Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for this is the law of the lever . Machine components designed to manage forces and movement in this way are called mechanisms . An ideal mechanism transmits power without adding to or subtracting from it. This means the ideal machine does not include a power source, is frictionless, and is constructed from rigid bodies that do not deflect or wear. The performance of a real system relative to this ideal is expressed in terms of efficiency factors that take into account departures from the ideal.
36-445: The lever is a movable bar that pivots on a fulcrum attached to or positioned on or across a fixed point. The lever operates by applying forces at different distances from the fulcrum, or pivot. The location of the fulcrum determines a lever's class . Where a lever rotates continuously, it functions as a rotary 2nd-class lever. The motion of the lever's end-point describes a fixed orbit, where mechanical energy can be exchanged. (see
72-428: A belt are designed to provide a specific mechanical advantage in power transmission systems. The velocity v of the chain or belt is the same when in contact with the two sprockets or pulleys: where the input sprocket or pulley A meshes with the chain or belt along the pitch radius r A and the output sprocket or pulley B meshes with this chain or belt along the pitch radius r B , therefore where N A
108-498: A hand-crank as an example.) In modern times, this kind of rotary leverage is widely used; see a (rotary) 2nd-class lever; see gears, pulleys or friction drive, used in a mechanical power transmission scheme. It is common for mechanical advantage to be manipulated in a 'collapsed' form, via the use of more than one gear (a gearset). In such a gearset, gears having smaller radii and less inherent mechanical advantage are used. In order to make use of non-collapsed mechanical advantage, it
144-417: A wick effect. It is extremely rare for a timing belt to break. More common is for the belt to delaminate, disconnecting the fabric strength member from the teeth that ride on the pulleys. The belt is then often thrown from the pulleys and may be further damaged, cut, or break. Although worn teeth may be detectable by careful inspection, internal deterioration is not considered to be reliably detectable and so
180-421: Is n times the input force, where n is the number of sections of rope that support the moving block. Mechanical advantage that is computed using the assumption that no power is lost through deflection, friction and wear of a machine is the maximum performance that can be achieved. For this reason, it is often called the ideal mechanical advantage (IMA). In operation, deflection, friction and wear will reduce
216-732: Is a flexible belt with teeth moulded onto its inner surface. Toothed belts are usually designed to run over matching toothed pulleys or sprockets . Toothed belts are used in a wide array of mechanical devices where high power transmission is desired. Timing belts , toothed belts , cogged or cog belts , and synchronous belts are non-slipping mechanical drive belts . They are made as flexible belts with teeth moulded onto their inner surface. The belts run over matching toothed pulleys or sprockets. When correctly tensioned, these type of belts have no slippage, and are often used to transfer motion for indexing or timing purposes (hence their name). They are often used in lieu of chains or gears, so there
252-461: Is given by The mechanical advantage for friction belt drives is given by Chains and belts dissipate power through friction, stretch and wear, which means the power output is actually less than the power input, which means the mechanical advantage of the real system will be less than that calculated for an ideal mechanism. A chain or belt drive can lose as much as 5% of the power through the system in friction heat, deformation and wear, in which case
288-427: Is gradual wear to the tooth shape, which may eventually lead to slippage over rounded teeth. The belt often continues to work, but the relative timing between shafts changes. The catastrophic failure mode is caused by delamination between the belt and its fabric reinforcement. Although this may be caused by age and wear, it is often accelerated by mistreatment of the belt, often during initial installation. Overloading
324-426: Is less noise and a lubrication bath is not necessary. Toothed belts are used widely in mechanical devices, including sewing machines , photocopiers and many others. A major use of toothed belts is as the timing belt used to drive the camshafts within an automobile or motorcycle engine. As toothed belts can deliver more power than a friction-drive belt, they are used for high-power transmissions. These include
360-421: Is necessary to use a 'true length' rotary lever. See, also, the incorporation of mechanical advantage into the design of certain types of electric motors; one design is an 'outrunner'. As the lever pivots on the fulcrum, points farther from this pivot move faster than points closer to the pivot. The power into and out of the lever is the same, so must come out the same when calculations are being done. Power
396-434: Is the number of teeth on the input gear and N B is the number of teeth on the output gear. The mechanical advantage of a pair of meshing gears for which the input gear has N A teeth and the output gear has N B teeth is given by This shows that if the output gear G B has more teeth than the input gear G A , then the gear train amplifies the input torque. And, if the output gear has fewer teeth than
