Biomechanics and Free Body Diagrams for the FRCSOrth

Courtesy: Rishi Dhir, FRCSOrth, Consultant Orthopaedic and Upper Limb Surgeon, Princess Alexandria Hospital, Harlow, UK

Basic Biomechanical Concepts

Force

• Definition: A load acting across a particular area.
• Measured in Newtons (N).
• Often related to the concept of stress.

Newton’s Three Laws of Motion

First Law – Law of Inertia

• A body remains at rest or in constant motion unless acted upon by an external force.
• When sum of forces and moments = 0, the body remains in equilibrium.

Second Law – Law of Acceleration

• When forces acting on a body are unbalanced, the body accelerates.
• Magnitude of acceleration is proportional to the applied force.

Formula:

Force = Mass × Acceleration

Third Law – Law of Action and Reaction

• For every action, there is an equal and opposite reaction.

Orthopaedic Examples

• Ground reaction force during walking.
• Joint reaction forces within joints.

Moments

Definition

• A moment (torque) is the turning effect of a force applied at a distance from a pivot.

Formula

Moment = Force × Perpendicular distance from pivot

Example

• Seesaw analogy:
  • Heavier person sits closer to fulcrum.
  • Lighter person sits farther away to balance moments.

Couples

Definition

• A couple is:
  • Two equal
  • Parallel
  • Opposite
    forces acting at different points.

Examples in everyday life

• Turning a steering wheel.
• Opening a bottle cap.

Clinical Examples of Force Couples

Shoulder Force Couples

Coronal Force Couple

• Deltoid
  • Pulls humeral head upwards.
• Rotator cuff
  • Pulls humeral head downwards and medially.

Function

• Maintains centering of the humeral head in the glenoid.

Rotator Cuff Tear

• Loss of downward force.
• Unopposed deltoid action ? superior migration of humeral head.
• Leads to rotator cuff arthropathy.

Transverse Force Couple

• Subscapularis (anterior)
• Infraspinatus and Teres Minor (posterior)

These maintain balance between internal and external rotation forces.

Force Couples in the Wrist

Lunate Function

• Acts as a torque converter.
• Balances forces between:
  • Scaphoid (flexion tendency)
  • Triquetrum (extension tendency)

Scapholunate Ligament Injury

• Causes scapholunate dissociation.
• Radiographic sign:
  • Terry-Thomas sign (scapholunate gap).
• Leads to:
  • Scaphoid flexion
  • Lunate extension
  • DISI deformity (Dorsal Intercalated Segment Instability).

Levers

Definition

A lever consists of:

• Fulcrum (pivot)
• Force (effort)
• Load (resistance)

Human body movements operate through lever systems.

Types of Levers

First Class Lever

• Fulcrum between force and load.

Examples

• Seesaw
• Scissors

Human body examples

• Atlanto-occipital joint
• Hip during single-leg stance

Second Class Lever

• Load between fulcrum and force.
• More efficient lever system.

Example

• Nutcracker

Human body example

• Metatarsophalangeal joint during tip-toe standing.

Third Class Lever

• Force between fulcrum and load.
• Least efficient lever system.

Examples

• Broom sweeping.

Human body examples

• Elbow joint
• Shoulder joint

Important Point

• Most levers in the human body are third-class levers.

Equilibrium

Definition

A system is in equilibrium when:

• Sum of all forces = 0
• Sum of all moments = 0

This condition is assumed when drawing free body diagrams.

Free Body Diagrams

Definition

• A conceptual representation used in biomechanics.
• Used to analyze forces and moments acting on a body segment.

Assumption

• System is in static equilibrium.

Assumptions in Free Body Diagrams

Forces

• Joint reaction forces are compressive.

Bones

• Considered rigid rods.

Joints

• Treated as frictionless hinges.

Muscles

• Act only in tension, not compression.

Additional assumptions

• Line of muscle action passes through center of muscle mass.
• No antagonistic muscle activity is considered.

Clinical Application of Free Body Diagrams

Free body diagrams are used to explain biomechanics of:

• Hip
• Shoulder
• Elbow
• Knee
• Spine
• Foot (MTP joint)

They are usually presented in clinical scenarios during examinations.

Hip Free Body Diagram

Lever Type

• First class lever

Components

• Fulcrum: Femoral head
• Load: Body weight
• Force: Hip abductors

Example Calculation

Assume:

• Body weight = 600 N
• Weight of limb = 1/6 body weight
• Effective body weight during single leg stance = 5/6 body weight = 500 N

Moment equilibrium:

Body weight × lever arm = Abductor force × lever arm

Example:

500 × 15 = Abductor force × 5

Abductor force = 1500 N

Joint Reaction Force

Joint reaction force =

Body weight + Abductor force

= 2000 N

Trendelenburg Gait – Biomechanical Explanation

Causes

• Weak hip abductors
• Nerve injury
• Hip joint pathology
• Altered center of rotation

Compensation

Patient shifts body weight toward the affected side to:

• Increase abductor lever arm
• Decrease body weight moment arm
• Reduce joint reaction force

Non-operative Management of Hip Arthritis

Example

Use of a walking stick in opposite hand.

Effect

• Creates an additional counteracting moment.
• Reduces joint reaction force.
• Decreases pain.

Charnley Low Friction Arthroplasty

Principle:

• Medialization of center of rotation
• Lateralization of greater trochanter

Result:

• Increased abductor lever arm.
• Reduced abductor force requirement.
• Reduced joint reaction force.

Shoulder Free Body Diagram

Lever Type

• Third class lever

Components

• Fulcrum: Center of humeral head
• Force: Deltoid muscle
• Load: Weight of arm

Reverse Shoulder Arthroplasty

Biomechanical Principle

• Medialization
• Inferiorization of center of rotation.

Result

• Increased deltoid lever arm
• Improved deltoid efficiency.

Elbow Free Body Diagram

Lever Type

• Third class lever

Components

• Fulcrum: Elbow joint
• Force: Brachialis muscle
• Load: Weight of forearm/hand

Increasing weight in hand:

• Increases clockwise moment
• Requires greater muscle force
• Increases joint reaction force.

Metatarsophalangeal Joint Free Body Diagram

Lever Type

• Second class lever

Components

• Fulcrum: MTP joint
• Load: Body weight
• Force: Gastrocnemius–soleus complex

Spine Free Body Diagram

Lever Type

• First class lever

Components

• Fulcrum: Vertebral body
• Force: Erector spinae muscles
• Load: Body weight or external load

Lifting posture

Squatting posture:

• Increases erector spinae lever arm
• Reduces joint reaction force
• Protects spine.

Knee – Patellofemoral Joint Biomechanics

Forces

• Quadriceps force
• Patellar ligament force

These produce a compressive joint reaction force at the patellofemoral joint.

Effect of Patellectomy

• Patella acts as a sesamoid bone.
• Increases quadriceps efficiency.

Without patella:

• Quadriceps force must increase.
• Patellar ligament force increases.
• Joint reaction force increases.

Therefore:

• Greater joint stresses occur.

Patellofemoral Arthritis and Stair Climbing

• Knee flexion increases angle between quadriceps and patellar ligament.
• This increases compressive joint reaction force.
• Hence pain is worse during:
  • Stair climbing
  • Descending stairs
  • Deep knee flexion

Key Points for Examination

Candidates should remember:

• Basic biomechanical principles:
  • Force
  • Moments
  • Couples
  • Equilibrium
• Assumptions in free body diagrams.
• Free body diagrams for major joints.
• Ability to apply biomechanics to clinical scenarios.