Levers
Levers are simple machines that consist of a rigid beam pivoting around a point known as the fulcrum. They are designed to manipulate three main forces: an applied effort, the load being moved, and the fulcrum's reaction. The effectiveness of a lever depends on the arrangement of these forces along the beam, allowing for either an increase in force or travel distance, with a corresponding decrease in the other. There are three classes of levers: first class (fulcrum between effort and load, like a see-saw), second class (load in the middle, like a wheelbarrow), and third class (effort in the middle, like tongs). Levers are prevalent in everyday tools such as bottle openers, hammers, and scissors, as well as in natural systems, where bones and muscles function as levers in the body. Historically, figures such as Archimedes contributed significantly to the understanding of levers, exploring their mechanical properties and applications. Levers also play vital roles in art and design, exemplified by the sculptures of Alexander Calder, and have metaphorical applications in various fields where resources are strategically utilized for greater outcomes.
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Levers
SUMMARY: Levers negotiate forces in ways useful in engineering.
Levers are rigid beams that pivot around a point called the “fulcrum” to mediate three forces: an applied effort, a load to be moved, and the fulcrum’s reaction. Depending on how the load, effort, and fulcrum are placed along the beam, either force or travel distance can be increased and the other decreased in proportion. There are three classes of lever, distinguished by the placement of the effort, load, or fulcrum. Levers of the first class have the fulcrum between the effort and load, like a see-saw on a playground, for changing direction of force and travel distance and increasing or decreasing either of them. The second class has the load in the middle, like a wheelbarrow for increasing force. The third class has the effort in the middle, like a pair of tongs for increasing travel distance. Other household levers include manual bottle openers, hammers, and scissors. As these examples illustrate, levers are everywhere in the mechanical world and have been for the entirety of civilization.
Levers also occur in animals: the bones in limbs function as rigid rods and fulcrums, with muscles pulling hard close to a joint (the fulcrum) to move the extremity through greater distances than the contracting muscle can cover but exerting a force weaker than the muscle exerts on the bone. A train of three levers—the hammer, stirrup and anvil bones—magnify tiny acoustic displacements as they transmit sound from the eardrum to the cochlea.
Early Study
Our present formulation of levers derives from the Equilibrium of Planes of Archimedes, who determined that “Magnitudes are in equilibrium at distances reciprocally proportional to their weights.” Using levers, Archimedes investigated the volumes of spheres and cones. Archimedes imagined the cone or sphere divided into thin slices: if a slice is hung on one side of a lever, what cylinder slice must be hung at what position to maintain equilibrium? By working through the entire volume of the cone or sphere, Archimedes constructed a cylinder of equal volume, thus giving the sphere’s and the cone’s volume. Levers also appear in Galileo’s 1638 book of mechanics, Two New Sciences. Whereas Archimedes had abstracted the lever as a perfectly rigid line, Galileo considered it as a three-dimensional, flexible object, leading to the first theory of beams. Combinations of levers, constrained in various ways, became a research topic during the Industrial Revolution. “Linkages,” as these devices are called, were important for converting the rotation of steam engines into linear motion. Researchers in the nineteenth century took a mathematical approach to the problem. Among the best-known linkages is the Peaucellier cell, invented in 1864. The Peaucellier cell also plays theoretical roles in computer science.
Applications
Aside from the various aforementioned household tools, levers are featured in mobiles and also, notably, in the sculptures of Alexander Calder, who often places the fulcrum slightly above the beam that assists in balancing. The raised fulcrum has long featured in balances for weighing; the pivot point is above the lever’s center of gravity so that, when the pans pull with equal torque, torque from the displaced beam’s own weight will pull it level. Not all balances rely on this feature. Chinese pharmaceutical balances, for example, require the operator to look for nonrotation rather than perfect leveling.
More generally, nonmechanical levers exploit length to multiply distance. Optical levers rely on a mirror doubling an angle and a long travel distance for the light ray to register a large displacement. Social, financial, intellectual, and political resources can be metaphorically “leveraged” by using them to achieve outcomes larger than the resource itself, though the metaphor generally neglects to acknowledge the loss required for a mechanical lever to provide any gain.
Bibliography
Heath, T. L., ed. The Works of Archimedes. New York: Dover, 1953.
Mihal, Jim. "Simple Machines - Levers." MATC eCampus, ecampus.matc.edu/mihalj/scitech/unit1/levers/levers.htm. Accessed 2 Oct. 2024.
Moon, Francis C. The Machines of Leonardo da Vinci and Franz Reuleaux. Dordrecht, Netherlands: Springer, 2007.
Reynolds, Laura. “How to Build Levers and Pulleys.” eHow, www.ehow.com/how‗4466340‗build-levers-pulleys.html. Accessed 2 Oct. 2024.
Ricketts, Mitch. “Understanding Levers.” American Society of Safety Professionals, Oct. 2020, www.assp.org/docs/default-source/psj-articles/mtricketts‗1020.pdf. Accessed 2 Oct. 2024.