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#1732773240589432-435: Is the number of teeth on the input sprocket and N B is the number of teeth on the output sprocket. For a toothed belt drive, the number of teeth on the sprocket can be used. For friction belt drives the pitch radius of the input and output pulleys must be used. The mechanical advantage of a pair of a chain drive or toothed belt drive with an input sprocket with N A teeth and the output sprocket has N B teeth
468-416: Is the product of force and velocity, so forces applied to points farther from the pivot must be less than when applied to points closer in. If a and b are distances from the fulcrum to points A and B and if force F A applied to A is the input force and F B exerted at B is the output, the ratio of the velocities of points A and B is given by a / b so the ratio of the output force to
504-412: Is threaded through the pulleys to provide mechanical advantage that amplifies that force applied to the rope. In order to determine the mechanical advantage of a block and tackle system consider the simple case of a gun tackle, which has a single mounted, or fixed, pulley and a single movable pulley. The rope is threaded around the fixed block and falls down to the moving block where it is threaded around
540-483: The primary drive of some motorcycles , notably later Harley-Davidsons ; and the supercharger used for dragsters . Microlight aircraft driven by high-speed two-stroke engines such as the Rotax 532 use toothed belt reduction drives to allow the use of a quieter and more efficient slower-speed propeller. Some amateur-built airplanes powered by automotive engines use cog belt reduction drive units. A gilmer belt
576-479: The Gilmer name, although enthusiasts are still likely to refer to toothed belts by the gilmer name. Toothed belts are made of a flexible polymer over a fabric reinforcement. Originally this was rubber over a natural textile, but developments in material science have had a substantial effect in increasing the lifetime of these belts. This included changes from natural to synthetic rubber and polyurethane and also
612-543: The IMA or using the first ratio yields the AMA. The ideal mechanical advantage (IMA), or theoretical mechanical advantage , is the mechanical advantage of a device with the assumption that its components do not flex, there is no friction, and there is no wear. It is calculated using the physical dimensions of the device and defines the maximum performance the device can achieve. The assumptions of an ideal machine are equivalent to
648-406: The adoption of steel , nylon , Kevlar (or other aramid fibres), and/or carbon fibres in their reinforcement. Toothed belts have two failure modes, one gradual and one catastrophic . There is an increased risk of either over the lifetime of the belt, so it is common for highly-stressed belts to be given a service lifetime and to be replaced before this failure can occur. One failure mode
684-417: The belt by bending it to a narrow radius is a common cause of damage, either by bending out of the belt's designed axis, twisting, levering it into place with tools, bending in the correct axis but to too small a radius, or even knotting a belt in storage. Another cause, particularly with natural rubber belts, is contamination by oil, especially to the edges where the reinforcing fabric is exposed and can cause
720-421: The efficiency of the drive is 95%. Consider the 18-speed bicycle with 7 in (radius) cranks and 26 in (diameter) wheels. If the sprockets at the crank and at the rear drive wheel are the same size, then the ratio of the output force on the tire to the input force on the pedal can be calculated from the law of the lever to be Now, assume that the front sprockets have a choice of 28 and 52 teeth, and that
756-399: The force on the pedals is greater than the force driving the bicycle forward (in the illustration above, the corresponding backward-directed reaction force on the ground is indicated). A block and tackle is an assembly of a rope and pulleys that is used to lift loads. A number of pulleys are assembled together to form the blocks, one that is fixed and one that moves with the load. The rope
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#1732773240589792-411: The fulcrum to the input force is less than from the fulcrum to the output force, then the lever reduces the input force. To Archimedes, who recognized the profound implications and practicalities of the law of the lever, has been attributed the famous claim, "Give me a place to stand and with a lever I will move the whole world." The use of velocity in the static analysis of a lever is an application of
828-403: The input force, or mechanical advantage, is given by This is the law of the lever , which Archimedes formulated using geometric reasoning. It shows that if the distance a from the fulcrum to where the input force is applied (point A ) is greater than the distance b from fulcrum to where the output force is applied (point B ), then the lever amplifies the input force. If the distance from
864-430: The input gear, then the gear train reduces the input torque. If the output gear of a gear train rotates more slowly than the input gear, then the gear train is called a speed reducer (Force multiplier). In this case, because the output gear must have more teeth than the input gear, the speed reducer will amplify the input torque. Mechanisms consisting of two sprockets connected by a chain, or two pulleys connected by
