PHTY 609: Clinical Biomechanics Exam 2

Angular Analogs of Laws of Motion

(1). A rotating body will maintain a state of constant angular motion unless acted on by an external torque (2). A net torque produces angular acceleration of a body that's directly proportional to the magnitude of the torque, in the same direction as the torque, and is inversely proportional to the body's moment of inertia - T = I⍺ - T = external torque - I = moment of inertia - ⍺ = angular acceleration (3). For every torque exerted on a body, there's an equal and opposite torque exerted on the second body by the first - Ex. in terminal gait, the knee extensors aren't active to straighten the knee. The hip flexors are eccentrically contracting to slow the femur, so the shank is moving faster than the femur and thus straightens the leg

Lever Systems

1, 2, 3; F, L, E MA = Effort Arm/Resistance Arm First Class - Fulcrum in the center - Non-weight bearing plantar flexion and elbow extension Second Class - Load/Resistance (object you want moved) is in the center - Weight bearing plantar flexion Third Class - Effort (applied pressure) is in the center - Most lever systems in the body - Have an excursion advantage and mechanical disadvantage

Normal synovial joint motion is resisted by what forces?

1. Inertia - Function of tissue mass and acceleration 2. Elasticity - Function of joint displacement - May enhance movement when released - Resistance is non-linear and increases with displacement (limits extreme joint motions) 3. Viscosity - Function of joint velocity - Typically maximum in the middle of a ROM since there's an acceleration and deceleration phase to movement 4. Friction - Function of joint loading - Higher in WBing, but all joints see compression due to muscle action - Minor contribution in healthy joints **Contributions of each component are a function of the joint - Ex: Finger ⟶ 90% elastic, 9% viscous, 1% friction, inertia insignificant - Ex: Knee ⟶ large inertia, viscous and friction also larger

Components of Generic Force Vectors

1. Point of application - Base of the arrow 2. Action line and direction - Represented as the shaft and arrowhead in the direction of the exerted force 3. Magnitude - Represented by the length of the arrow

What NK configuration provides a resistance torque that's similar to the torque generation capability of the extensor muscles?

1. Weight behind body → NO - Producing an extension torque - Activating flexors 2. Weight in line with leg → NO 3. Weight 45˚ in front of body → YES - Peaks at 45˚ and then becomes less as you go through the motion - Mimics the resistance load that's similar to what the knee can reproduce

Knee Extension With NK Table: Weight 45˚ in Front of Leg

45˚ Knee Flexion - Longer MA - Hardest position - Largest flexion torque 0˚ Knee Flexion - Shorter MA - Easier to hold Increases until 45˚, and then gets easier as you extend knee past that

Knee Extension With Pulley System: Which position produces the most flexion torque at the knee (90˚ vs full ext)?

90˚ Flexion - More flexion torque - Moment arm is longer Full Extension - Less flexion torque - MA is shorter Torque is decreasing as you approach full knee extension - If you add an ankle weight, you'd get a constant torque through the motions: created isotonic system

Torque

AKA moment of force Defined as the tendency (or effectiveness) of a force to cause a rotation Can be increased by increasing force or moment arm Torque results from an eccentric (or off-center) force - The result is rotation and some translation T = Force • ⊥distance to line of action Concept is prevalent in everyday life: intuitively grasp wrench at the end to loosen a bolt - MA is maximized and, for a given force, torque is maximized - If grasped at midpoint, the torque would be halved even tho the same force was applied - In rehab, PT holds distal to joint so they can resist pt torque w less force

Knee Extension With NK Table: Weight in Line with Leg

Acts just like an ankle weight in this position

Moment of Inertia

An object's resistance to angular acceleration - Change in angular velocity - AKA mass moment of inertia It is a function of object mass and the distribution of that mass with respect to the axis of rotation - This is different than inertia!! (the distribution of mass has no impact on the resistance to linear acceleration) Moment of inertia decreases as the body becomes more compact around the axis of rotation - As children grow, developmental changes impact the proportions of body seg lengths, masses, and radii of gyration - Segmental moments of inertia affect resistance to angular rotation and therefore performance (ex. female gymnast's decreased performance with growth beyond adolescence) Given the two bats in the image, B is easier to swing and A has the larger moment of inertia - The weight in B is closer to the axis of rotation - Warming up with something that's more difficult to swing (bc larger moment of inertia) so that when they're actually playing without the weight, the bat speed is higher - "Choking up" on the handle decreases the moment of inertia and, therefore, it's easier to swing

