Week 8 Angular Kinematics

What happens in angular motion?

• All points in an object or system move in a circle about a single axis of rotation. All points move through the same angle in the same time.

What is angular kinematics?

• The kinematics of particles, objects or systems undergoing angular motion (motion irrespective of cause)

  • Similar to linear kinematics

    • Angular: distance, displacement, speed, velocity, acceleration

What happens in angular kinematics?

• Most volitional is performed through rotation of the body segments

• The body is analyzed as a collection of rigid rotating segments linked (hinged) at the joint centres

What are the general questions that can be asked in angular kinematics?

• What is the shoulder range of motion during pitching? How fast is the pitcher adducting their arm at the instant of release?

• Does running require a greater range of ankle flexion / extension than walking? (No, Walking still does)

• How is range of motion related to performance or injury?

• Are sex - based differences in peak knee abduction during drop jump landing indicative of ACL injury risk?

How does angular kinematics differ for human joints?

• situation is not so simple

  • Most joints exhibit gliding / sliding during rotation

  • The axis of rotation moves during joint motion

  • Instant centre of rotation

    • The axis of rotation at a given instant

What are radians in angular displacement?

• a radian is the circle formed from an arc length on a circle equal to the radius of the circle

  • Where s = arc length [m]

  • r = radius [m]

  • theta = s/r [rad]

• The number of radians in a semicircle = pi

  • Pi (3.14) rad = 180 deg (1rad = 57.3deg)

What are positive and negative angles in angular kinematics?

• By convention (as with moments of force)

  • Positive angles - counterclockwise rotation

  • Negative - clockwise rotation

• Angular displacements are not vectors, because they do not add according to the parallelogram law; they do not posses the commutative property (commutative, meaning they can be added in any order)

What are absolute (segment) angles?

• Angular orientation of a segment with respect to a fixed line of reference.

How do you compute angular displacement?

• Done by subtracting angular positions.

• Theta = Final - initial

What should be considered when computing angular displacement?

• When computing kinematic variables, you can use whatever convention you like (or are asked to report)

  • Degrees, radians, revolutions (and counter parts for velocity and acceleration)

• If an object travels beyond 1 full revolution, those rotations must be included in the displacement

How do you measure relative angles?

• Angle between 2 line segments

  • Often the 2 line segments are body segments

  • Compute relative angle by subtraction of absolute angular positions

  • Angle of segments = Segment 2 - segment 1

What are joint angles measured like in angular kinematics?

• Joint angles are relative angles between adjacent segments

  • Rotation of proximal segment relative to distal?

  • Rotation of distal segment relative to proximal?

What can be said about constant angular acceleration?

Whenever a is constant the equations for constant linear acceleration can be modified to apply to angular kinematics.

• Use rads, deg or rev, but do not interchange within a solution

How does average angular velocity and acceleration change?

Angular velocity: Equation can be used to approximate instantaneous angular velocity if t is very small.

Angular acceleration: Equation can be used to approximate instantaneous angular acceleration if t is very small.