900-518: The load one foot. Both the ratios F out / F in and V in / V out show that the IMA is six. For the first ratio, 100 lb F of force input results in 600 lb F of force out. In an actual system, the force out would be less than 600 pounds due to friction in the pulleys. The second ratio also yields a MA of 6 in the ideal case but a smaller value in the practical scenario; it does not properly account for energy losses such as rope stretch. Subtracting those losses from
936-428: The mechanical advantage. The amount of this reduction from the ideal to the actual mechanical advantage (AMA) is defined by a factor called efficiency , a quantity which is determined by experimentation. As an example, using a block and tackle with six rope sections and a 600 lb load, the operator of an ideal system would be required to pull the rope six feet and exert 100 lb F of force to lift
972-476: The pitch circles of meshing gears roll on each other without slipping. The speed ratio for a pair of meshing gears can be computed from ratio of the radii of the pitch circles and the ratio of the number of teeth on each gear, its gear ratio . The velocity v of the point of contact on the pitch circles is the same on both gears, and is given by where input gear A has radius r A and meshes with output gear B of radius r B , therefore, where N A
1008-407: The principle of virtual work . The requirement for power input to an ideal mechanism to equal power output provides a simple way to compute mechanical advantage from the input-output speed ratio of the system. The power input to a gear train with a torque T A applied to the drive pulley which rotates at an angular velocity of ω A is P=T A ω A . Because the power flow is constant,
1044-438: The pulley and brought back up to be knotted to the fixed block. Let S be the distance from the axle of the fixed block to the end of the rope, which is A where the input force is applied. Let R be the distance from the axle of the fixed block to the axle of the moving block, which is B where the load is applied. The total length of the rope L can be written as where K is the constant length of rope that passes over
1080-463: The pulleys and does not change as the block and tackle moves. The velocities V A and V B of the points A and B are related by the constant length of the rope, that is or The negative sign shows that the velocity of the load is opposite to the velocity of the applied force, which means as we pull down on the rope the load moves up. Let V A be positive downwards and V B be positive upwards, so this relationship can be written as
1116-436: The rear sprockets have a choice of 16 and 32 teeth. Using different combinations, we can compute the following speed ratios between the front and rear sprockets The ratio of the force driving the bicycle to the force on the pedal, which is the total mechanical advantage of the bicycle, is the product of the speed ratio (or teeth ratio of output sprocket/input sprocket) and the crank-wheel lever ratio. Notice that in every case
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1152-519: The requirement that the machine does not store or dissipate energy; the power into the machine thus equals the power out. Therefore, the power P is constant through the machine and force times velocity into the machine equals the force times velocity out—that is, fulcrum A fulcrum ( pl. : fulcra or fulcrums ) is the support about which a lever pivots. Fulcrum may also refer to: Toothed belt A toothed belt , timing belt , cogged belt , cog belt , or synchronous belt
1188-429: The rope, which means the power input by the applied force F A V A must equal the power out acting on the load F B V B , that is The ratio of the output force to the input force is the mechanical advantage of an ideal gun tackle system, This analysis generalizes to an ideal block and tackle with a moving block supported by n rope sections, This shows that the force exerted by an ideal block and tackle
1224-403: The speed ratio where 2 is the number of rope sections supporting the moving block. Let F A be the input force applied at A the end of the rope, and let F B be the force at B on the moving block. Like the velocities F A is directed downwards and F B is directed upwards. For an ideal block and tackle system there is no friction in the pulleys and no deflection or wear in
1260-432: The torque T B and angular velocity ω B of the output gear must satisfy the relation which yields This shows that for an ideal mechanism the input-output speed ratio equals the mechanical advantage of the system. This applies to all mechanical systems ranging from robots to linkages . Gear teeth are designed so that the number of teeth on a gear is proportional to the radius of its pitch circle, and so that
1296-414: Was a brand or trade name for a mechanical belt used for transferring power between axles in a machine . The gilmer belt was originally sold by the L. H. Gilmer company after 1949, and represents one of the earliest toothed belt designs. Gilmer belts use trapezoidal teeth to engage matching grooves on toothed pulleys in order to maintain synchronicity between moving parts. Belts are no longer sold under
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