Pendulum Centripetal Force

At the maximum velocity (middle of the swing), the pendulum weighs the most - Max centripetal force - As it progresses through to the far end, the scale drops down to the actual weight of the element This is the pressure you feel at the bottom of the swing on a swing ster

Inertial Force

Based on Newton's 1st Law - Contact force In human systems, movements in one segment can exert inertial forces on adjacent forces. Generally, a proximal segment exerts an inertial force on a more distal segment - Helps provide motion While you're walking, the proximal thigh exerts an inertial force on the distal shank at toe off which helps carry the leg fwd and flex the knee - Don't have to drive hamstrings or gastroc to flex the knee (hip flexors are active and causing that inertia) Can exaggerate it or reduce it by adding weights to the pt or elastic to support them thru motion

Joint Reaction Force

Based on Newton's 3rd Law - Contact force When standing, the femur exerts a downward force and the tibia an upward force Force magnitude and direction can be calculated with kinetic and/or kinematic data - Kinetic data is the most straight forward bc it is the GRF data - Kinematic data makes assumptions JRF does not reflect forces from the contracting muscles - Just reflecting the reaction from the ground - Typically underestimates what's going on - Estimates of muscle force from EMG data can be used to compute muscle contraction contribution to JRF. - More EMG signal is correlated with more muscle force. Quasi-linear relationship - Every muscle is different

Friction

Based on Newton's 3rd Law - Contact force - Surfaces are pressed together F = µN - µ = friction coefficient - N = normal force - The only thing you can control is the normal force (ex. crutches that are too long decreases the normal force and will slide) Forces applied parallel to the surface are opposed by a reaction force, but also by a force that tries to prevent the sliding of one surface on another ⟶ FRICTION Provides the ability to walk or travel in any vehicle Exists because no practical surface can be perfectly flat/smooth. Increased pressure increases the contact/congruency between the surfaces and, therefore increases the frictional forces - When you increase the pressure, the surface differences are magnified

Collinear Forces

Common line-of-action

Concurrent Forces

Common point of intersection

Kinetic ↔︎ Potential Energy Relationship

Conservation of energy - Energy can't be created or destroyed - There's always energy losses due to friction...not rly lost, just converted to heat (we neglect this) TE = KE + PE - Total energy As you start to rise, KE decreases because velocity is decreasing and PE is increasing (height is increasing)

Elastic Force

Contact force Biological tissues typically operate within their elastic limits Energy may be stored during the loading of a tissue and returned to the system when the load is removed - Pre-stretch prior to movement will increase force output With elastic storage, there is a time limit on how long elastic forces can be stored prior to release...this is because the tissues will creep/stretch The elastic-displacement relationship is highly non-linear, but it is there May resist movement (or enhance movement when released) - Nonlinear force - Limits extreme joint motion

Fluid Resistance

Contact force Fluid resists movement Fluid Properties 1. Density - Mass per unit volume (m/v) - Water is more dense than air, so more resistance to movement 2. Viscosity - Fluid's resistance to flow - Viscous resistance increases as velocity increases - Viscosity decreases with temperature increase (related to things like joint space...synovial fluid is viscous)

Muscle Force

Contact force Muscle can only generate a "pulling" force - Generation capability is a function of L-T and F-V relationship - With some assumptions, muscle force vectors can be resolved into components

Knee Extensor Isometric Torque

Data to determine in what knee position are the knee extensors capable of producing the most torque Peak extension torque is somewhere between 45-60˚ - Where the knee system is strongest

Angular Momentum

Defined as the quantity of angular motion that an object possesses The product of moment of inertia and angular velocity H = I𝜔 = mk²𝜔 - Kg•m²/s Angular momentum requirements increase with the complexity of the skill being performed (number of flips and twists) - You need more energy to do it - Person should be able to overdo the base skill before they can add the twist

Power

Defined as work done per unit time - Rate of doing work - Rate at which energy is expended P = ∆W/∆t or P = Fv - Joules/second ⟶ watts - Function of applied force and velocity Can convert watts to calories This is important because exercise programs can be very specific. When training muscular response, the time needed for the movement can be important. Pt not only trains to increase force production, but the rate of movement must be considered - Make exercises harder by having them do it faster (using more energy)

NK Table

Designed to have an axis of rotation (x and y axis) and you put a weight on the system and person puts their foot on the ankle pad You can change the position of the weight relative to the leg Invented because your leg has the ability to produce torque differently based on the position of the NK table - Knee extensor isometric torque flashcard later

Which kinetic energy component has the largest contribution during running?

