KNES 361 L1

Biomechanics Overview

• Definition of Biomechanics

  • A bridge between biology and mechanics.

  • Bio: Refers to life, humans, tissues, and movement.

  • Mechanics: The study of forces and motion.

  • In essence: Biomechanics examines how forces create motion in living organisms and how motion affects the body.

• Forces in Biomechanics

  • Internal Forces:

  • Muscle forces

  • Tendon tension

  • Joint contact forces

  • External Forces:

  • Gravity

  • Ground reaction forces

  • Push or pull from other objects

  • Most injuries and performance outcomes stem from how these forces load tissues over time.

Approaches in Biomechanics

• Biomechanics is divided into two main sub-approaches:

  • Statics:

  • Study of systems in equilibrium (no acceleration).

  • Situations where objects are either at rest or moving at constant velocity.

  • Dynamics:

  • Refers to systems that experience acceleration (speeding up, slowing down, or changing direction).

Sub-branches of Dynamics

• Kinematics:

  • Study of motion without regard to the forces involved.

  • Focuses on the appearance of motion:

  • Position

  • Velocity

  • Acceleration

  • Does not focus on the forces that cause motion.

• Kinetics:

  • Study of the forces causing the motion.

  • Looks at:

  • Work

  • Power

  • Forces associated with movement

Planes and Axes of Motion

• Definition: Imaginary flat surfaces that slice through the body to describe movement.

• Axis of Motion: A point or line around which motion happens (perpendicular to the plane).

  • Movement occurs in a plane and around an axis, which are always perpendicular.

Primary Planes of Motion

1. Sagittal Plane (Anteroposterior Plane):

   • Divides the body into right and left halves.

   • Movements:

     • Bending forward/backward (e.g., sit-ups).

2. Frontal Plane (Coronal Plane):

   • Divides the body into front and back halves.

   • Movements:

     • Lateral or side-to-side movements (e.g., jumping jacks).

3. Transverse Plane (Horizontal Plane):

   • Divides the body into upper and lower parts.

   • Movements:

     • Twisting motions (e.g., torso twists).

Axes of Rotation

• Sagittal Axis:

  • Runs from front to back.

  • Perpendicular to the frontal plane.

  • E.g., movements occurring in the frontal plane (e.g., arm or leg moving sideways).

• Frontal Axis:

  • Runs side to side.

  • Perpendicular to the sagittal plane.

  • E.g., flexion and extension of the arm (e.g., bending forward or backward).

• Vertical Axis (Longitudinal Axis):

  • Runs vertically from top of the head to the feet.

  • Perpendicular to the transverse plane.

  • E.g., twisting motion.

Vectors and Units of Measurement

• Types of Quantities:

  • Scalar Quantities:

  • Has magnitude only (e.g., mass, time, distance, speed).

  • Example: "5 meters" or "10 seconds".

  • Vector Quantities:

  • Has both magnitude and direction (e.g., position, velocity, acceleration, force).

  • Example: "10 meters south" vs. "10 meters".

Vector Addition Scenarios

1. Collinear Vectors in Same Direction:

   • Add magnitudes directly.

   • Example: Walking 4 feet + 3 feet in the same direction = 7 feet.

2. Collinear Vectors in Opposite Direction:

   • Subtract magnitudes.

   • Example: Walking 4 feet forward and 3 feet backward = 1 foot.

3. Perpendicular Vectors:

   • Use the Pythagorean Theorem.

   • Formula: $c^2 = a^2 + b^2$, where "c" is the hypotenuse, "a" is one side, and "b" is the other side.

   • Example: If one vector is 4 feet and the other is 3 feet, hypotenuse = $ext{sqrt}(4^2 + 3^2) = 5$ feet.

4. Non-Collinear, Non-Perpendicular Vectors:

   • Resolve each vector into perpendicular components (horizontal and vertical).

   • Use trigonometric functions (sine, cosine) to find components given an angle.

   • Example formula for horizontal component:
     $ext{Horizontal Component} = ext{Magnitude} imes ext{cos}( heta)$

   • Example formula for vertical component:
     $ext{Vertical Component} = ext{Magnitude} imes ext{sin}( heta)$

Trigonometric Refresher

• SOH CAH TOA:

  • Sine: $ext{sin}( heta) = rac{ ext{Opposite}}{ ext{Hypotenuse}}$

  • Cosine: $ext{cos}( heta) = rac{ ext{Adjacent}}{ ext{Hypotenuse}}$

  • Tangent: $ext{tan}( heta) = rac{ ext{Opposite}}{ ext{Adjacent}}$

Example Problem: Resolving a Force

• Force Vector: A force of 100 Newtons at 60 degrees from horizontal.

  • Horizontal component (Adjacent)= $100 imes ext{cos}(60°) = 100 imes 0.5 = 50 ext{ N}$

  • Vertical component (Opposite)= $100 imes ext{sin}(60°) = 100 imes 0.866 = 86.6 ext{ N}$

Unit Conversion

• Common Units in Mechanics:

  • Mass: kilograms (kg)

  • Length: meters (m)

  • Time: seconds (s)

• Conversion Factors:

  • Example: 1 foot = 0.3048 meters

  • Example: 1 mile = 1609 meters; 1 hour = 3600 seconds

Example Problem: Converting Velocity

• Velocity of 100 miles per hour to meters per second:

  • Setup:
    $ext{Velocity} = rac{100 ext{ miles}}{1 ext{ hour}}$

  • Conversion:
    $ext{Velocity} = 100 imes rac{1609 ext{ meters}}{1 ext{ mile}} imes rac{1 ext{ hour}}{3600 ext{ seconds}}$

  • Simplified to $44.72 ext{ m/s}$

Conclusion

• Summary of topics covered:

  • Importance and definition of biomechanics

  • Understanding of planes and axes of motion

  • Comprehension of vectors in the context of biomechanics

  • Unit conversion principles and methods to apply them.