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45-406: The malleus , or hammer , is a hammer-shaped small bone or ossicle of the middle ear . It connects with the incus , and is attached to the inner surface of the eardrum . The word is Latin for 'hammer' or 'mallet'. It transmits the sound vibrations from the eardrum to the incus (anvil). The malleus is a bone situated in the middle ear. It is the first of the three ossicles , and attached to

90-432: 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 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

135-485: 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 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

180-429: A hammer", and the stapes gets its name from Modern Latin "stirrup", probably an alteration of Late Latin stapia related to stare "to stand" and pedem, an accusative of pes "foot", so called because the bone is shaped like a stirrup – this was an invented Modern Latin word for "stirrup", for which there was no classical Latin word, as the ancients did not use stirrups. Mechanical advantage Mechanical advantage

225-436: 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 is necessary to use a 'true length' rotary lever. See, also, the incorporation of mechanical advantage into

270-433: 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 the input gear, then the gear train reduces the input torque. If the output gear of a gear train rotates more slowly than

315-450: 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

360-409: Is superior and the handle is inferior. Embryologically, the malleus is derived from the first pharyngeal arch along with the incus . In humans it grows from Meckel's cartilage . The malleus is one of three ossicles in the middle ear which transmit sound from the tympanic membrane (ear drum) to the inner ear . The malleus receives vibrations from the tympanic membrane and transmits this to

405-449: 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 the load one foot. Both the ratios F out / F in and V in / V out show that

450-400: The eardrum (tympanic membrane). The head of the malleus is the large protruding section, which attaches to the incus . The head connects to the neck of malleus. The bone continues as the handle (or manubrium) of malleus, which connects to the tympanic membrane. Between the neck and handle of the malleus, lateral and anterior processes emerge from the bone. The bone is oriented so that the head

495-467: The malleus , incus , and stapes , terms that in Latin are translated as "the hammer , anvil , and stirrup ". Studies have shown that ear bones in mammal embryos are attached to the dentary , which is part of the lower jaw . These are ossified portions of cartilage —called Meckel's cartilage —that are attached to the jaw. As the embryo develops, the cartilage hardens to form bone. Later in development,

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540-469: 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

585-491: 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

630-410: The air would be transferred into the liquid. This is observed from the abrupt cessation of sound that occurs when the head is submerged underwater. This is because the relative incompressibility of a liquid presents resistance to the force of the sound waves traveling through the air. The ossicles give the eardrum a mechanical advantage via lever action and a reduction in the area of force distribution;

675-401: The bone structure breaks loose from the jaw and migrates to the inner ear area. The structure is known as the middle ear, and is made up of the stapes , incus , malleus , and tympanic membrane . These correspond to the columella , quadrate , articular , and angular structures in the amphibian, bird or reptile jaw. As sound waves vibrate the tympanic membrane (eardrum), it in turn moves

720-424: 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 is the number of teeth on the input sprocket and N B is the number of teeth on the output sprocket. For

765-429: 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 is threaded through the pulleys to provide mechanical advantage that amplifies that force applied to the rope. In order to determine

810-458: 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 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

855-402: The discovery of the malleus and incus to the anatomist and philosopher Achillini . The first written description of the malleus and incus was by Berengario da Carpi in his Commentaria super anatomia Mundini (1521), although he only briefly described two bones and noted their theoretical association with the transmission of sound. Niccolo Massa 's Liber introductorius anatomiae described

900-443: 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 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

945-416: 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 the pulleys and does not change as the block and tackle moves. The velocities V A and V B of

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990-408: 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 the force on the pedals is greater than the force driving the bicycle forward (in the illustration above,

1035-443: 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 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

1080-462: 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. 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

1125-516: The incus. The malleus may be palpated by surgeons during ear surgery . It may become fixed in place due to surgical complications, causing hearing loss. This may be corrected with further surgery. Several sources attribute the discovery of the malleus to the anatomist and philosopher Alessandro Achillini . The first brief written description of the malleus was by Berengario da Carpi in his Commentaria super anatomia Mundini (1521). Niccolo Massa 's Liber introductorius anatomiae described