During running, a single segment can undergo large angular velocities...is there more RKE or TKE associated with these segments? Remember that v = 𝜔𝑟 so... TKE = 1/2 m(𝜔𝑟)² and RKE = 1/2I𝜔² which makes both equations related based on angular velocity - Leg segment values: 3.53 kg; I=0.0393 kg•m²; r=0.146m - TKE= 0.376•𝜔² - RKE = 0.192•𝜔² - TKE > RKE

Translational Kinetic Energy

Energy resulting from motion TKE = 1/2 mv² - kg•m²/s² = N•m = joules Function of mass and velocity - If same velocity, larger mass has more energy - If same mass, higher velocity has more energy (consider squared term) 0 velocity = 0 KE

Basic Assumptions and Limitations in the Application of Statics

Entire list is untrue in human systems, but we use them to simplify 1. Anatomical axes of rotation are known 2. Only 1 muscle group controlling movement - Co-contraction would create a problem: anything the antagonist m is doing would have to be overcome by the agonist + whatever the agonist is doing to move, so we assume that doesn't happen 3. Muscle attachment locations are known 4. Line-of-action of muscle tension is known - Angle of pull 5. Segmental weights and COMs are known 6. Friction negligible, dynamics ignored, only 2D problems, deformation ignored - Joints don't have friction that they have to overcome; dealing with constant acceleration (no dynamics)

Elastic Force Pre-Stretch Effect Experiment

Experiment done with animal muscle that was broken up into 2 motor units First, had motor unit 1 fire and then motor unit 2 to get the base curves...they were basically equal Next, had them both fire at the same time and the curve had a single peak, much higher than when they were fired one by one Next, the had the 1st MU fire and then very quickly after (asynchronous) had the 2nd MU fire. Curve peaked higher than the 1+2 - As the delay between the two firings increased after that, the peak decreased - Basically, the first motor unit firing pre-stretched the tendon. So the second motor unit produced force + elastic force = greater total - Must happen very fast (0.2 seconds) - No energy is wasted by having to stretch the tendon (it's pre-stretched)

Relationship Between Law of Acceleration and Momentum

F = ma ⟶ F = m(∆v/∆t) ⟶ F = m∆v/∆t m•v = p ⟶ F = ∆p/∆t Force = rate of change of momentum

Local vs. Remote Components of Angular Momentum

For a multisegmental object (such as the human body) the angular momentum about a given axis of rotation is the sum of the angular momentums of the individual body segments - Local and remote components control the final motion Local angular momentum is the angular momentum/movement of a segment about its own COM Remote angular momentum is the angular momentum of a segment about the total body COM H𝑡𝑜𝑡𝑎𝓁= ∑H(local) + ∑H(remote) H(local) = I𝜔 H(remote) = md²𝜔'

Conservation of Angular Momentum

For airborne activities where gravity is the only external force, angular momentum remains constant during the flight phase The quantity of H is determined by the torque applied over time at the point of take-off Manipulating I (shape of the body) results in changes in 𝜔 The total momentum of the system remains constant in the absence of external torques

Non-Contact Forces

Force exerted by objects that are not in direct contact with one another Gravity F= (Gm₁m₂)/(r²) - G= universal gravitational constant - m₁= mass of one object - m₂= mass of second object - r= distance between the objects Changes with your relationship to the center of mass (but gravity is considered constant in physics) Gravitational pull of a small mass is small and is generally neglected

GRF Vertical Component: High versus Low Jump

Force-time plot - Vertical axis is often scaled in "times body weight" for GRF - 1= body weight and everything else is normalized to that Downward slope: bending knees before - Body is accelerating towards gravity Positive slope: push off force - Body is accelerating against gravity Area under curve: impulse for the jump - Larger area = larger velocity = larger jump height If you're trying to get off the floor quicker, you'd have to have a higher force if it's going to make you jump the same height as if you jumped later

Negative Work

Forces act parallel to the movement, but in the opposite direction Ex. lowering a box to the floor,decelerating a moving object, etc

Pressure

Forces are distributed across a surface How these forces are distributed = pressure Force per unit area P = F/A - P = N/m² ⟶ pascal - F = N - A = m²

Contact Forces

Forces exerted when one object is in direct contact with another 1. GRF 2. JRF 3. Friction 4. Fluid resistance 5. Intertial force 6. Muscle force 7. Elastic force

Conservation of Momentum: Vault Example

From the point at which they leave the horse and they are in the air, the angular momentum is constant, even though they are changing shape - Applying a torque to flip, but the torque once they leave can't be given or taken away If you're looking at angular velocity, you'll see that it increases while they're flipping in the air and then slows back down at they are landing

GRFV: Heel Strike/Initial Contact

Front foot in image Length of vector represents how much force was being produced Vector occurs at the heel Vector is facing forward and is pretty small

Impulse-Momentum Theorem

Ft = p = ∆mv Forces that act over a defined period of time or when a collision is involved Impulse is the area under the curve of a force-time plot Implication: if an object with mass (m) moving at a velocity (v) strikes a stationary target for time (t), then a force (f) will be imparted on the target ex. Newton's cradle To decrease the force, you can increase the amount of time it takes to slow down (impulse stays constant) - Ex. landing on soft surface, adding heel cushing - Area under the Ft curve is constant, but F is less

Knee Extension With Ankle Weight: Which position produces the most flexion torque at the knee (90˚ vs full ext)?

