Lever

LEVER, one of the so-called simple machines, representing a rigid rod to which forces can be applied at three points located along its axis. If one of the three forces can be conveniently considered as the reaction of a support, arising according to the law of equality of the forces of action and reaction, then the point of application of this force is called the fulcrum. If the fulcrum is the middle of the three points, then a lever of the first class takes place; if it is the extreme point, then we have a lever of the second class. Since regarding one of the forces as the reaction of the support is often entirely conventional, the same lever can frequently be considered as belonging to both the first and the second class. Examples from biomechanics: 1) A rower's oar is a lever. In relation to the external world, it is a lever of the second class, because its fulcrum is the point where it rests against the water (the extreme point), the hand end is the point of application of force, and the oarlock (the middle point) is the point of utilization of the force that pushes the boat. Meanwhile, biomechanically, the fulcrum is the oarlock, and the water end of the oar is the point of utilization of force and the point of repulsion from the water; therefore, biomechanically, the oar belongs to a lever of the first class. 2) The foot when rising onto the toes is, in relation to the external world, a lever of the second class (the fulcrum is at the extreme end near the toes, the point of application of muscular force is the other extreme, the calcaneal tuberosity; the point of utilization of force is the ankle joint _f which lifts the lower leg and with it the entire body upward). Biomechanically, it is also a lever of the first class, since the fulcrum for the calf muscles serves as the ankle joint (middle point), and the tip of the toes is the point of utilization of force and the point of repulsion from the ground. The most essential concept determining the statics of a lever, i.e., the conditions of its equilibrium, is the concept of the static moment, measured as the product of the force and the perpendicular distance from its direction to the fulcrum. For the equilibrium of a lever, it is necessary and sufficient that the static moments of the forces acting on its two points, calculated in relation to the fulcrum, are numerically equal and opposite in sign. In this case, if of the three points of the lever (a, b, c) we take a as the fulcrum and achieve equilibrium according to the above condition, then the same condition will also be met if we consider point b or point c as the fulcrum. In other words, if the sum of the static moments of b and c relative to a is zero, then the sum of the static moments of a and c relative to b is thereby also zero, and so on. From this it is already clear that the distinction between a lever of the first and second class has no scientific significance. The above condition of equilibrium of a lever is valid not only in relation to a rectilinear lever, but also for a lever of any shape. Finally, the same condition is valid for a lever having more than three points of application of forces. This indication is essential because the majority of the levers of the human body are not rectilinear and have more than three points of application of forces, being connected to more than one muscle.

N. Bernstein.