Force Composition and Resolution Notes

Force Composition

• Vectors can be summed, allowing for the addition of force vectors representing two or more forces into a single resultant force.
• $(A + B = C)$, but with vectors.
• When multiple internal and/or external forces act simultaneously, composition determines if the resultant action is:
  • Normal or typical motion.
  • Poor movement patterns/poor motor control motion.

Force Composition (Linear System)

• Example: Tug-of-war.

Force Composition (Non-Linear)

• Functional and Dysfunctional Movement
• Can represent forces generated by muscles to determine the action of combined forces, such as those of the rotator cuff.
• Rotator Cuff Muscles:
  • Subscapularis
  • Infraspinatus
  • Teres Minor
  • Supraspinatus: Resultant action of rotator cuff without Supraspinatus

Manual Muscle Testing (MMT)

• Applications/Discussion
• Why is manual muscle test (MMT) full deltoid muscle in shoulder abduction?

Pectoralis Major Adduction

• How does pectoralis major adduct?
• Pectoralis Major:
  • Attached to Humerus
  • Clavicle
  • Sternum

Patella Kinematics

• Compression force on the patellofemoral joint in a partial squat position
• Forces within the extensor mechanism are transmitted proximally and distally through the quadriceps tendon (QT) and patellar tendon (PT), much like a cable crossing a pulley.
• The resultant, or combined, effect of these forces is directed toward the trochlear groove of the femur as a joint compression force (CF).
• Increasing knee flexion by descending into a deeper squat significantly raises the force demands throughout the extensor mechanism, and ultimately on the patellofemoral joint.

Force Resolution

• Taking a single resultant and breaking it into two component parts.

Definition of Components

• The two component forces are perpendicular ($\perp$) to each other, with the resultant in between.
• All 3 parts (the 2 components and the resultant) have the same point of application.
• One component acts parallel to the lever, the other acts perpendicular ($\perp$) to the lever.
• Direction of vectors depends on direction of resultant.
• When lines drawn connecting tips, a rectangle will result.

Naming Components

• Component Parallel to Lever:
  • Parallel component
  • Tangential component
  • Radial component
  • Fx
  • Unit vector designation
  • Other vector designations depending on the FBD
• Component Perpendicular to Lever:
  • Perpendicular component
  • Normal component
  • Transverse component
  • Fy
  • Unit vector designation
  • Other vector designations depending on the FBD

Naming Convention

• Parallel component to the lever or segment on which it is acting will be the tangential component with a primary function of compression or distraction.
• Perpendicular component to the lever or segment on which it is acting will be the normal component with a primary function of providing rotary movement

Force Resolution: Functional Movement // Tissue Loading // Internal Forces

• The normal force, (Fy in the drawings) actually contributes to the joint angular motion.
• Tangential force (Fx) creates compression force on the joint (A – B) and distractive force (D).
• Tangential component can act as a stabilizing force for the joint.

External Forces: Gravity

• Normal force acts on segment to try to produce motion opposite to that of the muscle forces.
• Tangential may be compressive or distractive.

Tangential Components

• Examples are basic when the tangential component goes through the joint axis, resulting in:
  • Effect on joint is from linear force only
  • No moment arm for the tangential component
  • No moments
• Typically, the tangential components (internal and external) will not go directly through the joint:
  • Will have a small moment arm allowing for some rotation at the joint
  • As well as compressive/distractive forces

Applications/Discussion

• Examine the forces in the graphic presented. Provide some of the actions/functions of the forces and/or name some of their influences on the joint and other structures (QLf, FxQLf, FyQLf, GLf, FpLf).

Work Smarter Not Harder

• Forearm is your personal vector. How do you want to direct it?

Applications/Discussion: Making it ‘Harder’ or ‘Easier’

• Resisting or testing knee extension: Which hand placement makes it ‘easier’?
• Discuss the implications of the force applied by the PT in each situation (ES, MAES, MAHAT, HAT, MRC).

Wheelchair Pushing

• Is the PT pushing the wheelchair forward or downward? If both, in which direction is she pushing more?

Quadriceps Force Components

• If the Quadriceps force ($QLf = 63 N$) and its angle of inclination ($\theta = 25^\circ$) are known, determine the horizontal and vertical components of force.

Trigonometry Review

• SOH-CAH-TOA
  • Sine: $sin(\theta) = \frac{Opposite}{Hypotenuse}$ (SOH)
  • Cosine: $cos(\theta) = \frac{Adjacent}{Hypotenuse}$ (CAH)
  • Tangent: $tan(\theta) = \frac{Opposite}{Adjacent}$ (TOA)

Right Triangle Relationships

• Typically used when the angle is known and one side magnitude is known
• $cos \theta = \frac{QLfx}{QLf}$ (adjacent/hypotenuse)
• $sin \theta = \frac{QLfy}{QLf}$ (opposite/hypotenuse)
• $tan \theta = \frac{Fy}{Fx}$ (opposite/adjacent)
• Example Calculations:
  • $cos(25) = \frac{QLfx}{63}$
  • $QLfx = 63 * cos(25)$
  • $QLfx = 57.1$ (rounded)
  • $sin(25) = \frac{QLfy}{63}$
  • $QLfy = 63 * sin(25)$
  • $QLfy = 26.6$