# Dynamometry D. Gordon E. Robertson, PhD, FCSB Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, Canada 1Biomechanics Laboratory,

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Dynamometry D. Gordon E. Robertson, PhD, FCSB Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, Canada 1Biomechanics Laboratory, uOttawa

Dynamometry measurement of force, moment of force (torque) or power torque is a moment of force that acts through the longitudinal axis of an object (e.g., torque wrench, screw driver, engine) but is also used as another name for moment of force power is force times velocity (F.v) or moment of force times angular velocity (M  Examples of power dynamometers are the KinCom, Cybex, home electrical meter 2Biomechanics Laboratory, uOttawa

Force Transducers devices for changing force into analog or digital signals suitable for recording or monitoring typically require power supply and output device types: –spring driven (tensiometry, bathroom scale) –strain gauge (most common) –linear variable differential transformer (LVDT) –Hall-effect (in some AMTI force platforms) –piezoelectric (usually in force platforms) Examples: cable tensiometer, KinCom, Cybex, Biodex, fish scale, force platform 3Biomechanics Laboratory, uOttawa

Tensiometer measures tension (non-directional force) in a cable, wire, tendon, etc. Biomechanics Laboratory, uOttawa4

Strain Gauge Force Transducers uses the linear relationship between strain (deformation, compression, tension) in materials to the applied force (stress) materials are selected that have relatively large elastic regions if material reaches plastic region it is permanently deformed and needs replacement 5Biomechanics Laboratory, uOttawa

Stress-Strain Measurements Instron 5567 (Neurotrauma Impact Science Laboratory, uOttawa) accurately measures stress and strain for a wide variety of materials Biomechanics Laboratory, uOttawa6

Strain Gauges can be uniaxial, biaxial, multiaxial require DC power supply (battery) can be wired singly, in pairs, or quartets can measure force, torque, or bending moment Biomechanics Laboratory, uOttawa7

Strain Gauge Transducers 9Biomechanics Laboratory, uOttawa

Power Dynamometers potentiometer strain link lever arm 10Biomechanics Laboratory, uOttawa

Strain Gauge Lever CybexKinCom Biomechanics Laboratory, uOttawa11 use strain gauges to measure normal force moment is computed by multiplying by lever length

Bending Moment for Moment of Force 12Biomechanics Laboratory, uOttawa this knee brace was wired to measure bending moment it could therefore directly measure varus/valgus forces at the knee

Strain Gauge Force Transducers Advantages: –can measure static loads –inexpensive –can be built into wide variety of devices (pedals, oars, paddles, skates, seats, prostheses …) –portable Disadvantages: –need calibration –range is limited –easily damaged –temperature and pressure sensitive –crosstalk can affect signal (bending vs. tension, etc.) 13Biomechanics Laboratory, uOttawa

Force Platforms devices usually embedded in a laboratory walkway for measuring ground reaction forces Examples: Kistler, AMTI, Bertek Types: –strain gauge (AMTI, Bertek) –piezoelectric (Kistler) –Hall-effect (AMTI) Typically measure at least three components of ground reaction force (F x, F y, F z ) and can include centre of pressure (a x, a y ) and vertical (free) moment of force (M z ) 14Biomechanics Laboratory, uOttawa

Kistler Force Platforms standard in treadmill clear top portable 15Biomechanics Laboratory, uOttawa

Piezoelectric Force Platforms Advantages: –higher frequency response –more accurate –wide sensitivity range (1 N/V to 10 kN/V) Disadvantages: –electronics must be used to measure static forces, drift occurs during static measurements –expensive, cannot be custom-built –require 8 A/D channels 16Biomechanics Laboratory, uOttawa

AMTI Force Platforms small model standard model glass-top model 17Biomechanics Laboratory, uOttawa

Strain Gauge Force Platforms Advantages: –ability to measure static loads suitable for postural studies –inexpensive, can be custom-built –fewer A/D channels required (typically 6 vs. 8) Disadvantages: –typically fewer sensitivity settings –poorer frequency response –less accurate 18Biomechanics Laboratory, uOttawa

Equations for Computing Centres of Pressure centre of pressure locations are not measured directly Kistler: x = – (a[F x23 –F x14 ] – F x z) /F z y = (b[F y12 –F y34 ] – F y z) /F z AMTI:x = – (M y + F x z) /F z y = (M x – F x z) /F z Notice division by vertical force (F z ). This means centre of pressures can only be calculated when there is non-zero vertical force. Typically F z must be > 25 N. 19Biomechanics Laboratory, uOttawa

Impulse Force platforms can measure impulse during takeoffs and landings When the subject performs a jump from a static position, the takeoff velocity and displacement of the centre of gravity can be quantified Impulse = ≈ (  F )  t 20Biomechanics Laboratory, uOttawa

Takeoff Velocity To compute takeoff velocity divide the impulse by body mass For the vertical velocity, body weight must be subtracted v horizontal = Impulse horizontal / m v vertical = (Impulse vertical – W t ) / m where m is mass, W is body weight, and t is the duration of the impulse 21Biomechanics Laboratory, uOttawa

Centre of Gravity Displacement Displacement of the centre of gravity can also be quantified by double integrating the ground reaction forces. First divide the forces by mass then double integrate assuming the initial velocity is zero and the initial position is zero. Be sure to subtract body weight from vertical forces. Care must be taken to remove any “drift” from the force signals. 22Biomechanics Laboratory, uOttawa

Centre of Gravity Displacement s horizontal = s vertical = To compensate for drift (especially with Kistler force platforms) high-pass filtering is necessary. 23Biomechanics Laboratory, uOttawa

Squat Jump (BioProc2) Example of a vertical squat jump (starts in full squat) red is vertical force, cyan is AP force body weight line airborne phase 24Biomechanics Laboratory, uOttawa

Centre of Gravity (BioProc3) Squat depth was 1.39 cm Takeoff height was 79.6 cm Jump height was 28.3 cm 25Biomechanics Laboratory, uOttawa

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