# Chapter 6

Biomechanical Factors & Concepts

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:

• Statics: The study of systems when there is no acceleration. This includes all situations when the body is at rest or is moving at a constant velocity (unchanging speed and unchanging direction). Forces acting on the body are in balance (sum of the Forces equal zero). This is Newton’s 1st law of motion or the law of Inertia.

• Dynamics: The study of systems when there is acceleration. This includes all situations when the body’s speed and/or direction of movement are changing. Forces acting on the body are not balanced (sum of the Forces do not equal zero). This is known as Newton’s 2nd law of motion or the law of Acceleration.

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).

• In the human body, the contracting muscle applies a force to the bone on which it attaches and causes the bone to rotate about an axis at the joint causing angular movement.

• The amount of torque can be determined by multiplying the amount of force (force magnitude) by the force arm (lever arm, moment arm, or torque arm).

 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 the lever arm, the 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.  Angle of Muscle Pull: Formed by the intersection of the line of muscle pull and the bone on which the muscle inserts. Note: The reference angle is the angle on the joint side of the line of pull.

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 3

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 4

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.  Figure 5

 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 12 Figure 13 Figure 14 Figure 15 Non-Rotary Component: At a  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 16 Dislocating Element           Figure 17 1 Newton = the amount of force required to accelerate a mass of one kilogram (kg) one meter per second squared. 1 Newton = .225 lbs1 Pound = 4.448 Newtons

 Inverse relationship between length of force arm and force required
• The longer the force arm, the less force required to move the lever if the resistance and resistance arm remain constant
• Shortening the resistance arm allows a greater resistance to be moved if force and force arm remain constant

 Proportional relationship between force components and resistance components
• Greater resistance or resistance arm requires greater force and/or longer force arm
• Greater force or force arm allows a greater amount of resistance
• Even slight variations in the location of the force and resistance are important in determining the mechanical advantage and the required muscle torque

 The Human Leverage System
• Built mainly for speed and range of motion at the expense of force
• Short force arms and long resistance arms require great muscular force to produce movement
• The longer the lever (or summation of several levers), the more effective it is in generating velocity (produces greater linear velocity)

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 equationFor 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 NewtonsAn 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 NewtonsA 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 NewtonsDecreasing 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.

• These machines are used to increase or multiply the applied force (muscular contraction) in performing a task, making it easier to lift heavy objects. They also can balance forces to enhance stability or enhance the speed and range of motion of the desired movement.
• We use our musculoskeletal machines in an effort to achieve a mechanical advantage.
• Mechanical advantage describes the use of a machine to improve one of three things: force, balance, or speed/ROM..

Mechanical Advantage can be calculated by:

Dividing the length of the force arm (FA) by the length of the resistance arm (RA):

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:

1.     Axis (A): the point of rotation (usually the joint) about which the lever moves

1.     Force (F): the point of force application (usually the muscle’s insertion)

1.     Resistance (R): the point of resistance application which is either the:
• Center of mass of a lever - the point at which all of the body’s (or limb) mass and weight is equally distributed in all directions, OR
• Location where external resistance is being applied to the lever system.

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)

 If axis is midway between force and resistance = balanced movement (seesaw)If axis is close to the force = speed and range of motion (scissors)If axis is close to resistance = force (crowbar) Second Class Lever: Resistance (R) is between Force (F) and Axis (A

 Large resistance can be moved with relatively small force (wheelbarrow), (nutcracker)Designed to provide force advantage. Third Class Lever: Force (F) is between Axis (A) and Resistance (R)

 Requires large force to move a relatively small resistance (catapult, paddle rowing) Designed for speed and range of motion advantageMost levers in the human body are this type! Levers Working in the Body

 Force Application: ________________________Resistance Point: _________________________Axis: __________________________________Class Lever: ____________________________ Force Application: ________________________Resistance Point: _________________________Axis: __________________________________Class Lever: ____________________________ Force Application: ________________________Resistance Point: _________________________Axis: __________________________________Class Lever: ____________________________ Force Application: ________________________Resistance Point: _________________________Axis: __________________________________Class Lever: ____________________________ Force Application: ________________________Resistance Point: _________________________Axis: __________________________________Class Lever: ____________________________ Force Application: ________________________Resistance Point: _________________________Axis: __________________________________Class Lever: ____________________________ Force Application: ________________________Resistance Point: _________________________Axis: __________________________________Class Lever: ____________________________ Force Application: ________________________Resistance Point: _________________________Axis: __________________________________Class Lever: ____________________________

 Torques or Moments of Force

 Torquemuscle = Muscle Force (N) x Force Arm (m) x sin ƟmuscleƟmuscle is the angle of muscle pull.The muscle creates “internal” torques or moments.

 Torqueresistance = Resistance Force (N) x Resistance Arm (m) x sin ƟresistanceƟresistance is the angle of resistance pullThe 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
• Mechanical advantage depends: If force is applied to the axle → speed/ROM advantage. If force is applied to the wheel → force advantage.
• Center of the wheel and the axle both correspond to the fulcrum or axis
• Both the radius of the wheel and the radius of the axle correspond to the lever arms
• If a wheel radius is 3 times greater than the radius of the axle, due to the longer force arm, the wheel has a mechanical advantage over the axle (force advantage)
1. the outside of the wheel will turn at a speed 3 times that of the axle
2. the distance that the outside of the wheel turns will be 3 times that of the outside of the axle

Anatomical Example

1. Joint: Shoulder (glenohumeral)
2. Axle: ___________________________________________
3. Outside of Wheel: _________________________________
4. Force: __________________________________________

 Pulleys

1. Single pulleys have a fixed axle and function to change the effective direction of force application and have a mechanical advantage of 1.
2. Every additional “rope” (or tendons) connecting to moveable pulleys increases the mechanical advantage by 1.

Anatomical Example

1. Joint: Ankle and subtalar
2. Pulley: _________________________________________
3. Force: __________________________________________
4. Force Application: ________________________________
5. Movement: ______________________________________