Kinetics and Forces Lecture Notes

Kinetics - The Basics

• Kinetics examines the forces that cause or influence movement, as well as forces that allow maintenance of equilibrium or balance.

• Kinematics describes HOW movement occurs, while kinetics explains WHY movement occurs.

Force

• Force is described as the action of one body on another.

• It is a vector quantity, possessing both magnitude and direction.

• Like kinematics, force has linear and angular components.

• Forces can be added together; the mathematical symbol for summation is \sum. Therefore, when looking at multiple forces, you pl see \sum F = Linear Forces.

Linear Forces

• Forces create linear or translatory action.

• SI units: Newtons (N)

Rotational/Angular Forces

• Generally known as 'moment' or 'torque'. For our purposes, moment = torque.

• Just as a linear force is represented by an arrow, an angular force is represented by a curved arrow, still indicating direction.

• Angular forces can be added if there is more than one.

• SI Units for moments: Newton-meters (N.m)

• To generate a moment or the potential for producing rotation or angular movement, three elements are needed:

  • Linear force

  • Axis (denoted by a circle with a point in the center, or a triangle \triangle, or by a \land)

  • A distance from the linear force to the axis. This distance is a perpendicular distance – the distance would be at right angles to the linear force.

• Therefore, if a linear force is applied a distance from an axis, then there a potential exists for rotation or angular movement around that axis – there the potential exists for a moment to exist

External & Internal Forces

• External forces (linear and/or angular) are exerted on the body from outside sources: gravity, weights, backpacks, resistance.

• Internal forces are usually in response to some external stimuli or external forces

Tissue Forces (Internal and/or External)

• Have different names for the effect of the directed force(s)

Tension / Tensile

• Equal and opposite loads extending outward from surface of structure; applied in parallel to long axis of object

• Lengthens and narrows

Joint Distraction / Distractive

• A force that is perpendicular to a joint surface, is directed away from that joint surface, and allows for separation of the joint surfaces.

Compression / Compressive

• Equal and opposite loads are applied toward the surface of a structure.

Joint Compression / Compressive Forces

• Opposite of joint distraction.

• Applying perpendicular forces to joint surfaces directed toward the surface in attempt to bring the surfaces together.

Shear

• Any force (or component of a force) that has an action line parallel to contacting surfaces (or tangential to curved surfaces) that creates or limits movement between surfaces.

• i.e., Two parallel forces applied in opposite directions – not in line with each other.

• Tries to cause movement between those two contacting surfaces.

Bending

• Load applied to structure in a manner that causes it to bend about an pivot point.

• Combination of compression/tension.

Torsion

• Load applied to a structure in a manner that causes it to twist about the structure’s long axis.

• Shear stresses distributed over the entire surface

• Further stresses are from axis, higher their magnitude

Combined Loading

• Combination of more than one loading modes

Terminology/Concepts/Factors/Relationships Involving or Influences Force

Mass

• Amount of matter of which a body is composed

Center of Mass (CoM, CM)

• Point at which a body’s mass is concentrated in equilibrium (evenly distributed).

• Point where acceleration of gravity acts on the body (whole body and segment).

• AKA Center of Gravity (CG, CoG).

• Often represented by the symbols:. For single object or rigid body → CoM will not change regardless of orientation.

• For segment → will not change location as the mass of a given segment is fixed for an individual (e.g. hand)

System CoM Location in body or object

• For linked systems → as the masses of the links move, orientation of masses also changes and the CoM for the entire system will move

• CoM for the entire system will move.

• May even lie outside of system

• Move towards the added weight.

• When external mass is removed, the CoM will move again more towards center of system

• CoM for body is just anterior of S2

Gravity

• Defined as a force (typically denoted ‘g’ for gravity) on a mass pulled by earth’s mass causing object to accelerate toward the earth

• This gravitational pull gives an object weight:

• Weight = mass * g

• Notice that this makes weight a force and is a vector quantity

Line of Action

• Represents the orientation (internal and/or external) – or – the line along which a force acts – or – along the shaft of the vector

• Look at the name – it is the line along which an action can occur
  *

External forces

• Usually related to some form of resistance (will tend to use the term resistance for external sources of force)

• For gravity acting on segment//system//additional resistance – the line of action of gravity is usually vertical (with arrowhead pointing downward).