1170-420: 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 a belt are designed to provide a specific mechanical advantage in power transmission systems. The velocity v of

1215-413: 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 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

1260-405: The malleus in slightly more detail and likened both it and the incus to little hammers terming them malleoli . The malleus is unique to mammals, and evolved from a lower jaw bone in basal amniotes called the articular , which still forms part of the jaw joint in reptiles and birds. Ossicles The ossicles are, in order from the eardrum to the inner ear (from superficial to deep):

1305-404: 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 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

1350-422: 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 the rope, which means the power input by the applied force F A V A must equal

1395-408: 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 the mechanical advantage. The amount of this reduction from the ideal to

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1440-404: The nearest ossicle, the malleus, to which it is attached. The malleus then transmits the vibrations, via the incus, to the stapes, and so ultimately to the membrane of the fenestra ovalis (oval window), the opening to the vestibule of the inner ear. Sound traveling through the air is mostly reflected when it comes into contact with a liquid medium; only about 1/30 of the sound energy moving through

1485-513: The ossicles become rigid. One condition, otosclerosis , results in the fusing of the stapes to the oval window. This reduces hearing and may be treated surgically using a passive middle ear implant . There is some doubt as to the discoverers of the auditory ossicles and several anatomists from the early 16th century have the discovery attributed to them with the two earliest being Alessandro Achillini and Jacopo Berengario da Carpi . Several sources, including Eustachi and Casseri , attribute

1530-400: The ossicles, in order to protect the inner ear from excessively loud noise (theory 1) and that they give better frequency resolution at higher frequencies by reducing the transmission of low frequencies (theory 2) (see acoustic reflex ). These muscles are more highly developed in bats and serve to block outgoing cries of the bats during echolocation (SONAR). Occasionally the joints between

1575-426: 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 the speed ratio where 2 is the number of rope sections supporting

1620-429: 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 is n times the input force, where n is the number of sections of rope that support

1665-438: 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 the efficiency of the drive is 95%. Consider the 18-speed bicycle with 7 in (radius) cranks and 26 in (diameter) wheels. If

1710-423: 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 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

1755-413: The resulting vibrations are stronger but don't move as far. This allows more efficient coupling than if the sound waves were transmitted directly from the outer ear to the oval window. This reduction in the area of force application allows a large enough increase in pressure to transfer most of the sound energy into the liquid. The increased pressure will compress the fluid found in the cochlea and transmit

1800-491: The same bones in slightly more detail and likened them both to little hammers. A much more detailed description of the first two ossicles followed in Andreas Vesalius ' De humani corporis fabrica in which he devoted a chapter to them. Vesalius was the first to compare the second element of the ossicles to an anvil although he offered the molar as an alternative comparison for its shape. The first published description of

1845-418: 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 the rear sprockets have a choice of 16 and 32 teeth. Using different combinations, we can compute the following speed ratios between

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1890-596: The stapes came in Pedro Jimeno 's Dialogus de re medica (1549) although it had been previously described in public lectures by Giovanni Filippo Ingrassia at the University of Naples as early as 1546. The term ossicle derives from ossiculum , a diminutive of "bone" ( Latin : os ; genitive ossis ). The malleus gets its name from Latin malleus , meaning "hammer", the incus gets its name from Latin incus meaning "anvil" from incudere meaning "to forge with

1935-409: The stimulus. Thus, the lever action of the ossicles changes the vibrations so as to improve the transfer and reception of sound, and is a form of impedance matching . However, the extent of the movements of the ossicles is controlled (and constricted) by two muscles attached to them (the tensor tympani and the stapedius ). It is believed that these muscles can contract to dampen the vibration of

1980-419: 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, 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

2025-399: 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 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

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