KIN 216 Angular Kinematics

linear motion includes

translation, change in position, move in the same direction

angular motion includes

rotation, change orientation, spin around the same fixed axis

most movement is

a combination of linear and angular movement

a combination of linear and angular movement

general motion

angular motion occurs when

a body moves along a circular path, revolving around a central line or point

It’s also referred to as ‘rotation’

Three types of angular movements or rotations

Yaw: rotating to the left or right

Pitch: rotating up and down

Roll: tilting to the left or right

unlike translation, angular motion

keeps a fixed point called axis of rotation

types of axis of rotation

external and internal

external axis of rotation

imaginary/actual line found outside of the body. system moves in a circular path around the axis

internal axis of rotation

imaginary line found inside the body. system moves in a circular path around the axis

common reference system for human body

Anatomical position

Body is erect

Facing forward

Feet parallel to each other

Toes forward

Arms hanging below shoulders

Fingers extended

Palms facing forward

what is anatomical position used for

Standard reference position for the body to describe how it moves

e.g. if we’re lying down top of body is still head

anatomical position is

the standard reference position for the body when we describe locations, positions, or movements of the body

cardinal planes

a plane that passes through the midpoint or centre of gravity of the body

Movements occurs in a plane, and axis of rotation is perpendicular to that plane

how many cardinal planes

3

the planes are useful for

locating anatomical structures. also describing limb movements.

How do movements occur? And how does rotation occur in relation to it

Movement occurs as rotations of the limbs.

Rotations occur around an axis and within specific planes

Yaw (AOR, POM, e.g.)

●Yaw (Rotation around a Vertical Axis)

•Axis of rotation: Vertical (superior-inferior)

•Plane of motion: Transverse plane

•Example: Turning your head left or right

Pitch (AOR, POM, e.g.)

●Pitch (Rotation around a Mediolateral Axis)

•Axis of rotation: Mediolateral (left-right)

•Plane of motion: Sagittal plane

•Example: Nodding your head up and down (like saying “yes”)

roll (AOR, POM, e.g.)

●Roll (Rotation around an Anteroposterior Axis)

•Axis of rotation: Anteroposterior (front-back)

•Plane of motion: Frontal plane

•Example: Tilting your head toward your shoulder (ear moving toward the same side shoulder)

direction of axis of rotation is

perpendicular to plane of motion

Examples of movement in sagittal, frontal, transverse

Sagittal: flexion, extension

Frontal: ad/abduction

Transverse: horizontal ab/adduction

how do you identify an angle on the body

1. Identify 3 joint centers of rotation (instant center)

2. Identify the orientation of the two longitudinal segments

3 joint centers and 2 longitudinal segments will give you 1 angle

relative angle

space between the longitudinal axes of adjacent segments

ie the angle at a joint

angle formed inside joint (relative)

internal angle

angle closing the spaces

e.g. (anterior forearm is closing)

external angle

angle formed outside of joint (relative)

absolute angle

Absolute angle is the space between a body segment and a fixed line of reference usually the global x or y axis.

It is used to find the orientation of a single body segment in relation to the env.

absolute angle can be between

longitudinal and x axis or longitudinal and y axis

Exam Q: which is better for measuring angles. relative or absolute

Doesn’t matter. All that matters is that the measurements are consistent

Which is better: degree or revolutions?

Better to use revolutions

what is a revolution (rev)? how many degree is 1 rev?

simple and natural measurement around a circle. 1 full turn

360 degree = 1 revolution

what is a radian (rad or unitless)

A ratio between the angle inside a circle and the length of the arc where the radius = length of the arc

It is a dimensionless, unit-less number that explores relationship between linear and angular variables

radians take ___ into account

pi (3.14)

radians is based on

when radius and arc length are equal (57.3 degrees)

1 rad = 57.3 degrees

1 revolution or 360 degrees in rad

2 pi rad

1 revolution is how many radians

2 pi rads

2 pi rad is how many degrees

360 degrees

1 radian is how many degrees

57.3

Which of the following is the standard unit of measure for angular variables when measuring human movement?

●degrees

a)Radians

●

b)Revolutions

●

c)All the above are acceptable units of measure

No standard default unit of measure for angular movement so all of the above are acceptable units of measure

●Degrees to revolutions?

●Revolutions to radians?

●Radians to degrees?

●Degrees to radians?

360° = 1 revolution

1 revolution = 2𝜋 rad

2𝜋 rad = 360°

57.3° = 1 rad

If a wheel rotates 7.25 revolutions, how many radians did it complete?

45.5 radians

what is used to measure angle

goniometer

basic goniometer (protractor)

Useful for measuring angles in pictures

Static analysis

electrogoniometer

taking measurements during movement, dynamic analysis

e.g. of electrogoniometer

strain gauge

goniometers are widely used in

physiotherapy to assess range of motion before and after intervention (tracking progress over time)

Do we know axis of rot for joints?

No, we don’t so we just estimate the axis of rot at a joint

instant center

precisely located center of rotation at a joint at a given instant in time

when analyzing human movements, how do we find the axis of rot?

we estimate the position of the axis of rotation

angular distance or displacement describes what?

describes the object's angular position or location in space

angular distance symbol

Φ = Phi

angular distance is?

what kind of quantity?