• From other sources (weights, manual contact, etc) will vary according to the situation

Internal forces

• Usually are forces created by muscle, but can be other tissues

• The line of action is usually parallel to the direction of the muscle fibers (with the arrowhead directed toward the stabilizing segment to complete the vector)

• So you can say that the line of action of the muscle is along or parallel to its fibers

Point of Application

• When the vector is drawn, this is where the tip of the tail goes

External forces:

• Point of application is at the segment/system’s CoM

Internal forces:

• Point of application is the attachment site for the tissue on the bone that force is acting upon

• Most of the time we will be referring to muscle so the point of application of a given muscle is at the attachment is the proximal or distal insertion site of the muscle with the arrow going from the moving segment towards the stabilizing segment

Line of Gravity (LoG)

• Typically represents effect of gravity on the body

• In anatomical position, LoG is parallel to the trunk and extremities

• If in supine (or prone), then LoG is perpendicular to the body

Base of Support (BOS)

• Define by contact of system to ground – may include assistive devices or other objects

Ground Reaction Force Vector (GRFv)

• Contact with the ground in turn results with the ground reacting or ‘pushing back’

• Occurs with all 3 planes/axes

• If orthogonal (at right angles or 90° to each other) – have 3 components:

  • Vertical force (Z in graphics below)

  • Front – back (anterior-posterior or Y in graphic)

  • Side-to-side (medial-lateral or X)

• When add all 3 components together → GRFv

Applications/Discussion

1. Linear and Angular Forces

• Need to know the differences between linear and angular forces and their relationship to each other

• Need to know the terminology and associated with linear and angular forces

• Often use the term ‘translatory’ or ‘translation’ to describe linear forces. For example, you need to make sure that the force you are exerting is a translatory force to test and mobilize a joint. You do not want to create rotation at the joint.

• Angular force → called a moment or torque

1. Internal and External Forces

• Need to know the difference between internal and external forces

• Be able to give examples of internal and external forces

• Later need to be able to understand and discuss which forces can be changed or manipulated to change how much force an individual must exert to perform an action and the consequences if they cannot create sufficient force for a given activity.

• The effect of a given force (compression, tensile, etc.) becomes important in understanding how the tissues of the body are loaded and the effect the load has on the tissues.

• Later need to be able to understand which forces can be changed or manipulated and how they can be changed/manipulated for exercise objectives

  • To increase or decrease how much a muscle needs to contract for an exercise objective

  • Progression of exercises

1. CoM, Gravity, Line of Action, Point of Application

• To be able to distinguish differences in segmental vs. system CoM

• To be able to determine the general reaction of CoM to changes and added/subtracted weight

• Understand the meaning and applications of the line of action

• Be able to “see” the line of action visually on paper, in your actions, the actions of your patients and conceptual or ‘imaginary’ lines such as gravity

• Understanding the line of action of muscles along with planes and axes helps determine the muscle actions on a joint.

  • For example, muscle fibers that do not run strictly horizontal or vertical cross more than one plane so the muscle will have more than one action

  • The line of action of a muscle may change its orientation to an axis – be superior to it in one position but then become inferior to the axis in another position changing its action on that joint

• The point of application can have influence on how ‘hard’ or how ‘easy’ a muscle or a person may have to work. It can be involved in levers, moments, and helps standardize the depiction of forces on a body

1. LoG, GRFv

• Applications of the information presented above – forces, line of action, point of application, etc.

• They are specific depiction of linear forces that act on the body and are important in balance, gait, mechanism of injury, injury prevention and potential creation of moments

• LoG involved with balance and stability as presented below

• GRFv will be covered in detail with gait

1. BoS

• Strongly involved in balance and stability as presented below

Balance vs. Stability

Stability:

1. Can refer to the ability to maintain or return to a steady state in presence of perturbations

2. Degree to which one can stand still or move without falling (full body)

• Assessed through CoM, LoG and BoS

Conditions for Stability:

• Line of gravity within base of support

• Larger the base of support, more stable

• The lower the CoM is to the base of support, more stable

• The closer to the center of the base of support that the LoG falls, the more stable

Balance:

1. Can refer to the capability of a system to move without falling – control is lost and the “fall” is to the ground or supporting surface

2. The integration of systems whose ultimate goal is to maintain static or dynamic stability

• Can be assessed through either CoM and/or CoP depending on application and instrumentation:

  • Force plates

  • Pressure mats

  • Biodex Balance System

  • Balance Master (etc.)

Mobility

Conditions for Mobility

• LoG falls outside of the base of support

• Controlled mobility → alternates with LoG falling within and out of the BOS

• Uncontrolled mobility → fall

Moments

• Term used to mean angular forces

• Also called torque

• May create movement or may be in equilibrium

• Named for action on joint or tissue (usually osteokinematic action, e.g., flexor moment, adduction moment)

• Have both internal and external moments

• Remember that there are 3 conditions (parts/components/items) necessary for a moment to be produced:

  1. Linear force

  2. Axis around which the angular motion can occur

  3. A perpendicular distance from the linear force to the axis

• So when taken together …Mathematically:

  • \sum M = \sum(F * \perp d)

  • where M is the sum of the moments generated, F are the applied linear forces, and d are the \perp distances between the axis of rotation and the line of action of the applied forces (called moment arms – more on this later)

Examining Each Part for: Internal Moment

1. Linear force – any tissue (tendon, ligament, etc.) but here the focus will be: Muscle Need to know:

   • As it is a linear force, it can be represented by a vector

   • Line of action → usually parallel to the direction of the muscle fibers

     • One vector can represent entire muscle so do not have to represent each muscle fiber

     • May need more than one vector if the muscle is a pennate (angled in which not all muscle fibers are parallel to each other (e.g. gastrocs)

   • Point of application → is at attachment of the muscle on the moving segment

   • Direction → is toward the stabilizing segment

   • Orientation → Angle of Application (Inclination)

     • Angle is created by: 1) line of action of the muscle (represented by the tendon) and 2) the long axis of the bone onto which the tendon inserts (on the side of the joint axis.)