Full extension because there is no MA in 90˚ flexion Torque is increasing as you approach full knee extension

Centripetal Force (F𝑐) and Centrifugal Force

F𝑐 = m𝜔²/r = mv²/r - Related to tangential velocity Bodies undergoing rotary motion around a fixed axis are subject to linear forces Centripetal force prevents the rotating body from leaving the path - Always directed towards the axis of rotation Centrifugal force is the equal and opposite reaction force countering centripetal force - These forces act on different bodies - Picture example: the line exerts a centripetal force on the ball causing the ball to remain in a circular path. The ball exerts a centrifugal force on the line, and thus the person holding the line, keeping the line taut. If the line breaks, the ball flies off in a tangent direction and the forces cease to exist With a larger mass, these forces increase and may require more force to counter - Ex. a person with a large mass doing giants on bars requires more grip strength

Statics Application: Consider the weight lifter who is bent forward (θ) lifting a weight (W₀). Determine the magnitude of F𝑚 and F𝑗

Given: - W = W₀ - W₁ = 0.4W - θ = 45˚ - a = 0.02h - b = 0.08h - c = 0.12h 1. Create an equations of the sum of the moments/torques - Equation won't include JRF because its MA is 0! Στ = 0 ⟶ -a•F𝑚 - bW₁ + c(W+W₀) = 0 2. Isolate F𝑚 from the previous equation ⟶ F𝑚 = [c(W+W₀) - bW₁]/a - For given numerical values, you can determine the magnitude of F𝑚 and then its components ⟶ F𝑚𝑥 = F𝑚•sinθ F𝑚𝑦 = F𝑚•cosθ 3. Now use the sum of the forces in the X and Y directions to determine the JRFs ⟶ ∑F𝑥 = 0 → F𝑗𝑥 = F𝑚𝑥 ∑F𝑦 = 0 → F𝑗𝑦 = F𝑚𝑦 + W + W₀ - W₁ ⟶ F𝑗 = √(F𝑗𝑥²+F𝑗𝑦²) 4. Results - F𝑚 = 10.4 x W - F𝑗 = 11.7 x W ⟶ very large forces ⟶ can use during functional capacity eval...test done to see if pt is ready to return to work. Can calculate how much force they are putting on their joint. Pain is also reported - Can catch ppl who are malingering: "can't lift" things that are like their job, but they can produce that much force doing other things 3 equations are necessary to determine JRF: sum of the moments, sum of forces in x, and sum of forces in y

GRF BL AKA Example

Has an impact peak, but no active peak because there's no musculature driving the joint Through the use of mechanistic components in the joint, you get a curve sort of simulates what you'd expect for normal gait, though - There's hydraulics and pistons in there, so it's mechanical in nature, not active - Prosthetist did a good job

Transferring Angular Momentum From a Primary to a Secondary Axis: Double Double Example

Have to be taught how to increase the energy of a single skill first - First, learn triple back and over-rotate - Manipulating moment of inertia to result in changes in angular velocity It's possible for a rotating body to transfer angular momentum from a primary axis (M/L flip) to a secondary axis (A/P twist) - The vector sum of both of these energies is still going to be the same!! Progression → one flip with a twist (2) + one flip without a twist (1) = still 3 things - Taking the energy you have and splitting it up in a different way - Still over-rotating ⟶ flip-twist, flip-twist **Side note about the bar: bar system actually has elastic potential (strain) energy.

