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Dynamometry. D. Gordon E. Robertson, PhD, FCSB Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, Canada. Dynamometry. measurement of force, moment of force (torque) or power

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D. Gordon E. Robertson, PhD, FCSB

Biomechanics Laboratory,

School of Human Kinetics,

University of Ottawa, Ottawa, Canada

Biomechanics Laboratory, uOttawa

  • 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 (Mw)
  • Examples of power dynamometers are the KinCom, Cybex, home electrical meter

Biomechanics Laboratory, uOttawa

force transducers
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

Biomechanics Laboratory, uOttawa

  • measures tension (non-directional force) in a cable, wire, tendon, etc.

Biomechanics Laboratory, uOttawa

strain gauge force transducers
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


deformed and needs


Biomechanics Laboratory, uOttawa

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

Biomechanics Laboratory, uOttawa

strain gauges
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, uOttawa

strain link
Strain Link

Biomechanics Laboratory, uOttawa

strain gauge transducers
Strain Gauge Transducers

Biomechanics Laboratory, uOttawa

power dynamometers
Power Dynamometers


lever arm

strain link

Biomechanics Laboratory, uOttawa

strain gauge lever
Strain Gauge Lever

Cybex KinCom

  • use strain gauges to measure normal force
  • moment is computed by multiplying by lever length

Biomechanics Laboratory, uOttawa

bending moment for moment of force
Bending Moment for Moment of Force

this knee brace was wired to measure bending moment

it could therefore directly measure varus/valgus forces at the knee

Biomechanics Laboratory, uOttawa

strain gauge force transducers1
Strain Gauge Force Transducers


  • can measure static loads
  • inexpensive
  • can be built into wide variety of devices (pedals, oars, paddles, skates, seats, prostheses …)
  • portable


  • need calibration
  • range is limited
  • easily damaged
  • temperature and pressure sensitive
  • crosstalk can affect signal (bending vs. tension, etc.)

Biomechanics Laboratory, uOttawa

force platforms
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 (Fx, Fy, Fz) and can include centre of pressure (ax, ay) and vertical (free) moment of force (Mz)

Biomechanics Laboratory, uOttawa

kistler force platforms
Kistler Force Platforms



clear top

in treadmill

Biomechanics Laboratory, uOttawa

piezoelectric force platforms
Piezoelectric Force Platforms


  • higher frequency response
  • more accurate
  • wide sensitivity range (1 N/V to 10 kN/V)


  • electronics must be used to measure static forces, drift occurs during static measurements
  • expensive, cannot be custom-built
  • require 8 A/D channels

Biomechanics Laboratory, uOttawa

amti force platforms
AMTI Force Platforms

small model

standard model

glass-top model

Biomechanics Laboratory, uOttawa

strain gauge force platforms
Strain Gauge Force Platforms


  • ability to measure static loads suitable for postural studies
  • inexpensive, can be custom-built
  • fewer A/D channels required (typically 6 vs. 8)


  • typically fewer sensitivity settings
  • poorer frequency response
  • less accurate

Biomechanics Laboratory, uOttawa

equations for computing centres of pressure
Equations for Computing Centres of Pressure
  • centre of pressure locations are not measured directly
  • Kistler:x = – (a[Fx23–Fx14] – Fxz) /Fz

y = (b[Fy12–Fy34] – Fyz) /Fz

  • AMTI:x = – (My + Fx z) /Fz

y = (Mx – Fx z)/Fz

  • Notice division by vertical force (Fz). This means centre of pressures can only be calculated when there is non-zero vertical force. Typically Fz must be > 25 N.

Biomechanics Laboratory, uOttawa

  • 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 =≈ (SF ) Dt

Biomechanics Laboratory, uOttawa

takeoff velocity
Takeoff Velocity
  • To compute takeoff velocity divide the impulse by body mass
  • For the vertical velocity, body weight must be subtracted

vhorizontal = Impulsehorizontal / m

vvertical = (Impulsevertical – W t ) /m

  • where m is mass, W is body weight, and t is the duration of the impulse

Biomechanics Laboratory, uOttawa

centre of gravity displacement
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.

Biomechanics Laboratory, uOttawa

centre of gravity displacement1
Centre of Gravity Displacement
  • shorizontal =
  • svertical =
  • To compensate for drift (especially with Kistler force platforms) high-pass filtering is necessary.

Biomechanics Laboratory, uOttawa

squat jump bioproc2
Squat Jump (BioProc2)
  • Example of a vertical squat jump (starts in full squat)
  • red is vertical force, cyan is AP force

airborne phase

body weight line

Biomechanics Laboratory, uOttawa

centre of gravity bioproc3
Centre of Gravity (BioProc3)
  • Squat depth was 1.39 cm
  • Takeoff height was 79.6 cm
  • Jump height was 28.3 cm

Biomechanics Laboratory, uOttawa