AngularMotion …...Angular Velocity Joint 2 Torque Angular Inertia Application Time of the Joint...

Angular Motion Maximum Hand, Foot, or Equipment Linear

Speed

Joint Linear Speeds 2

Radius of Rotation

Joint 2 Angular Velocity

Joint 2 Torque

Angular Inertia

Application Time of the Joint Torque

Mass Radius of Resistance

Muscle Force

Moment Arm


Radius of Rotation


Joint 1 Torque

Angular Inertia



Muscle Force

Moment Arm

Hand, Foot, or Equipment Linear Speed


Radius of Rotation


Joint 3 Torque

Angular Inertia



Muscle Force

Moment Arm


Radius of Rotation


Angular Inertia

Joint 4 Torque


Moment Arm

Muscle Force

Radius of Resistance Mass

Joint Linear Speeds5

Radius of Rotation


Angular Inertia

Joint 5 Torque


Moment Arm

Muscle Force


External Forces

Friction Force

Vertical Ground Reaction Force

Coefficient of Friction

Cleat Force

Biomechanical Model: Angular Mo3on Maximum Hand, Foot, or Equipment Linear Speed

Sum of Joint Linear Speeds Principle

Slide 1 of 6

Slide 2 of 6

Slide 3 of 6

Slide 4 of 6

Slide 5 of 6

Slide 6 of 6


Radius of Rotation


Joint 1 Torque

Angular Inertia



Muscle Force

Moment Arm

Biomechanical Model: Angular Mo3on Maximum Hand, Foot, or Equipment Linear Speed (Slide 1 of 6)



Radius of Rotation


Joint 2 Torque

Angular Inertia



Muscle Force

Moment Arm



Radius of Rotation


Joint 3 Torque

Angular Inertia



Muscle Force

Moment Arm


Radius of Rotation


Angular Inertia

Joint 4 Torque


Moment Arm

Muscle Force




Radius of Rotation


Angular Inertia

Joint 5 Torque


Moment Arm

Muscle Force


Biomechanical Model: Angular Mo3on Maximum Hand, Foot, or Equipment Linear Speed (Slide 5 of 6) Linear Speed –

Angular Velocity Principle

Angular Impulse – Momentum Principle

Joint Torque Principle

Angular Inertia Principle

External Forces

Friction Force



Muscle Forces

Cleat Force


External Forces Principle

Friction Force Principle

Action-‐Reaction Principle

=

� Sum of Joint Linear Speeds Principle

Biomechanical Model Angular Mo3on (Slide 1 of 6)

Joint Linear

Speeds 5


Joint Linear

Speeds 1

Joint Linear

Speeds 3

Joint Linear

Speeds 2

Joint Linear

Speeds 4

rtωr=s

� Linear Speed – Angular Velocity Principle

Biomechanical Analysis: Angular Mo3on Max. Hand, Foot, or Equipment Linear Speed

Joint Linear Speed

Radius of Rotation

Joint Angular Velocity

ITtω =

� Angular Impulse – Momentum Principle


Angular Inertia


Joint Torque


⊥= dFT MJ

�  Joint Torque Principle


Joint Torque

Moment Arm

Muscle Force

2rsmrI =

� Angular Inertia Principle


Angular Inertia


� Action – Reaction Principle


Muscle Force

External Forces

� External Forces Principle


External Forces

Friction Force


Cleat Force

VGRFR µFF =

� Friction Force Principle


Friction Force



Biomechanical Model: Angular Mo3on Maximum Linear Hand Speed for a Baseball Throw

Joint Linear Speed of the RT Shoulder & All Joints

Lateral to the Longitudinal Axis of the RT Upper Arm

Radius of Rotation


RT Shoulder IR Torque

Angular Inertia



Muscle Force

Moment Arm

Joint Linear Speed of the RT Wrist & All Joints

Distal to the RT Wrist

Radius of Rotation


RT Wrist FL Torque

Angular Inertia



Muscle Force

Moment Arm


Joint Linear Speed of the SH Girdle & All Joints

Lateral to the Spine

Radius of Rotation


SH Girdle LR Torque

Angular Inertia



Muscle Force

Moment Arm

Joint Linear Speed of the LT Hip & All Joints Superior to the LT Hip

Radius of Rotation


Angular Inertia

LT Hip FL Torque


Moment Arm

Muscle Force


Joint Linear Speed of the LT Hip & All Joints

Medial to the Longitudinal Axis of LT Upper Leg

Radius of Rotation


Angular Inertia

LT Hip IR Torque


Moment Arm

Muscle Force


External Forces

Friction Force



Cleat Force

The increase in joint linear speeds distal to the _________

Biomechanical Model: Angular Mo3on Maximum Linear Hand Speed for a Baseball Throw