Free Body Diagram

ID forces acting on individual parts of a system Each force has a reaction force

Particle-Mass Method of Determining Moment of Inertia

If all object are considered to be made up of a number of small particles, each with its own mass and distance from the axis of rotation, then the moment of inertia can be expressed mathematically... Moment of inertia of a body is the sum of the moments of inertia of all the mass particles the object contains I = ∑mᵢ•rᵢ² - I = moment of inertia (kg•m²) - m = mass (kg) - r = distance from axis of rotation (m)

Friction and Tilted Surface

If the surface is tilted, the force pressing the two surfaces together diminishes and some part of the downward force acts against the frictional force The more you tilt it, the less weight is perpendicular to the surface to create the normal force, which is related to friction - The reaction force decreases with increased surface angle At a sufficient angle, the object will move - The force of static friction (µ𝑠) has been overcome

GRF: Impact vs Active Peak (Walking v Running)

Impact Peak - Forces that result form the collision of two objects Active Peak - Forces generated by movement that is controlled by muscle activity Both happen with every activity we do Part of the vertical component of GRF There's 2 active peaks during walking: one for deceleration phase (foot flat), one for acceleration phase (heel off) There's a larger impact peak with running vs walking A-P component: during contact, foot pushes anterior and plate pushes posterior. Same for both running and walking M-L component: more variable response...initial lateral reaction force followed by medial rxn force (less than lateral)

Radius of Gyration: In sprinting, why does the sprinter flex their leg so much?

In sprinting, maximum angular acceleration of the legs is desired Increased knee flexion decreases the moment of inertia of the advancing limb and, thereby, reduces the resistance of the limb to hip flexion - In the flexed position, the combined radius of gyration for the LE is decreased - k1 = radius of gyration for thigh - k2 = shank - k3 = foot **During walking, minimal angular acceleration is required, so knee flexion is small during swing phase - Moment of inertia with respect to hip is relatively large

Radius of Gyration

In the human body, segments are irregularly shaped and contain heterogeneous mass distributions: masses differ and aren't uniformly distributed Radius of gyration (k) denotes mass distribution about a single axis - Distance from the axis of rotation to a point at which the mass can be concentrated without changing the inertial characteristics of the segment Moment of inertia can be calculated using radius of gyration - Use this method bc the particle method isn't practical to use Varies with respect to different body axis - The relationship of body parts to one another affects the "systems" moment of inertia I = m(𝜌l)² = mk² - I = moment of inertia (kg•m²) - m = mass - 𝜌 = radius of gyration as a proportion of segment length - l = segment length - k = radius of gyration (m)

Kinetic Energy Related to Work

KE is the ability of an object to do work resulting from its motion W = Fs = mas ⟶ s = (v²𝑓 - v²𝑖)/2a ⟶ W = (m(v²𝑓 - v²𝑖)/2 = 1/2mv² So...work due to motion = kinetic energy e.g. carnival swing hammer to ring bell... hammer has kinetic energy, converted into work as you hit and the block is raised to strike the bell.

GRF Vertical Component: Rigid vs Soft Landing

Landing component of the jump Rigid = no knee bend - Higher GRF First peak = impact peak Second peak = active peak

Ground Reaction Force

Law of action-reaction - A subject pushes against the ground and the ground pushes back - Can be measured with a force plate - 3D bathroom scale is capable of dynamic measurements Represents the force necessary to accelerate the entire body - Can't be directly associated with LE only - Use caution when using GRF data to describe LE function GRFV = ground reaction force vector - Can be resolved into x, y, and z components - F𝑧 = vertical load - F𝑥 = medio-lateral load - F𝑦 = antero-posterior load

Moment Arm vs. Lever Arm

Lever Arm - Distance from the axis of rotation to the point of the applied load - Stays fixed Moment Arm - The perpendicular distance from the line of action to the axis of rotation - Can change throughout the movement (and thus changes torque and the force required by muscle) - Can be affected by muscle alignment, anatomical pulleys, and instantaneous axis of rotation - Changes may act to "counter" compromised length-tension relationships At 90º elbow flexion, the moment arm and lever arm are the same

Human-System Force Vectors

Line of action is towards to origin of the muscle Point of application is the insertion of the muscle Magnitude is based on the size of the muscle In order to simplify these problems, you can tilt the axis so that x isn't horizontal and is ligned up with the bone the muscle is moving - Angle of pull is based on a line that is parallel to the forearm - Vector angle of pull is related to the forearm (in this pic) and constitutes a local coordinate system - Makes the system easier to work with

Linear vs Angular Momentum, Mechanical Work, Energy, and Power Overview

Linear •Momentum: p = mv - kg•m/s •Mechanical Work: W = F*cosθ*s - Joules •Energy: TKE = 1/2mv²; PE = mgh; SE = 1/2k∆x² - Nm or Joules •Power: P = Fv - Watts Angular •Momentum: H = I𝜔 = 𝑚𝘬²𝜔 - kg•m²/s •Mechanical Work: W = T∆θ - Joules - Angular distance must be in radians •Energy: RKE = 1/2I𝜔² - Nm or Joules •Power: P = T𝜔 - Watts

