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**Forces and Moments of Force**

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

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Force a push or pull physical property that causes a mass to accelerate (i.e., change of speed, v, or direction, w) vector possessing both a magnitude and a direction and adds according to the Parallelogram Law a resultant force is the sum of two or more forces Fa+b = Fa + Fb

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**The Resultant Force F = m a**

sum of all external forces acting on a body according to Newton’s Second Law the resultant force is proportional to the body’s acceleration. I.e., using a consistent system of units: F = m a Where, m = mass in kilograms a = acceleration in m/s2 F = force in newtons

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Types of Forces External forces are environmental forces which act on the body or the forces exerted by other objects that come into contact with the body. Examples: gravitational forces especially the earth’s frictional forces of surfaces and fluids ground reaction forces (includes friction) drag (viscous) forces of air (wind) or water impact forces of objects springs (poles, cables, springboards) buoyant force of water

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Types of Forces Internal forces are forces that originate and terminate within the body. Sum of all internal forces within any body is always equal to zero (zero vector). Examples: muscle forces (through tendons) bone-on-bone forces (including cartilage) ligamentous forces joint capsular forces and skin fluid (viscous) forces

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**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, motor) 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, BioDex and electrical meters

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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: tensiometer, KinCom, Cybex, Biodex, spring scale, force platform

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**Tensiometer essentially a spring-type sensor**

measures tension (magnitude of a force)

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Strain Link uses strain gauges to measure tiny length changes in a material that are proporional to the applied force

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**Strain Gauge Transducers**

S-link load cell (used in underwater weighing lab) strain link transducer strain link measured forces from a rowing ergometer S-link used during underwater weighing to compute body density and lean body mass

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Power Dynamometers potentiometer lever arm strain link

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Strain Gauge Lever uses strain gauges to measure bending moment, which can then be used to compute applied force (Cybex, Kincom, Biodex)

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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)

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**Kistler Force Platforms**

portable standard clear top in treadmill

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AMTI Force Platforms small model standard model glass-top model

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**Pressure Mapping Systems**

Pedar measures pressures from a matrix of capacitive sensors to display a pressure map Tekscan F-Scan measures normal forces using resistive ink sensors to display a force tensor of the pressure distribution

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**Moment of Force turning effect of a force**

physical property which causes a rigid body to change its angular acceleration vector quantity with units of newton metres (N.m) also known as a torque or force couple depending upon its application

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**The Resultant Moment of Force**

sum of all external moments of force acting on a rigid body according to Newton-Euler equations the resultant moment of force is proportional to the body’s angular acceleration. I.e., using a consistent system of units and a particular axis (A, usually at the centre of gravity) MA = IA a where IA = moment of inertia about A in kg.m2 a = acceleration in rad/s2 MA = moment of force in N.m

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**Types of Moments of Force**

External moments are environmental forces which act on the body or the forces exerted by other objects which come into contact with the body. Examples: vertical moment of ground reaction force force couple of ground reaction forces drill eccentric forces

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**Types of Moments of Force**

Internal moments are moments of force that originate and terminate within the body. Sum of all internal moments of force within any body is always equal to zero (zero vector). Examples: muscle forces (through tendons) bone-on-bone forces (including cartilage) ligamentous forces

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Moment Transducers devices for changing force into analog or digital signals suitable for recording or monitoring typically require power supply and output device types: springs strain gauge (most common) piezoelectric (usually in force platforms) Examples: KinCom, Cybex, Biodex, force platforms

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**Strain Gauge Transducers**

torque transducer (for forearm axial torque) bending moment (rowing oar lock pin)

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Strain Gauge Lever uses strain gauges to measure bending moment and torque (Cybex, Kincom, Biodex)

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Force Platforms devices usually embedded in a laboratory walkway for measuring ground reaction forces and moments of force Typically measures vertical (free) moment of force (Mz) but can also be designed to measure gripping moments

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Force Platforms Kistler In laboratory stairway AMTI Bertec

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Moments of Inertia

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**Quick Release Experiment**

used to measure moments of inertia non-invasively assumes no friction in the joints performed in the horizontal plane to eliminate gravity effects angular acceleration is measured by video analysis or electrogoniometry

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**Law of Reaction Third Law of Motion**

For every force there must be a reaction force, equal in magnitude but opposite in direction, that acts on a different body (e.g., ground) F = – R to increase the size of an action force you must be able to have an object or surface that can create a large reaction action and reaction are arbitrary designations

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Reaction Forces

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Reaction Forces

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Banking of Tracks Ground reaction force (Fg) should pass through centre of gravity, otherwise the person rotates (about A/P axis). To run the bend, Fg must provide a radial acceleration. I.e., SFr = mar = –mvt2/r (recall ar = rw2 = vt2/r) where r is radius of curvature of the bend vt is transverse velocity (race speed) m is mass

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Banking of Tracks

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Banking of Tracks

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Banking of Tracks

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Banking of Tracks Ideal angle of banking = q = tan-1(vt2/rg)

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Banking of Tracks Ideal angle of banking = q = tan-1(vt2/rg)

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**Banking of Tracks since q = s / r thus r = s / q**

for sprinting at 10.0 m/s 100 bend: r = 100 / p = 31.8 metres q = tan-1 [102 / (31.8 x 9.81) ] = 17.8 degrees 50 m bend: r = 50 / p = 15.9 metres q = tan-1 [102 / (15.9 x 9.81) ] = 32.6 degrees

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