Joint Linear Speed of the RT Shoulder & All Joints

Lateral to the Longitudinal Axis of the RT Upper Arm

Radius of Rotation


RT Shoulder IR Torque

Angular Inertia



Muscle Force

Moment Arm

Joint Linear Speed of the RT Wrist & All Joints

Distal to the RT Wrist

Radius of Rotation


RT Wrist FL Torque

Angular Inertia



Muscle Force

Moment Arm




Radius of Rotation


SH Girdle LR Torque

Angular Inertia



Muscle Force

Moment Arm

Joint Linear Speed of the LT Hip & All Joints Superior to the LT Hip

Radius of Rotation


Angular Inertia

LT Hip FL Torque


Moment Arm

Muscle Force




Radius of Rotation


Angular Inertia

LT Hip IR Torque


Moment Arm

Muscle Force


External Forces

Friction Force



Cleat Force

____ to push against

Allows ____ to be exerted

The coordinated increase in joint linear speeds distal to the _________


Biomechanical Model: Angular Mo3on Maximum Linear Clubhead Speed for a Golf Swing

Joint Linear Speed of the LT Forearm & All Joints Lateral to the Longitudinal

Axis of the LT Forearm

Radius of Rotation


LT Forearm SUP Torque

Angular Inertia



Muscle Force

Moment Arm

Joint Linear Speed of the RT Forearm & All Joints Lateral to the Longitudinal

Axis of the RT Forearm

Radius of Rotation


RT Forearm PRO Torque

Angular Inertia



Muscle Force

Moment Arm


Joint Linear Speed of the LT Shoulder & All Joints

Distal to the Anterior-Posterior Axis of the LT Shoulder

Radius of Rotation


LT Shoulder ABD Torque

Angular Inertia



Muscle Force

Moment Arm



Radius of Rotation


Angular Inertia

SH Girdle LR Torque


Moment Arm

Muscle Force




Radius of Rotation


Angular Inertia

LT Hip IR Torque


Moment Arm

Muscle Force


External Forces

Friction Force



Cleat Force





Biomechanical Model: Angular Mo3on Maximum Linear Foot Speed for a Soccer Goal Kick

Radius of Rotation


LT Hip IR Torque

Angular Inertia



Muscle Force

Moment Arm


Radius of Rotation


RT Hip FL Torque

Angular Inertia



Muscle Force

Moment Arm

Radius of Rotation


Angular Inertia

RT Knee EXT Torque


Moment Arm

Muscle Force


External Forces

Friction Force



Cleat Force











Locomotion – Minimum Movement Time

Fundamental Biomechanical Principles

Sum of Joint Linear Speeds Principle � A body’s total linear speed is the result of an optimal combination of individual joint linear speeds.

� The identification of this optimal combination of joint linear speeds is a skill that all individuals interested in understanding human movement must develop

Linear Speed – Angular Velocity Principle � Radius of Rotation (rrt)

�  The straight-‐line distance from a joint/body axis of rotation to a point on a body segment

� Unit of measurement �  meters (m)

�  Linear Speed (s) �  This is the straight-‐line speed of a point on a body segment (i.e., the hand, the foot, the torso, the head, etc.)

� Unit of measurement �  meters per second (m/s)

Linear Speed – Angular Velocity Principle � Angle (θ)

�  An angle is formed by the intersection of two lines � Unit of Measurement

�  Radians (rad)

� Angular Velocity (ω) � How fast does an angle’s value (Δθ) change �  The speed of joint/body rotation � Unit of measurement

�  Radians per second (rad/s)

Linear Speed – Angular Velocity Principle � Real-‐World Application

�  An increase in linear speed (s) of a point on a rotating body segment is caused by an increase in the body segment’s angular velocity (ω) and/or an increase the radius of rotation (rrt).

rtωrs =

Δθ Radius of rotation (r

RT)

Axis of rotation

Time 2 location Time 1 location s21

s11

s22

s21

180 degrees π radians

Conversion Factor 180 degrees = π radians

90 degrees radians 2π

135 degrees radians 43π

Example: radians2π

180(ππ(90)degrees90 ==

Angular Impulse-‐Momentum Principle � Newton’s 2nd Law of Motion (Angular)