Parallel Forces

Lines-of-action are parallel

Lubricants and Friction

Lubricants can reduce the frictional component by separating the two surfaces. Movement occurs between the lubricant molecules instead

Work

Mechanical work = force applied x distance moved - Done as resistance is overcome and movement occurs W = F x s = Nm = joule - If force is applied at an angle, W = F x cosθ x s - θ = angle between the force vector and the line of displacement Implies that work is only done during movement - No work is done during isometric contraction Often consider work as using a force to lift an object against gravity - Not always the case Work is also done as an object is accelerated ⟶ W = Fs = mas

Cineplastic Amputations

Muscle force data collected in vivo - Usually we collect this data indirectly Designed for upper limb use Basically take the biceps and loop it back on itself allowing a stirrup to go through the space - A cable is attached to the stirrup so when the muscle contracts it puts tension on the cable and weights can be lifted - Can be hooked to prosthetic and make it move as a function as their own muscle movement Able to do experiments to generate length-tension curves - First time we could do this in humans Big positive = proprioception - They have way more control over their hands than people have in other prosthetics because they can feel how much force they're producing

Statics Application: Determine force required by the deltoid to hold the load in abduction.

Muscle pull and JRF are pulling in opposite directions and at the same θ - Weight in hand (W₀) acting at distance "c" - Weight of arm acting at "b" - m force acting at "a" a= 15 cm b= 30 cm c= 60 cm θ= 15˚ W= 40 N W₀= 60 N 1. Break down muscle force into x and y components - FM𝑥 = FM cosθ → compressive force - FM𝑦 = FM sinθ → rotational force 2. Solve for FM𝑦 (∑M=0) ∙ aFM𝑦 - bW - cW₀ = 0 ∙ FM𝑦 = (1/a)(bW + cW₀) ∙ FM𝑦= 320 N ∙ What's actually creating the torque 3. Use FM𝑦 to get FM - FM= 1236 N 4. Use FM to get FM𝑥 - FM𝑥= 1194 N - Acting to compress the joint - LARGER THAN THE TORQUE PIECE - Implies that a large stabilization force is required...this position isn't very stable

Law of Acceleration

Newton's 2nd Law The change of motion is proportional to the force impressed and is made in the direction of the straight line in which that force is impressed This statement relates force, mass, and acceleration: F=MA - Newtons (kg-M/S2) You can rearrange this equation to help define momentum

Law of Action-Reaction

Newton's 3rd Law For every action there is an equal and opposite reaction

Law of Inertia

Newton's First Law Every body continues in its state of rest, or uniform motion in a straight line, unless compelled to change that state by forces impressed upon it The inertia of an object is used to describe its resistance to motion - The greater the mass, the greater its inertia

Knee Extension With NK Table: Weight Behind the Body

Now, the weight is producing an extension torque - Have to engage hamstrings to stay in this position 90˚ Flexion - Longer MA - Larger extension torque 0˚ Flexion - MA becomes smaller - Smaller extension torque - Easiest to hold here

Strain Energy

PE subset Energy stored as a result of material deformation - Storing energy in an elastic tissue SE = 1/2k•∆x² - k = constant dependent on material ⟶ stiffness (slope of stress-strain plot) - x = deformation distance/how far it was stressed Happening in tendons and ligaments in the body Ex. trampoline, pole vaulting poles, bows Ex. "tuned" running track: runners can run faster if the track is tuned to store some of their energy and release it back - 3% speed advantage - Optimal track surface

Center of Pressure

Point of application of GRFV COP can be obtained from force plate data - Dynamic data At any instant in time, the four corner load cells measure the force being applied to each - A centrally applied force would result in equal distribution among the load cells - Proportional differences determine the COP location relative to the top of the force plate A typical COP pattern starts at the calcaneus, proceeds up the lateral border, then heads medially and exits through the 1st toe

Coplanar Forces

Points that lie on the same plane Acting on a 2D surface

Pressure Map

Pressure distribution patterns in the foot during ground contact can be determined via pressure mats (relative vs. absolute) - Not resolving into single COP - Info can be used to determine effects of orthotic insert. Esp important with diabetic foot Lots of pressure over 2nd met head and the distal 1st metatarsal

Impulse

Quantifies the overall effect of a force acting over time. Change in momentum force x time

Rotational Kinetic Energy

RKE = 1/2I𝜔² - I = moment of inertia (kg•m²) - 𝜔 = angular velocity (rad/s) Joules

