1. Fundamentals of Biomechanics

Biomechanics applies mechanical principles to biological systems to understand how living organisms move and interact with their environments.

Biomechanics: The study of the structure, function, and motion of the mechanical aspects of biological systems, using the methods of mechanics.

Core Concepts

  • Kinematics: Description of motion without considering forces
  • Kinetics: Study of forces that cause or result from motion
  • Statics: Analysis of systems in equilibrium (no acceleration)
  • Dynamics: Analysis of systems in motion
  • Mechanics of materials: Study of how materials deform under loads

Coordinate Systems in Biomechanics

Different coordinate systems are used to describe body movements:

  • Global (laboratory) coordinate system: Fixed reference frame
  • Local (segment) coordinate system: Attached to body segments
  • Anatomical coordinate system: Based on anatomical planes (sagittal, frontal, transverse)

2. Statics in Biomechanics

Statics involves analyzing systems in equilibrium where the sum of forces and moments is zero.

∑F = 0 (Sum of forces equals zero)
∑M = 0 (Sum of moments equals zero)

Free Body Diagrams (FBD)

Essential tool for solving biomechanics problems:

  1. Isolate the body or segment of interest
  2. Identify all external forces and moments acting on the body
  3. Draw the body with all forces represented as vectors
  4. Establish coordinate system
  5. Apply equilibrium equations

Example: Elbow Joint Force

Calculate the joint reaction force at the elbow when holding a 10kg weight in hand. Assume the forearm weight is 2kg, distance from elbow to weight is 30cm, and distance from elbow to forearm center of mass is 15cm.

Solution approach: Create FBD of forearm, apply ∑M = 0 about elbow to find muscle force, then apply ∑F = 0 to find joint reaction force.

3. Dynamics: Kinematics and Kinetics

Kinematic Variables

Variable Description Units
Position Location in space relative to reference point m
Displacement Change in position (vector) m
Velocity Rate of change of position m/s
Acceleration Rate of change of velocity m/s²
Angular position Orientation angle rad
Angular velocity Rate of change of angular position rad/s

Newton's Laws Applied to Biomechanics

  1. First Law (Inertia): A body remains at rest or in uniform motion unless acted upon by a net external force.
  2. Second Law (F=ma): The acceleration of a body is proportional to the net force acting on it and inversely proportional to its mass.
  3. Third Law (Action-Reaction): For every action force, there is an equal and opposite reaction force.

4. Mechanics of Materials in Biological Tissues

Stress and Strain

Stress (σ) = Force / Area (Pa or N/m²)
Strain (ε) = Change in length / Original length (unitless)

Material Properties

Property Description Formula
Young's Modulus (E) Stiffness in tension/compression E = σ/ε
Shear Modulus (G) Stiffness in shear G = τ/γ
Poisson's Ratio (ν) Ratio of transverse to axial strain ν = -εtransverse/εaxial
Ultimate Strength Maximum stress before failure -
Yield Strength Stress at which permanent deformation begins -

Viscoelasticity

Biological tissues exhibit time-dependent mechanical behavior:

  • Creep: Continued deformation under constant load
  • Stress relaxation: Decrease in stress under constant deformation
  • Hysteresis: Energy loss during loading-unloading cycles