�  If a net torque is exerted on an object, the object will angularly accelerate in the direction of the net torque, and its angular acceleration will be proportional to the net torque and inversely proportional to its angular inertia

�  The equation for Newton’s 2nd Law of Motion (Angular) is

IαΣT =

Angular Impulse-‐Momentum Principle � The Angular Impulse-‐Momentum Principle is derived from Newton’s 2nd Law of Motion (Angular)

IαΣT =

⎟⎠

⎞⎜⎝

⎛=tΔωIΣT

( )ΔωIΣTt =

Angular Impulse-‐Momentum Principle � ΣTt is known as angular impulse

� Unit of measurement �  Newton-‐meter-‐sec (N-‐m-‐s)

�  I(Δω) is known as the change in angular momentum � Unit of measurement

�  kilogram meter squared per second (kg-‐m2/s)

Angular Impulse-‐Momentum Principle � Real-‐World Application

�  An increase in angular velocity of a body segment is caused by an increase in the joint torque, and/or an increase in the application time of the joint torque and/or a decrease in the body segment’s angular inertia.

IΣTtΔω =

Angular Iner3a Principle � The property of an object to resist changes in its angular momentum �  The smaller the body segment’s angular inertia; the easier it is for the body segment to rotate quickly

�  Factors Influencing Angular Inertia � mass (m) �  radius of resistance (rrs)

�  the linear distance from the body segment’s axis of rotation to the center of mass of the body segment

Angular Iner3a Principle � Real-‐World Application

�  A decrease in a body segment’s angular inertia is caused by a decrease in the body segment’s mass (m) and/or a decrease in the radius of resistance.

� Unit of measurement �  kilogram meter squared (kg-‐m2)

2rsmrI =

Angular Iner3a Principle � An object may have more than one moment of inertia

�  an object may rotate about more than one axis of rotation

� Body movements may change the distribution of mass about a specific axis of rotation, thus changing the angular inertia about that axis �  A human's angular inertia about any axis is variable �  Examples

�  Figure Skating �  Diving

Joint Torque Principle � What is a Torque?

�  It is the effect of a muscle force to cause a joint rotation � Muscle Force

� Muscle forces are caused by muscle contractions �  These contractions pull on bones

� Muscle forces are known as eccentric forces �  An eccentric force is a force that does not pass through the joint connecting two body segments

Joint Torque Principle � Torque is directly related to the size of the muscle force that creates it �  The larger the muscle force, the larger the torque

� Torque is also influenced by �  The distance from the line of action of the muscle force relative to the axis of rotation of the joint

�  This distance is called the moment arm (d⊥) �  See Figure 5.6

Joint Torque Principle � Real-‐World Application

�  An increase in joint torque is caused by an increase in a muscle force pulling on the bones that are held together at the joint and/or an increase in the moment arm.

�  The line of pull of the muscle force is determined by connecting a line between the attachments (origin and insertion) of the muscle into bones held together at the joint.

⊥= dFT MJ

d⊥

axis of rotation

muscle force

moment arm

Ac3on – Reac3on Principle � This principle is derived from Newton’s 3rd Law of Motion (Linear) �  For every action there is an equal and opposite reaction

� This principle may be interpreted in several different ways. �  For this Biomechanical Model, the principle is interpreted as follows: �  for any muscle to create its greatest amount of muscle force, an oppositely directed external force of equal magnitude must exist.

External Forces Principle � This principle may be interpreted in several different ways. �  For this Biomechanical Model, the principle is interpreted as follows: �  Whenever the body is in contact with the ground, there are two ground reaction forces (one vertical and one horizontal) that can oppose the muscle forces create inside the body.

Fric3on Force Principle �  Friction Force

�  The horizontal ground reaction force between your foot and the ground

VGRFR µFF =

Fric3on Force Principle � Real-‐World Application

�  An increase in friction force is caused by �  an increase in the coefficient of friction (µ) and/or �  an increase in the vertical ground reaction force

�  The coefficient of friction is a number that represents the material properties of a surface that influence friction force: �  hardness/softness �  smoothness/roughness

�  Friction force does not increase if the contact area increases!

AngularMotion …...Angular Velocity Joint 2 Torque Angular Inertia Application Time of the Joint...

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Transcript of AngularMotion …...Angular Velocity Joint 2 Torque Angular Inertia Application Time of the Joint...