Segmental Method to Determine COM

Requires digitized kinematic data and anthropomorphic info to determine the %BW and location of the segmental COMs Segments are weighted and summed to determine total COM location ⟶ mathematical equivalent to the graphical method we did in lab x𝑐𝑚 = ∑mᵢxᵢ/M y𝑐𝑚 = ∑mᵢyᵢ/M

Force Couples

Result from a pair of forces acting on a single axis Forces with equal magnitudes acting in opposite directions Cause pure rotation without translation - Remember that each torque causes a translation, but opposite translation directions result in translation cancellation

2 Ways to Calculate Torque

Rotary component of force x lever arm OR Force x moment arm

Centripetal Force: Running on a curved path

Runner is applying a shear force to the ground - As you're running to the right, the shear force is going to drive you to the left The reaction force constitutes the centripetal force - Combining this force with the vertical GRF produces a resultant vector that goes through the COM - This is why you must lean over to speed up....increased velocity increases Fc, which changes the line of action of the resultant vector If the centripetal/friction force has a limit, then you must decrease velocity to compensate so you don't slip as you decrease the radius - As you decrease the radius, you're increasing the horizontal component of GRF (centripetal force)...you need a certain amount of vertical (normal) force to have enough friction to keep you from sliding (AKA if Fc required to keep you there < Ff, then you will slide) Banked Curves - Banked curves allow the normal force to be the "resultant" vector - The centripetal force is supplied by the horizontal component of the normal force and higher speeds can be reached before the centripetal force is higher than friction force

Step Test Example

Step test used to examine a pt's knee strength pt mass: 60 kg MA𝑎 = 0.17 m MA𝘣 = 0.18 m 1. What is the knee torque required for each step? T𝑎= 100 Nm T𝘣 = 106 Nm 2. Why is it harder to step onto a higher bench? - More lifting work required - Greater knee flexion position requires greater torque based on MA of joint - Hip extensor muscle must counter flexion torque at the hip (bc the trunk is bending so far forward) 3. If you only have the low step available in clinic, how can you make the exercise harder? - Make them do it faster - Requires more power

Relationship Between Radial Acceleration, Force, and Centripetal Force

System = total human body or parts of the human body and any other objects that may be important in the analysis Radial Acceleration: A𝑟 = V²/r - Radial acceleration is caused by centripetal force - Acceleration towards the center of the circle aᵣ = rω² = V²/r F = ma ⟶ a = F/m F/m = V²/r F𝑐 = mV²/r

What energy components make up the total energy of the system?

TE = TKE + PE + RKE + SE - TE = total energy - TKE = translational kinetic energy - PE = potential energy - RKE = rotational kinetic energy - SE = strain energy/elastic potential energy Single segments often undergo large angular velocities during activity (e.g., running). This may lead to the conclusion that angular energy components have a larger contribution to total energy than do translational components - Which wouldn't be very efficient (basically running in place)

Composition of Vectors

The addition of coplanar forces - Can be illustrated graphically - Can also be accomplished mathematically by first resolving forces into horizontal and vertical components Important bc in many systems there are multiple forces acting on an object, so you need to understand how to combine and manipulate vectors - Ex. in muscle itself, each muscle fiber has its own line of action and force generation capabilities The addition of vectors follows a commutative property - No matter which way/order you add them, you'll always get to the same location

Energy

The capacity to do work 2 forms: kinetic and potential energy Same units as work - Joules

Potential Energy

The capacity to do work because of position PE = mgh - Nm = joules W = Fs = mas ↔︎ mgh = PE So the work done to lift a barbell overhead is also its potential energy. Mass of someone walking oscillates up and down during walking. The KE is stored as PE and released into KE when COM drops again - So no energy is lost, it's just transformed into different types Ex. having someone jumping up and down from a box: - The height of the box matters bc it affects the amount of energy to get up there and the amount of energy they have when they get back down - Having someone jump up onto a box yields much less load on landing than jumping up and landing on something that's the same height...you don't have as much speed when you make contact - Basically, the KE on impact is lower because the person still has some PE stored - Release the energy by stepping back down to decrease the impact load

GRF Active-Impact Peak Comparison: Walking, Running, Sprinting, Jumping

The faster you go, the higher the active GRFs are Impact peak for takeoff of a jump is way higher than run and walk - Have to take off super fast so that the force can be high...if you take off slow, the force is less There's an increase in active peak with increased velocity ⟶ decrease walking speed to decrease GRFs and, subsequently, JRFs

GRFV: Foot Flat (Loading Response)

The instant that the rest of the foot comes down to contact the ground and usually is where full body weight is being supported by the leg (just preceding SLS) Vector has changed direction (facing posterior) and is much larger - Starting to form the first peak of GRF gait graph

