Lever system of the body

Lever system of the body 16.4.12

Levers and types of levers • Lever: A simple machine consisting of a rigid bar that turns about an axis of rotation or a fulcrum (A). An effort or exertion (F) is applied to cause movement against resistance or weight (R). Resistive Force (R) opposes motive force

Torque and levers • Levers utilize torque to assist us in lifting or moving objects. • Torque is the cross product between a force and the distance of the force from a fulcrum (the central point about which the system turns). The cross product takes only the component of the force acting perpendicular to the distance. Using trigonometry the torque is defined as: Torque = Force × Distance to fulcrum × sin (θ) Remember that work was also force multiplied by the distance, but it was the dot product and used the cosine of the angle between the force and distance: force × distance × cos(θ)

Principle of lever • For a lever in mechanical equilibrium, sum of all the torques acting is zero or the total anticlockwise moment (torque) is equal to the total clockwise moment. • According to principle of moments equilibrium is established when the sum of the moments of the forces acting in a clockwise direction is equal to the sum of the moments of the forces acting in a counterclockwise direction • Therefore, a lever will balance or turn uniformly about the point of support when the product of the force and force arm equals the product of the resistance and resistance arm

Principle of lever • According to the principle of lever, ∑τ=0 Anticlockwise torques = clockwise torques Effort Х Effort arm = Resistance Х load arm Effort arm = Resistance Load arm Effort

Mechanical Advantage • M. A. = Load = Effort arm Effort Load arm If the effort is farther from the fulcrum than the load (effort arm >load arm) then the lever is a force multiplier. If the effort is closer to the lever than the load (load arm> effort arm) then the lever is a speed multiplier.

Types of Levers • Class 1: In this case fulcrum, i.e. axis of rotation is located between force and resistance. Force arm (FA) is greater than resistance arm (RA) and the lever is at mechanical advantage e.g. seesaw. In seesaw, the load is the person that goes up, and the effort applied is the weight of the person that goes down. The fulcrum is in the center in between them

Types of Levers • Class II: Here the fulcrum is at one end of the lever, the force is applied to the other end and the load is situated in between. Hence force arm is (FA) is greater than resistance arm and the lever is at mechanical advantage • Examples: wheel barrow, nut cracker

Types of Levers • Class III: A class three lever has the effort between he fulcrum and the load. Here RA is larger than FA and hence lever is at mechanical disadvantage because the force required to counter the load is higher • Although it requires relatively great force to move even small resistances, it can produce speed and range of motion

Lever system of the body • The arrangement of muscles, bones and joints in the body form lever systems • For understanding one should know about the point of muscle insertion, its distance from the fulcrum. Force developed by the muscle-tendon complex produces a torque around the joint. Center of the joint (elbow, shoulder, knee or hip acts as the axis of rotation • Muscles operate by applying tension to their points of insertion into bones. Most muscles act in pairs known as antagonistic pairs. Each muscle in the pair acts in the opposite way to the other

Lever system of the body • The lever system amplifies the movement of the muscle so that short, relatively slow movements of the muscle produce faster movements. • Movement in the body is produced by a system of levers. These series of levers work together to produce coordinated action • Let’s look at various levers in the body

Nodding the head employs a first-class lever. The head acts as resistance. The counteracting force comes from the muscle of neck and upper back. They prevent the head from falling forward. The atlanto-occipital joint of head and spinal column is the fulcrum

Forearm extension • Triceps applying force to olecranon (F) in extending the non-supported forearm (R) at the elbow (A) • In extending the fore-arm, as in boxing, a lever of the first order is illustrated; the hand being the weight, the extensor of the elbow the power, and that joint the fulcrum placed between the weight and power.

Forearm flexion • Flexion or bending of the arm forms a lever of third class • The biceps (flexor) muscles in front of the upper arm act when lifting the forearm; and, as they are situated between the fulcrum (elbow joint) and weight (of the forearm), a lever of the third order is brought into action • The biceps muscles of the arm may contract only about 10cm, but the hand will move about 60cm. A small contraction of the biceps (the effort) can produce a large movement of the forearm (load) around the elbow joint (fulcrum)

Forearm flexion

Raising the body on hands • When the elbow is straightened in raising the body on the hands, then the weight falls at the elbow, between the extensor muscle, which is still the power, and the hand, which is now the fulcrum; and the second order of levers is illustrated

Straightening arm • When the arm (right/left) is at right angle to body, a third kind of lever is illustrated • Deltoid muscle is attached to the upper arm and spans the shoulder joint Working a pedal • When the foot is raised as in working a pedal, the weight is at the center of foot, and the ankle-joint is the fulcrum of a lever of the first order

Standing upright on tiptoes • When we rise on tiptoe it is the muscles of the calf which raise the heel, the fulcrum is at the toes, and the weight of the body falls on the ankle after the fashion of a lever of the second order

Most levers in the body are third order levers designed to maximize the speed rather than maximize the force

Force in the biceps • Suppose a person is holding his/her forearm in a horizontal position with the upper arm vertical • The biceps muscle pulls the arm upwards by muscle contraction with a force F, the opposing force is the weight of the arm W at its center of gravity (CG) • The weight of the average person’s forearm (and hand) is about 2% of the total body weight. Say if a person weighs 72kg then the weight of his forearm is about 1.44kg Sum of clockwise torques= Sum of anticlockwise torques 14W=4F F=14W/4 For W= 15N, F= 52.5 N

Force in the biceps • Let’ complicate the problem. Suppose now the person is holding a ball with weight of 44N

Force in the biceps • The force in the biceps is quite large about twenty six times the weight of the arm and about ten times the weight of the ball • For mechanical equilibrium, the forces must balance. This means that 383N upward force must be balanced by the downward forces • Therefore a 324N downward force is exerted on the elbow due to weight of the bone in the upper arm

Force in the biceps The lower arm can be hold by the biceps muscle at different angles q. What muscle forces are required for the different arm positions? • The force developed by biceps is independent of the angle between the lower and upper arm

Lever system of the body