Biomechanical Concepts of Angular Kinetics in Human Motion

Analogues to Newton’s Laws of Motion

• Law 1
  • A rotating body will continue to turn about its axis with constant angular momentum unless an external couple is exerted upon it.
• Law 2
  • The rate of change of angular momentum of a body is proportional to the torque causing it, and the change takes place in the direction in which the torque acts.
• Law 3
  • For every torque that is exerted by one body on another, there is an equal and opposite torque exerted by the second body on the first.

Centric Force

• Definition:
  • A force whose line of action passes through an object's center of gravity (if there is no fixed axis) or through a fixed axis of rotation for an object.
• Effect:
  • Linear acceleration.
  • No angular motion.

Eccentric Force

• Definition:
  • A force whose line of action passes off-center (i.e., eccentric) to an object's center of gravity or its fixed axis of rotation.
• Effect:
  • Linear & Angular acceleration.

Biomechanical Application: Muscle Force Alone

• Example:
  • Contracting quadriceps for knee extension.
• Effect:
  • Linear and angular motion.
• Result:
  • Angular motion (knee extension) & linear motion (tibia anterior glide)

Torque (T)

• Definition:
  • The rotary (turning) effect of a force.
  • The angular equivalent of force.
  • Also known as the moment of force.

Moment Arm (d⊥)

• Definition:
  • The perpendicular distance from the line of action of the force to the axis of rotation (i.e., shortest possible distance between axis and line of action).

Torque Equation

• T = Fd
  • T represents torque.
  • F represents force.
  • d represents the perpendicular distance from the force’s line of action to the axis of rotation.

Torque and Balance

• Balanced weights create equal torques on either side of the fulcrum.

Torque Application

• If one child on a seesaw is heavier than the other, they can balance by adjusting their distance from the fulcrum.
• When not in balance, the system rotates in the direction of higher torque.

Torque and Muscle Force

• T = Fd
• Muscle force calculation:
  • Ratio = moment arm / force arm
  • Example:
    • 35 cm / 5 cm = 7
    • FA is 7 times smaller than MA.
    • MA is 7 times greater than RA.
    • If RA = 20 lbs, then 7 \times 20 = 140 lbs.
    • Muscle force needed to maintain position.

Force Couple

• Definition:
  • A pair of eccentric forces which are equal in magnitude, parallel, and opposite in direction.
• Effect:
  • Angular acceleration.
  • No linear acceleration.

Moment of Inertia (MI)

• Definition:
  • Resistance to change in the state of angular motion.
• Formula:
  • MI = Mass \times radius of rotation (rr)
  • Where rr = the distribution of the mass about a fixed axis.

Angular Momentum (AM)

• Formula:
  • MI \times angular velocity
• Factors affecting AM:
  • Moment of Inertia (MI)
  • Angular velocity
  • Distribution of mass
• Transfer of Angular Momentum
• Changing Angular Momentum

Conservation of Angular Momentum

• Angular momentum remains constant unless acted upon by some external torque.
• Distribution of mass affects angular momentum conservation.

Levers

• Definition:
  • A simple machine that allows you to gain a mechanical advantage in moving an object or applying a force to an object.
• Examples:
  • Commonly used tools and the human body.

Skeletal System as a Lever System

• Lever system consists of:
  • Lever (long bone).
  • Axis (fulcrum) (joints).
  • Force (muscle pulling on a tendon).
  • Resistance (what we are attempting to move).
• Torque:
  • A rotatory or turning force.
  • Torque (moment) = force x moment arm.
  • Moment arm: distance from applied force to the axis.
• Human movement is determined mostly by the torque produced, not just the force applied.

Lever Classification

• Relative locations of the applied force (F), the resistance (R), and the axis of rotation (A) determine lever classifications.
• First class: F - A - R
• Second class: A - R - F
• Third class: A - F - R
• Mnemonic: Keep in mind “A R F” for lever classification.

Mechanical Advantage

• FA > RA: Better mechanical advantage.
• RA > FA: Less mechanical advantage.

First Class Levers: F - A - R

• Advantage: can be either force or speed.
• Depends on relative sizes of F and R moment arms.
  • Higher speed and range of motion at R when the axis is close to F.
  • Smaller F is required as the axis is close to R.
• Anatomical Examples:
  • Triceps curl.
  • Neck extension.

Second Class Levers: A - R - F

• Advantage: always force at the expense of ROM or speed because F moment arm > R moment arm.
• Example: wheelbarrow.
• Anatomical Examples:
  • Rising on the toes.
  • Advantage: Lower applied force.
  • Disadvantage: Lower ROM or speed at R.

Third Class Levers: A - F - R

• Advantage: always speed and ROM at the expense of force because R moment arm > F moment arm.
• Example: swinging a baseball bat.
• Anatomical Examples:
  • Most body segments function as 3rd class levers.
  • Concentric action of quadriceps (knee extension) during seated leg curl.
  • Biceps curl.
  • Advantage: Provides a high ROM and speed.
  • Disadvantage: Requires high Fbiceps.

Implications of Third Class Levers for Human Movement

• Muscles usually insert close to the joint; resistances often carried on distal aspects of extremities.
• Result: muscles must generate high forces relative to resistances that must be moved.

Problem: Torque and Movement

• The body must create torque to move objects, while objects create an opposite torque that must be overcome.
• Weight of the ball creates torque:
  • resistance x moment arm
  • weight of ball x distance ball is from the axis
• Weight of the forearm creates torque:
  • Weight of arm x distance arm from the axis
• To lift the ball, torque created when the muscle contracts must be > torque created from gravity pulling on the ball.
• Example:
  • Resistance (dumbbell) = 5 lbs.
  • Moment Arm = 18 inches.
  • Torque = 90 units.
  • Weight of the arm = 2 lbs.
  • Moment arm = 10 inches.
  • Torque = 20 units.
  • To hold ball still, total torque needed = 110 units.
  • If Moment Arm = 2 inches, then Force = 55 lbs (T/d).
• Longer limbs create "mechanical disadvantage in force production".

Effect of Angle of Attachment on Force

• Muscle angles change throughout ROM and affect the ability to move objects.
• If a small angle, most of the force will produce a force pulling one bone of the joint into the other, which will tend to stabilize the joint (stabilizing component).
• Closer to a 90-degree angle, there will be a much larger rotary component of force.

Nautilus’s “cam”

• In the 1970s, Arthur Jones created resistance machines that incorporate the rotary and stabilizing components.
• Called the “cam”.
• Provides variable resistance.