400882 Introduction to Biomechanics - Angular Kinematics

Define and list several important features of the Centre of Rotation.

• Difficult to locate moving axis of rotation

• Needs to be identified so angles can be measured

• Position of center of rotation changes

• Joint motion is often accompanied by displacement of one bone with respect of the other

• Instant center of location of jt from X-rays is the only accurate way but it is impractical

What is meant by the 'Instant Centre' of a joint?

Is the center of rotation at a given joint angle or instant in time is known as the instant center

• It moves throughout the ROM of the joint

What are the three conventional units used to measure angular motion?

• Degree (°)

• Revolution (rev)

• Radian (rad)

1 rotation of a circle = 360o = 44/7 rads or 2 π radians

Which unit of angular motion is most appropriate for use in biomechanics?

Best to use radian (rad) when angular motion is involved (it is dimensionless)

Explain how to convert degrees to radians and radians to degrees.

• Degrees to radians (divide by 57.3°)

• Radians to degrees (multiply by 57.3°)

Define Relative Angle.

Angle at a joint formed between the longitudinal axes of adjacent body segments (e.g. Humerus and ulna)

Full extension of a joint is considered to represent what angle?

0°

Define Absolute Angle.

Are the angles measured between the body segment of interest and a fixed reference line → usually horizontal e.g. inclination of trunk relative to the ground

• Describes orientation of segment in space

• Must be measured in the same direction

List 4 tools that are commonly used for joint angle data collection in biomechanics.

• Goniometers

• Electrogoniometers - inexpensive difficult set up over fat/muscle

• Motion analysis system (2D & 3D)

• Accelerometers (dynamic use only)

Explain the convention known as the Right Hand Rule and when it is applied.

• The Right hand is placed in a loose fist with the thumb extended (hitching a ride fashion. Then if the fingers follow the direction of rotation the thumb points to the direction of angular vector

• Is regardless of position in space

Define angular DISTANCE, provide its symbol/s, unit of measurement and state whether it is a scalar or vector quantity.

• Angular distance- the sum of all angular changes that have occurred

• Symbol = Φ :phi

• Units = degrees (°) or radians (rad)

• It is a scalar quantity

(is similar concept to linear distance)

Define angular DISPLACEMENT, provide its symbol/s, unit of measurement and state whether it is a scalar or vector quantity.

• The smallest angle between initial and final positions

Δ θ = θ final - θ initial

• Symbol θ: theta

• Units = degrees (°) or radians (rad)

• It is a vector quantity

(is similar concept to linear displacement)

Explain the convention used to define the direction of angular motion.

• CW (clockwise) is -ve

• CCW (counter clockwise) is +ve

To remember → it is the opposite of what you expect

Define angular SPEED, provide its symbol/s, unit of measurement and state whether it is a scalar or vector quantity.

• Angular distance travelled per unit of time:

(σ = Φ / t) or angular distance/time

• Symbol = σ: sigma

• Units = degrees/s or rads/s

• It is a scalar quantity

Define angular VELOCITY, provide its symbol/s, unit of measurement and state whether it is a scalar or vector quantity.

• Angular velocity is the rate of change of angular position:

(ω = Δθ / Δt) or ang displacement/unit of time

• Instantanious ang vel: (represents the slope of a tangent)

ωav = ω1 + ω2 / 2

• Symbol = ω omega

• Units = degrees/s or rads/s

• It is a vector quantity

Define angular ACCELERATION, provide its symbol/s, unit of measurement and state whether it is a scalar or vector quantity.

• Rate of change of ang velocity with respect to time

(α = Δω / Δt) change in ang vel / change in time

• Symbol = α alpha

• Units = degrees/s² or rads/s²

• Is a vector quantity - direction must be determined

e.g. +ve ang acc may mean a decreased ang vel in a -ve direction or an increased ang vel in a +ve direction

How can the linear distance of a point on a segment be calculated when that segment is undergoing rotation?

M

Define TANGENTIAL VELOCITY, provide its symbol/s, unit of measurement and state whether it is a scalar or vector quantity.

Component of acceleration of a body in angular motion directed along a tangent to the path of motion, represents change in linear speed

at = v2 - v1 / t

Explain how a hammer thrower could increase the tangential velocity of the hammer on release.

To ↑ linear vel of hammer a thrower can either ↑ ang vel of upper extremity segments or ↑ length of extremity by extending at joint (or both to gain max range of throw)

Define RADIAL ACCELERATION, provide its symbol/s, unit of measurement and state whether it is a scalar or vector quantity.

Component of acceleration of a body in angular motion directed toward the center of curvature, represents change in direction

• ar = v2 / r

• symbol = ar

• unit =

Radial acceleration is also known as what and in which direction does it act?

Also known as centripetal acceleration

• Pointing toward center of rotation,

Define TANGENTIAL ACCELERATION, provide its symbol/s, unit of measurement and state whether it is a scalar or vector quantity.

Tangential acceleration is a component of linear acceleration (along with radial acceleration. aT is perpendicular to aR)

It is a vector quantity because it has direction as well as magnitude.

aT = r α

(α = ωf - ωi / t)

ω = θ / t