) Energy loss rates can vary from 5% for a flat belt drive to up to 80% for a multi-stage gear transmission (higher and lower rates can occur too).īefore the analysis we first define some notation: Indeed, one always has some energy loss in a Power Transmission. The law of energy conservation dictates that one can never get more energy in the output motion than provided by the energy source. The analysis below shows how one calculates the Gear Ratio and Mechanical Advantage of a Power Transmission component. The term Mechanical Advantage is used to describe components that include translation. For rotary devices the term Gear Ratio is used to define the Mechanical Advantage. Mechanical Advantage refers to an increase in torque or force that a mechanism achieves through a power transmission element. With a given power source you can either achieve high velocity output or high force/torque output but not both. This tradeoff is fundamentally due to the law of energy conservation and is the key concept of Mechanical Advantage.
Conversely a high gear provides a higher bicycle speed, but more torque is required to turn the crank arm of the pedal. One can use a low gear that allows one to pedal easily up hill, but with a lower bicycle speed. A classical example is the gears on a bicycle. A Gear Ratio can increase the output torque or output speed of a mechanism, but not both. The Power Transmission often includes a Gear Ratio or Mechanical Advantage. Examples of Power Transmission elements include: gears, friction drives, timing belts, flat belts, levers, and screw drives. In machine design one often needs to incorporate a Power Transmission between an energy source and the desired output motion.
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