Possible UoM

the total amount of rotation

Scalar

UoM: degrees, revolutions, radians

angular displacement symbol

θ = theta

angular displacement is?

Type of quantity

UoM:

the change in angular position, change in orientation.

Vector quantity

UoM: degrees, revolutions, radians (rad)

what kind of quantity is angular displacement

vector

units of angular displacement

degree, rev, rad

angular speed is

symbol

quant type

UoM

change in angular distance over time

σ = Sigma

scalar

UoM: deg/s, rev/s, rad/s

Angular velocity is

symbol

quant type

UoM

change in angular displacement over time

ω = omega

Vector quant

UoM: deg/s, rev/s, rad/s

angular velocity is

change in angular displacement over time

the sign for angular displacement represents

direction

+ = counter clockwise

— = clockwise

the sign for angular velocity represents

direction

Describe dynamic motion

Acceleration. dynamic motions is characterized by change in angular velocity

what produces change in angular velocity

torques

Angular acceleration

angular acceleration symbol
Quant type

UoM

change in angular velocity over time

α = alpha

Vector

deg/s² , rev/s² , rad/s²

sign for angular acceleration represents

direction

• Sign reflects direction of torque and change in angular velocity

• To know if speeding up or down, we’d need to know the sign for angular velocity.

  • If ang vel and ang acc both same sign = speeding up

  • If ang vel and ang acc diff signs = slowing down

a clock's second hand angular acceleration after one revolution

0 degrees/s^2 (no displacement, no velocity, no acceleration)

angular kinematics tells us

how far you rotate, at what speed, and what state (dynamic or static)

+ sign for angular displacement and velocity means

- sign for angular displacement and velocity means

counter clockwise

clockwise

example of + direction

example of - direction

Positive sign means CCW movement.

• The degree numbers get larger

• From 200 to 270 degrees = +70 displacement

Negative sign means clockwise movement

• The degree numbers get smaller

• From 270 to 200 degrees = -70 displacement

●What do positive values tell us about direction of rotation?

●What do negative values tell us about direction of rotation?

●Pos values: rotating counterclockwise

●Those numbers as we move around circle get bigger and bigger.

●Neg values: rotating clockwise.

●Those numbers as we move around circle get smaller.

a bike spins at a rate of +2500 degrees/s^2. what does this mean

either turning counterclockwise and speeding up or turning clockwise and speeding down

object rotates at -3.5 rev/s^2. what does this mean

either rotating counterclockwise and slow down or turning clockwise and speeding up

An angular acceleration of −3.5 rev/s² indicates a clockwise torque and a negative change in angular velocity. Without knowing the angular velocity, the object could be rotating clockwise and speeding up or rotating counterclockwise and slowing down.

Linear Kinematics

Describing changes in position in space

Scalar quantities

Distance (l)

Speed (s)

Vector quantities

Displacement (d)

Velocity (v)

Acceleration (a

Angular kinematics

Describing rotations in space

Scalar quantities

Angular distance = Phi

Angular speed = sigma

Vector Quantities

Ang displacement = Theta

Ang Velocity = omega

Ang accerlation = alpha

key takeaways

...

Q6: what challenges exist when studying angular movements of the human body?

Axis of rot of a joint is not fixed. The longitudinal segment shifts position bc the axis migrates thus, it is hard to determine the axis of rot (the precisie origin of movement).

Instead we just estimate it because you can’t be certain of the “Instant center” of the origin of the movement

Q5: Which two Greek letters represent angular speed and velocity?

Angular speed = sigma

Angular velocity = omega

●What is the angular acceleration of the second hand on a clock after one complete revolution?

a)60°/s²

b)6°/s²

c)0°/s²

d)Need more information

No change in angular position.

No change in velocity-> no acceleration present

Answer: c)

So maybe scalar quantity is more appropriate or measuring over diff time frame to actually get smth meaningful

●If an object is rotating at -3.5 rev/s², what is happening?

a)The object is rotating clockwise AND speeding up

b)The object is rotating counterclockwise and slowing down

c)Neither A nor B is correct

d)Either A or B are correct

Answer; d), either a or b are correct because both scenarios are possible depending on the initial direction of rotation.

Bc in absence of context, sign can reflect change in velocity or direction of rotation of the torque.

Torque produces the change in angular velocity.

It matters which direction velocity and direction of torque is going in.

Sign in acceler reflects impact on system.

So without context, you can say either

But most likely, he will give you those details and you’ll know what is happening and what the sign in the acceleration value reflects.

1. The direction of the torque applied (which influences how the object’s rotation changes).

2. The direction of the change in angular velocity (which determines whether the object speeds up or slows down).

Since angular acceleration (α) is the rate of change of angular velocity (ω), its effect depends on the initial direction of ω:

If ω and α have the same sign, the object speeds up.

If ω and α have opposite signs, the object slows down.

This dual interpretation explains why both option A (clockwise + speeding up) and option B (counterclockwise + slowing down) can be correct!

The sign on the acceleration value just means the direction of change (if neg, clockwise; if pos, counterclockwise)