Levers and Moment Arm

Example of a 2nd class lever n the musculoskeletal system.

Standing on your tip toes places the muscle force in advantage. In a second class lever system, the mechanical advantage favors the force arm. (The force arm will always be longer.)

What is moment of force?

Tendency that a force has to cause motion of a segment or body around an axis.

What variables affect the moment of force?

The force that the muscle generates and the moment arm of the muscle.

Define the angle of application?

The moment arm depends on the location of the muscle's attachment on the bone and on the angle between the line of pull of the muscle and the limb to which the muscle attaches. This angle is called angle of application.

Most of the musculo-skeletal system consists of third class levers.

The muscle is always in disadvantage, since the moment arm of the resistance is longer than the moment arm of the muscle.

The 3rd lever system produces a disadvantage for force but an advantage for speed of movement

The time that the muscle insertion moves a given distance (red arrow), the resistance moves a much greater distance (blue arrow).

The muscles moment arm change according to the joint angle.

At d1 the elbow joint is maximally extended and the moment arm is very small. At 90 degrees the moment arm of the biceps muscle is at it's maximal length. d3>d2>d4>d1

What is a Lever?

A lever is a rigid structure that can move around a fixed point called a fulcrum or axis

What are the three types of levers?

First Class - The applied force and the resistance are on opposite sides of the fulcrum. Second Class - The resistance is between the applied force and the fulcrum. Third Class - The applied force is between the resistance and the fulcrum.

Most common type of lever in the human body is the 3rd class lever.

Force is closer to the axis and the resistance farthest away. The muscles in the body are always in disadvantage in relation to external forces. The mechanical advantage of a third class lever system favors the resistance arm. (The resistance arm is always longer.)

What are the components of a lever system?

Fulcrum - The center or axis of rotation of the system. Moment Arm - The distance from any force or weight that produces torque to the fulcrum. Force Arm - The distance from an applied force to the fulcrum. (The moment arm of the force.) Resistance Arm - The distance from the resistance to the fulcrum. (The moment arm of the resistance.)

The effectiveness of a lever at moving a resistance can be calculated by dividing the moment arm of the force (muscle) by the moment arm of the resistance.

Mechanical Advantage = moment arm of the force /moment arm of the resistance

A muscle inserts 3 cm from a joint axis (Fa = 3 cm) The distance to the weight that the muscle is resisting is 30 cm (Ra = 30 cm). What is the mechanical advantage?

Mechanical advantage = 3/30 = 0.1 this means that, when Fa and R are both perpendicular to the limb, Fa must be 10 times greater than R to move the resistance.

The formula to calculate moment of force in a static condition.

Mf = F x d (perpendicular distance)

Example of a 1st class lever in the musculoskeletal system.

Neck extensors muscles contract to balance the weight of the head. This lever is important to maintain the head straight. The fulcrum in a first class lever system can often vary in position to favors the force arm or the resistance arm.