13_KINE426_Linear_Kinematics1

1 Andrew Nordin, PhD Assistant Professor, Division of Kinesiology KINE 426 Exercise Biomechanics Linear Kinematics – Introduction Chapter 8 Biomechanical analyses – Kinematics • Observable movement outcomes (quantitative or qualitative) • Characteristics of motion in time & space • Without consideration for forces • Position, velocity, acceleration – Motion capture/videography – Accelerometer – Kinetics • Cause of movement • Forces (cannot be seen) – Force platform – Electromyography (EMG) • Electrical muscle activity – Electrodes attached to skin – Needles embedded in muscle

2 Translation with Rotation Linear vs. Angular Motion • Linear motion – Translation • Movement on straight or curved path – Rectilinear – Curvilinear • All points move through same distance in same amount of time • Center of mass (COM) – Theoretical point where mass is concentrated – Point of gravity application • Angular motion – Motion around a fixed point • Axis of rotation • Radius Rectilinear translation Curvilinear translation r Δθ axis Kinematics • Motion capture/videography – Digitization • Active markers (LED) • Passive markers (retro-reflective)

4 Reference Systems • Global reference system (external) – Relative to external point • Local reference system (internal) – Joint/segment specific • X: mediolateral • Y: anteroposterior • Z: longitudinal Reference Systems • Length – Resultant (Pythagorean Theorem) – 2D – 3D !"#$% ℎ = ! ! − ! ! ! + ( ! ! − ! ! ) ! y x (0,0) (x,0) (0,y) (x,y) ! = ! ! + ! ! z y x (0,0) (x,y,z) ! = ! ! + ! ! + ! ! !"#$% ℎ = ( ! ! − ! ! ) ! + ( ! ! − ! ! ) ! + ( ! ! − ! ! ) !

5 Units of Measurement • Système International (SI) – Metric system • Dimension/quantity • Mass, length, time, temperature • Kilogram, meter , second , degrees (Kelvin → Celsius + 273K) Kinematic Data • Movement occurs over time (position vs. time → time series) • Digitization of frames/pictures • Sampling rate (frame rate) – fs = 1/Δ t → Hz = 1/s 1 2 3 4 5 Δ t Δ t Δ t Δ t

7 Kinematics Kinematics Linear Angular Scalar Vector Distance Speed Acceleration Displacement Velocity !"##$ = !"#$%&'() !"#$% !"#$% !"# = !"#$%&'()*)+, !"#$% or ! ! ! ! ! ! ! − ! ! !""#$#%!&'( ! = !"#$%&'() !"#$% ! ! − ! ! ! ! − ! ! • Spatial & temporal components of motion • Ignores forces causing motion Magnitude Magnitude & direction or