2. Axis – can be

   • Fulcrum around which angular motion occurs

   • Pivot point for angular motion

   • Typically for the joint it is the “instantaneous center of joint rotation” (which can move as joint moves)

3. Perpendicular distance from line of action to the axis

   • Line that is perpendicular (at right angle to or is at 90°) to the line of action of internal force to joint axis of rotation

   • Goes by many names:

     • Moment arm

     • Force arm

     • Effort arm

Examining Each Part for: External Moment

1. Linear force – something external to the body (gravity//added resistance in the form of a weight or a person//object pushing against or pulling on the body )

   • Need to know:

     • As it is a linear force, it can be represented by a vector

     • Line of action:

       • Gravity is generally vertical with the arrow pointing down

       • If added resistance from a free weight → usually vertical with arrow pointing down

       • If added resistance from manual resistance or object → the orientation of however the force is being directed

     • Point of application:

       • Gravity is at the CoM of the segment being acted upon

       • Added resistance / free wt – also at the weight’s CoM

       • Added resistance / manual - at the point of contact

     • Direction and orientation→ as given above with line of action

2. Axis – same axis as for internal – can be

   • Fulcrum around which angular motion occurs

   • Pivot point for angular motion

   • Typically for the joint it is the “instantaneous center of joint rotation” (which can move as joint moves)

3. Perpendicular distance from line of action to the axis

   • Line that is perpendicular (at right angle to or is at 90°) to the line of action of external force to joint axis of rotation

   • Goes by many names:

     • Moment arm

     • Resistance arm

     • Effort arm

Further Applications/Discussions of Linear & Angular Forces

• Using what has been presented thus far:

1. Determining muscle action and type of internal moment produced at a joint

   • If line of action of muscle passes anterior to frontal axis, muscle will flex the joint (exception -- knee); It creates an internal flexion or flexor moment

   • If line of action of muscle passes posterior to frontal axis, muscle will extend the joint (exception -- knee); It creates an internal extension or extensor moment

   • If line of action of muscle passes superiorly to sagittal or A/P axis (thick line going front/back), muscle will abduct creating an abduction moment

   • If line of action of muscle passes inferiorly to sagittal or A/P axis (thick line going front/back), muscle will adduct creating an adduction moment

   • Location of muscle to longitudinal axis determines whether or not it will internally or externally rotate:

2. External moments follow the same concepts as for the internal moments above:

   • If the line of action of the external force is anterior to a frontal axis, it can create a flexor moment

   • If the line of action of the external force is posterior to the frontal axis, it can create an extensor moment

   • Line of action is superior to sagittal axis → abductor moment

   • Line of action is inferior to sagittal axis → adductor moment

   • Same relationship for longitudinal axis for internal and external rotator moments

   • Same exceptions as above

3. Relationship of internal ↔ external moments

   • When an external moment is acting on a joint, we usually want the body to respond by creating an opposing internal moment

   • For example, when going from sit-to-stand, gravity may try to flex the hip, flex the knee and dorsiflex the ankle joint such that if there is no opposing or countering force, the body will collapse

   • The muscles contract to try to overcome the effect of gravity creating extensor moments to allow the motion to be completed

4. Posture

   • Examine the effect of gravity on the joints of the body and what external moment(s) gravity can produce

   • This is one of the uses of the LoG

   • In ‘normal’ or ideal posture, slight moments will be created by gravity pulling down on the spinal segments and lower extremities

   • In postural deviations, these moments may increase or change directions

5. GRFv and Gait

   • When walking (or running or other forms of gait), the foot makes contact with the ground and the ground “pushes back” and creates a GRFv

   • Where the GRFv is located in relation to the joints can influence the immediate external moment created and subsequently, the internal moment that needs to be created to offset the external moment

   • For example, the GRFv at initial contact (heels strike) falls posterior to the ankle in the sagittal plane creating an external plantarflexion moment (graphic below on left); the muscles/tissues in the body then create an internal dorsiflexor moment (graphic on right)

   • In individuals with no impairments, this is done seemingly automatically

   • However, in individuals with some form of ankle impairment (restricted ROM, decreased strength in the dorsiflexors, etc.), it can be a problem and the PT needs to be aware of the possibilities that exist in this situation