Center of Gravity

The point about which all body particles are evenly distributed Where the gravity field is uniform, this is equal to COM

Center of Mass

The point about which the mass is evenly distributed - BW is a product of mass and acceleration due to gravity - The BW vector originates at the COG Also the balance point of the body Can be further defined as the point about which the sum of the external torques acting on the system equals 0 Can be calculated using a reaction bored or geometric/segmental method

Linear Momentum

The quantity of motion of a moving body The product of an object's mass (inertial property) and velocity p = kg•m/s

Statics

The study of systems in equilibrium The forces acting on the system are balanced - Newton's 1st law

Reaction Board Method to Determine COM

Used to determine where the COM is in the system RF₁ is acting as the fulcrum with 2 torques associated with it 1st torque is BW x d 2nd torque is the reaction force measured at the other end (RF₂) x l - Doesn't matter how long l is, because l determines the torque associated with RF₂ location, but it will always equal BW x d So you solve for d which is the location of the COM - Torque around RF₁ equals 0 d = RF₂ x l/wt

A/P GRF: Actual vs. Calculated

Using kinematic data to calculate GRF - Very similar to the kinetic data we get from force plate COM movement can be used to compute/estimate the expected A/P profile Use horizontal velocity of COM - First derivative ⟶ horizontal acceleration ⟶ multiply times BW ⟶ A/P force curve F𝑦 = m•a𝑦

GRF Gait Graph

Vectors typically point up through the COM of the subject

Angular Work

W = T∆θ Torque applied (Nm) • angular distance moved (rads) Joules - Identical in units to translational work, so they can be added Positive work ⟶ concentric contraction Negative work ⟶ eccentric contraction 0 work ⟶ isometric contraction

GRFV: Midstance

When the COM is directly above ankle joint center - Also used as the instant when the hip joint center is above the ankle joint bc it's very difficult to evaluate the precise location of the COM as the segments of the body move relative to the trunk Vector is vertical and shorter than it was in the last stage - No forces pushing forward or backward (no acceleration or deceleration) - Dip in the GRF graph

GRFV: Heel Raise (Terminal Stance)

When the heel begins to lift off the ground in preparation for the forward propulsion of the body Vector is bigger and in the forward/opposite direction - Starting to propel yourself forward (pushing backwards on floor). Floor is pushing in opposite direction - Has a forward component and vertical component - Vertical component is equal to the height of the 2nd peak in the GRF plot

ABS Brakes vs. Locked Wheels and Friction

When the wheels are locked and skidding, braking is by kinetic friction When the wheels are rotating, braking is by static friction The coefficient of static friction is greater than that of kinetic friction The larger the coefficient of friction, the greater the frictional force from breaking. A larger frictional force means the car stops in less time and less distance. - Anti-lock brakes prevent the wheels from locking up and skidding so that the braking force is from static friction instead of kinetic friction

Angular Power

Work done per unit time - Rate of doing work - Rate at which energy is expended Watts P = ∆W/∆t - Angular work over time P = T𝜔 - Torque • angular velocity Angular power often used to describe mechanical muscle power - Muscle power is determined by computing the net torque of a muscle acting across a joint and multiplying it by the angular velocity of that joint

Statics Application: Ankle

You can look at the example in the ppt, but basically, JRF is double what the muscle has to pull - Almost 3x BW The muscle force is almost twice the BW This is in a static situation, standing on one foot. If you start doing things dynamically, these numbers go way up - This is why eccentrics are often done bc the m can produce more force This is a second class lever...mechanically advantaged

A 200lb man with a COM 40" above the ground falls on hip after tripping. What is the force on the floor if the contact time in 0.1s?

mv=Ft Use constant acceleration equations to get the time of the fall ⟶ 0.43 s Use acceleration due to gravity x time of fall ⟶ impact velocity ⟶ 4.2 m/s 200lb ⟶ 91 kg 91 kg x 4.2 m/s = F x 0.1s ⟶ 867 lbs impact force This force may be sufficient to break the hip How do you decrease the force? - Increase the contact time. Bending the hips and knees or "rolling" with the fall - Protective equipment

Coefficient of Kinetic/Dynamic Friction

µ𝑘 exists once motion begins Kinetic friction is typically less than the max static friction Friction force stays the same as applied force changes

Coefficient of Static Friction

µ𝑠 varies with the material and the nature of the surfaces involved The lower the coefficient, the less friction The µ𝑠 of synovial fluid is less than ice on ice in healthy joints - Increases in weight bearing

GRFV: Toe Off (Pre-Swing)

⟶ initial swing, mid-swing, terminal swing No vector Last event of contact the stance phase