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 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, with 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: Both linear and angular acceleration (linear translation and spin).

Biomechanical Application: Muscle Force

• Example: Contraction of quadriceps for knee extension.
• Effect: Linear and angular motion, resulting in both glide and knee extension, as well as anterior shear translation of the tibia.

Torque (or Moment)

• An eccentric force produces a turning effect on an object which is called torque.
• Factors influencing the magnitude of a torque:
  • Magnitude of the eccentric force
  • Distance from the axis of rotation that the force is applied

Torque Defined

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

Torque is only for angular movements.

Moment Arm

• Moment arm (d_\perp) is the perpendicular distance from the line of action of the force to the axis of rotation.

Torque Equation

• T = Fd where:
  • T = Torque
  • F = Force
  • d = Perpendicular distance from the force’s line of action to the axis of rotation (moment arm)

Torque Example

• If a force of F = 10N is applied at a distance of d = 2m from the axis of rotation, then the torque is T = 10N \times 2m = 20Nm.

Balancing Torques

• Torques are balanced when equal torques are created on either side of a fulcrum.
• If one child on a see-saw is heavier than the other, they can balance by shortening the moment arm on the side with the larger force.

Muscle Force and Torque

• T = Fd
• To determine how much muscle force is needed, consider the ratio of the moment arm to the force arm.
• Example:
  • If the ratio of moment arm to force arm is 35 cm / 5 cm = 7, then the force required is seven times smaller than the moment arm, or the moment arm is seven times greater than the resistance arm.

Examples of Torque

• Examples include the triceps force, brachioradialis force, and biceps brachii force at the elbow joint.
• Mechanical advantage allows the generation of more force than the weight to achieve torque, especially in 3rd class levers.

Torque and Joint Angle

• The moment (Nm) changes with the joint angle (degrees).

Force Couple

• Definition: A pair of eccentric forces which are equal in magnitude, parallel, and opposite in direction.
• Effect: Angular acceleration with no linear acceleration.
• Examples: Stabilization at the shoulder joint, psoas and erectors muscles.

Moment of Inertia (MI)

• Definition: Resistance to change in the state of angular motion.
• MI = Mass \times radius of rotation^2

Angular Momentum

• Angular Momentum = MI \times angular velocity
• Three factors that affect angular momentum are mass, angular velocity, and the distribution of mass (radius of rotation).

Conservation of Angular Momentum

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

Levers

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

Skeletal System as a Lever System

• Lever System Components:
  • Lever (long bone)
  • Axis (fulcrum) (joints)
  • Force (muscle pulling on a tendon)
  • Resistance (what we are attempting to move)
• Torque (Moment) = Force x Moment Arm
• 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 (e.g., seesaw, neck extension)
  • Second Class: A-R-F (e.g., rising on toes)
  • Third Class: A-F-R (e.g., elbow flexion)
• Mnemonic: "ARF" to remember the order for lever classification.

Mechanical Advantage

• FA > RA: better mechanical advantage (less force needed).
• RA > FA: less mechanical advantage (more force needed).
• 2nd class levers move an object with the least amount of resistance
• 3rd class levers require more force/energy for a resistance that is less than that being applied.

First Class Levers (F-A-R)

• Advantage: Can be either force or speed, depending on the relative sizes of F and R moment arms.
• Examples: Triceps curl and Neck extension

Second Class Levers (A-R-F)

• Advantage: Always force at the expense of ROM or speed because the force moment arm is greater than the resistance moment arm.
• Examples: Rising on the toes.

Third Class Levers (A-F-R)

• Advantage: Always speed and ROM at the expense of force because the resistance moment arm is greater than the force moment arm.
• Most body segments function as 3rd class levers.
• Examples: Concentric action of quadriceps (knee extension) during seated leg curl, biceps curl.

Implications of Third Class Levers

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

Problem: Overcoming Torque

• The body must create torque to move objects, while objects create an opposite torque that must be overcome.
• Examples:
  • Weight of a ball creates torque: Resistance x Moment Arm = Weight of ball x distance ball is from axis
  • Weight of the forearm creates torque: Weight of arm x distance arm from axis

Effect of Angle of Attachment on Force

• Muscle angles change throughout ROM and affect ability to move objects.
• Small angle: Most of the force stabilizes the joint.
• Closer to 90 degrees: Larger rotary component of force.

Nautilus’s “Cam”

• Created by Arthur Jones in the 1970s, resistance machines incorporate rotary and stabilizing components using a "cam".
• The cam allows for variable resistance by adjusting the moment arm throughout the range of motion.