dynamometry d. gordon e. robertson, phd, fcsb biomechanics laboratory, school of human kinetics,...

Dynamometry

D. Gordon E. Robertson, PhD, FCSB

Biomechanics Laboratory,

School of Human Kinetics,

University of Ottawa, Ottawa, Canada1Biomechanics 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, uOttawa 4

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, uOttawa 6

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 7

Strain Link

8Biomechanics Laboratory, uOttawa

Strain Gauge Transducers

9Biomechanics Laboratory, uOttawa

Power Dynamometers

potentiometer

strain linklever arm

10Biomechanics Laboratory, uOttawa

Strain Gauge Lever

Cybex KinCom

Biomechanics Laboratory, uOttawa 11

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

14Biomechanics Laboratory, uOttawa

Kistler Force Platforms

standard

in treadmill

clear topportable

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[Fx23 –Fx14 ] – Fx z) /Fz

y = (b[Fy12 –Fy34] – Fy z) /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.

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 ) t1

0

t

tFdt

20Biomechanics Laboratory, uOttawa

Takeoff Velocity

• To compute takeoff velocity divide the impulse by body mass

• For the vertical velocity, body weight must be subtractedvhorizontal = Impulsehorizontal / m

vvertical = (Impulsevertical – 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

• shorizontal =

• svertical =

• To compensate for drift (especially with Kistler force platforms) high-pass filtering is necessary.

1

0

1

0

2)/(t

t

t

tdtmF

1

0

1

0

2)/]([t

t vertical

t

tdtmWF

1

0

1

0

2)/(t

t horizontal

t

tdtmF

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 lineairborne 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