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Biomechanics: The study of mechanics as it relates to functional and anatomical analysis of biological systems.
Mechanics: The study of physical actions of forces. Divided into:
Force: A push or pull action that can be represented as a vector, or arrow with the direction being in alignment with the arrow head.
Force is a vector quantity which means it has both magnitude and direction. The force equation is Force = Mass x Acceleration and is measured in Newtons (N) or Pounds (lbs). Roughly 4.45 N = 1 lb.
Vector: A quantity represented as an arrow, having both magnitude (length of the arrow) and direction (direction the arrow points).
Torque: A force applied some distance from an axis which produces rotary or angular movement (rotation about an axis).
Force Arm – the perpendicular distance from the axis of rotation to the force vector of the muscle (muscle line of pull). When the angle of muscle pull is 90 degrees, it is the distance from the axis of rotation to the muscle’s insertion. The force arm is also known as the lever arm, the moment arm, or the torque arm of the muscle.
Figure 1
Resistance Arm – the perpendicular distance from the axis of rotation to the force vector of the resistance (resistance line of pull). When the angle of resistance pull is 90 degrees, it is the distance from the axis of rotation to the center of mass of the weight being lifted. The resistance arm is also known as a lever arm, a moment arm, or the torque arm of the resistance.
Center of Mass: the balance point of an object at which an object’s mass and weight is equally distributed. This is where the force of gravity is acting on the mass being lifted.
Figure 2
Angle of Muscle Pull: Formed by the intersection of the line of muscle pull and the bone on which the muscle inserts.
Figure 3
When the angle of muscle pull is 90º, 100% of the muscle force is causing the lever (bone) to rotate around its axis (joint). This is known as the Rotary Component of the muscle force. Therefore, all of the muscular force is contributing to the movement, or in other words, causing the bone to rotate around its joint.
Figure 4
At all other angles of muscle pull, the force vector is divided into a rotary component and a non-rotary component. Depending on the angle of muscle pull, the non-rotary component will either have a stabilizing or a dislocating effect on the joint.
Stabilizing Component – If the angle of pull is <90º, the non-rotary component of the muscle force will pull the moving bone toward the joint axis. This increases the compression force at the joint and serves to provide stability to the joint.
Figure 5
Dislocating Component – If the angle of pull is >90º, the non-rotary component of the muscle force will pull the moving bone away from the joint axis. This creates a distractive or dislocating force at the joint, thereby applying a tension force on the joint ligaments.
Angle of Resistance: the angle (point at which two lines converge) formed between the line of pull of the resistance and the bone on which the resistance is applied (or where the resistance is causing movement at a joint).
Note: To help determine at which joint the resistance is causing movement, we can rule out other uninvolved joints by determining if there is a zero degree (0º) angle of resistance, and therefore, no force is causing rotation of the lever/bone around the axis/joint. To determine this, apply the following:
The angle of resistance is zero degrees (0º) if the *center of mass of the distal segment lies on a line between the joint and the direction of the resistance.
*Center of Mass: a point representing where gravity is acting on the segment(s). A point in a body (or body segment) about which all the parts exactly balance each other.
Rotary Component: at a 90º angle of resistance, 100% of the resistive force (energy) is causing the lever/bone to rotate around is axis/joint.
Figure 6
Figure 7
Figure 8
Figure 9
Non-Rotary Component: At a 0º angle of resistance, 100% of the resistive force (energy) is causing either a stabilizing element or a dislocating element. The resistive force is not causing the lever/bone to rotate about its axis.
Stabilizing Element
Figure 10
Dislocating Element
Figure 11
1 Newton = the amount of force required to accelerate a mass of one kilogram (kg) one meter per second squared.
1 Newton = .225 lbs
1 Pound = 4.448 Newtons
Inverse relationship between length of force arm and force required
Proportional relationship between force components and resistance components
The Human Leverage System
The distal end of a longer lever travels farther, and therefore faster, than the distal end of a shorter lever when traveling the same number of degrees (same angular displacement).
Lever equation
For use in force calculations. Evaluation of torque with modifications in force arms, resistance arms, and resistance (relevant to static equilibrium)
F x FA = R x RA
(force x force arm) = (resistance x resistance arm)
Initial Example:
F x 0.1 = 45 Newtons x 0.25 meters
F x 0.1 = 11.25 Newton-meters
F = 112.5 Newtons
Example A – Lengthening the force arm
Increase the (FA) by moving the insertion distally 0.05 meters:
F x 0.15 = 45 Newtons x 0.25
F x 0.15 = 11.25 Newton-meters
F = 75 Newtons
An increase in insertion from the axis by 0.05 meters results in a substantial reduction in the force necessary to move the resistance
Example B – Shortening the resistance arm
Reduce the (RA) by moving the point of resistance application proximally by 0.05 meters:
F x 0.1 = 45 Newtons x 0.2 meters
F x 0.1 = 9 Newton-meters
F = 90 Newtons
A decrease in the resistance application from the axis by 0.05 meters results in a considerable reduction in the force necessary to move the resistance.
Example C – Reducing the resistance
Reduce the (R) amount by reducing the resistance 1 Newton:
F x 0.1 = 44 Newtons x 0.25 meters
F x 0.1 = 11 Newton-meters
F = 110 Newtons
Decreasing the amount of resistance can decrease the amount of force needed to move the lever.
Machines of the Human Musculoskeletal System
The body’s musculoskeletal system is designed to apply forces to generate or control movement and basically involves three (3) types of machines: 1. Levers 2. Wheel/Axels 3. Pulleys.
Mechanical Advantage can be calculated by:
Dividing the length of the force arm (FA) by the length of the resistance arm (RA):
Mechanical Advantage = FA
RA
If MA equals 1, the machine is balancing the forces being applied to the system.
If MA is <1, the machine is providing a speed/ROM advantage.
If MA is >1, the machine is providing a force advantage (requires less force to lift a heavy object).
LEVERS
Humans move through a system of levers that cannot be changed anatomically, but can be used more efficiently
to maximize the muscular efforts of the body.
Lever: A rigid bar that turns around an axis of rotation, or fulcrum. The three Points of a Lever are:
NOTE: The arrangement of these three points determines the type of lever and the type of mechanical advantage provided by lever system.
First Class Lever: Axis (A) is between Force (F) and Resistance (R)
Second Class Lever: Resistance (R) is between Force (F) and Axis (A
Designed to provide force advantage.
Third Class Lever: Force (F) is between Axis (A) and Resistance (R)
Most levers in the human body are this type!
Levers Working in the Body
Force Application: ________________________
Resistance Point: _________________________
Axis: __________________________________
Class Lever: ____________________________
Torques or Moments of Force
Torquemuscle = Muscle Force (N) x Force Arm (m) x sin Ɵmuscle
Ɵmuscle is the angle of muscle pull.
The muscle creates “internal” torques or moments.
Torqueresistance = Resistance Force (N) x Resistance Arm (m) x sin Ɵresistance
Ɵresistance is the angle of resistance pull
The resistance creates “external” torques or moments.
Example:
A person contracts their elbow flexors exerting a force of 200 Newtons while the elbow is in a 90º flexed position. The distance from the person’s elbow joint axis to the point of muscle insertion is 0.0525 meters. The person is holding a resistance of 50 newtons and the distance from the person’s elbow joint axis to the center of mass of the segment (forearm + hand + resistance) is 0.3 meters.
NOTE: When working these problems determine: a) type of muscle contraction, and b) relative speed of movement
Wheels & Axles
radius of the axle
Anatomical Example
Pulleys