Biomechanics and Rehabilitation Engineering

Biomechanics and Rehabilitation Engineering is a specialized field of biomedical engineering that applies the principles of classical mechanics to understand the structure and function of biological systems, particularly the human body. This discipline analyzes the forces, motion, and material properties of tissues, joints, and limbs to gain insights into both normal and pathological conditions. This fundamental understanding is then used to design, develop, and evaluate innovative technologies and therapeutic interventions—such as prosthetics, orthotics, assistive devices, and targeted exercise regimens—aimed at restoring physical function, improving mobility, and enhancing the quality of life for individuals with disabilities or injuries.

1. Foundational Principles of Biomechanics
   1. Mathematical Prerequisites
      1. Vector Mathematics
         1. Vector Representation in 2D and 3D
         2. Vector Addition and Subtraction
         3. Dot Product and Cross Product
         4. Unit Vectors and Vector Components
      2. Calculus Applications
         1. Derivatives for Velocity and Acceleration
         2. Integration for Displacement and Work
         3. Partial Derivatives
      3. Linear Algebra Basics
         1. Matrix Operations
         2. Coordinate Transformations
         3. Eigenvalues and Eigenvectors
      4. Statistics and Data Analysis
         1. Descriptive Statistics
         2. Hypothesis Testing
         3. Regression Analysis
         4. Error Analysis and Uncertainty
   2. Review of Classical Mechanics
      1. Statics
         1. Force Concepts
            1. Definition and Units of Force
            2. Types of Forces
            3. Force Vectors in 2D and 3D
            4. Vector Addition and Resolution
         2. Moment and Torque
            1. Definition of Moment
            2. Moment Arms
            3. Couples and Pure Moments
            4. Moment Vector Representation
         3. Equilibrium Analysis
            1. Conditions for Static Equilibrium
            2. Translational Equilibrium
            3. Rotational Equilibrium
            4. Equilibrium of Particles
            5. Equilibrium of Rigid Bodies
         4. Free Body Diagrams
            1. Construction Principles
            2. Identifying All Forces
            3. Identifying All Moments
            4. Support Reactions
            5. Internal Forces
      2. Dynamics
         1. Kinematics
            1. Linear Motion
               1. Position and Displacement
               2. Velocity
                  1. Average Velocity
                  2. Instantaneous Velocity
                  3. Velocity Vectors
               3. Acceleration
                  1. Average Acceleration
                  2. Instantaneous Acceleration
                  3. Acceleration Vectors
               4. Motion Equations for Constant Acceleration
            2. Angular Motion
               1. Angular Position and Displacement
               2. Angular Velocity
               3. Angular Acceleration
               4. Relationship Between Linear and Angular Motion
            3. Motion in Multiple Dimensions
               1. Projectile Motion
               2. Circular Motion
               3. General Curvilinear Motion
            4. Reference Frames
               1. Inertial Reference Frames
               2. Non-Inertial Reference Frames
               3. Coordinate System Transformations
         2. Kinetics
            1. Newton's Laws of Motion
               1. First Law of Motion
               2. Second Law of Motion
               3. Third Law of Motion
               4. Applications to Biomechanical Systems
            2. Work and Energy
               1. Definition of Work
               2. Kinetic Energy
               3. Potential Energy
               4. Work-Energy Theorem
               5. Conservation of Energy
               6. Power and Efficiency
            3. Impulse and Momentum
               1. Linear Impulse and Momentum
               2. Conservation of Linear Momentum
               3. Angular Impulse and Momentum
               4. Conservation of Angular Momentum
            4. Rigid Body Dynamics
               1. Moment of Inertia
               2. Parallel Axis Theorem
               3. Rotational Kinetic Energy
               4. Combined Translation and Rotation
   3. Biomechanical Material Properties
      1. Fundamental Concepts
         1. Stress
            1. Normal Stress
            2. Shear Stress
            3. Principal Stresses
            4. Stress Tensor
         2. Strain
            1. Normal Strain
            2. Shear Strain
            3. Principal Strains
            4. Strain Tensor
         3. Stress-Strain Relationships
            1. Linear Elastic Behavior
            2. Nonlinear Behavior
            3. Stress-Strain Curves
      2. Mechanical Properties
         1. Elastic Properties
            1. Young's Modulus
            2. Shear Modulus
            3. Bulk Modulus
            4. Poisson's Ratio
         2. Strength Properties
            1. Yield Strength
            2. Ultimate Tensile Strength
            3. Compressive Strength
            4. Shear Strength
            5. Fatigue Strength
         3. Failure Criteria
            1. Maximum Stress Theory
            2. Maximum Strain Theory
            3. Fracture Mechanics
      3. Time-Dependent Behavior
         1. Viscoelasticity
            1. Creep Behavior
            2. Stress Relaxation
            3. Hysteresis
            4. Viscoelastic Models
         2. Rate Effects
            1. Strain Rate Sensitivity
            2. Dynamic Loading Effects
      4. Biological Tissue Properties
         1. Anisotropy
            1. Directional Dependence
            2. Orthotropic Materials
            3. Transversely Isotropic Materials
         2. Inhomogeneity
            1. Spatial Variation of Properties
            2. Composite Nature of Tissues
         3. Nonlinearity
            1. Stress-Strain Nonlinearity
            2. Geometric Nonlinearity