biomechanics 2

Introduction to Biomechanics

Objectives: After studying this topic, the students will be able to

1. define the terms of biomechanics, statics, dynamics, kinematics, kinetics, and kinesiology

2. understand the development of Biomechanics 3. identify the scope of biomechanical studies and their application 4. describe the common used physical quantities and their symbols

About BiomechanicsDefinition of BiomechanicsDevelopment of BiomechanicsScope of BiomechanicsPhysical Quantity

1. Hall, 2003：Chap 1 2. Chaffin & Andersson, 1999： Chap 1 3. Luttgens, K. & Hamilton, N., 2002：  Chap 1 4. Nig & Herzog, 1999: Chap 1

About Biomechanics

Applications of Biomechanics

physical therapy occupational therapy medicine

o orthopedics o sports medicine o rehabilitation medicine o occupational medicine o forensic medicine

engineering o ergonomics (industrial medicine) o bioengineering

kinesiology o movement science o physical education

arts o performance arts o fine arts o entertainment arts

Who should take biomechanics class?

physical therapist/ occupational therapist orthopedic/ occupational medicine/ rehabilitation medicine physician or nurse industrial/ production/ manufacturing/ process engineer ergonomist/ biomechanist/ kinesiologist coach/ athlete/ sports manager industrial hygienist/ safety manager/ labor relations manager forensic medicine physician, scientist, staff, spy..... entertainment specialist/ actor or actress dancer/ painter

Definition of Biomechanics

Broad Definition of Biomechanics： the application of the principles and technology of the physics and mechanics in the study of the living systems, which is a multidisciplinary study including

physical properties of biological materials biological signals and their measurements biomechanical modeling and simulation applications of biomechanics

Limited Definition of Biomechanics： the science that examines forces acting upon and within a biological structure and effects produced by such forces (Hay, 1973)

forces： external and internal forces effects：

1. movements of segments of interest 2. deformation of biological materials 3. biological changes in the tissues

Knowledge Needed in Biomechanical Studies

Mathematics Physics Mechanics

o statics o dynamics o fluid mechanics

Biology and Medicine Neurophysiology Behavior science

Development of Biomechanics

*** Please read Chaffin's book chapter 1 ***

Galioleo Galilei William Harvey Stephen Hales YC Fung WT Dempster Don B Chaffin David Winter Frankel and Nordin

Scope of Biomechanical Research of Human Movement

Some research directions

*** Please read Hall's book chapter 1 ***

structure and/or physical properties of muscle, tendon, ligament, capsule, cartilage, and bone

effect of load and under-load of specific structures factors influencing performance

Subjects for biomechanical studies of human movement

elderly vs. young kids vs. adults

women vs. men disable vs. able people athletes vs. sedentary people workers vs. non-workers

Methodology in Biomechanical Studies

anthropometric method performance limit evaluation kinesiological analysis

o kinematic analysis o kinetic analysis

biomechanical modeling method task analysis method

Physical Quantity

DefinitionDimension systemUnit conversionStandard prefix

Definition of Physical Quantity

Definition

the quantity that can be used in the mathematical equations of science and technology

When you can measure what you are speaking out and express it in numbers, you know something about it!! -- Lord Kelvin

Physical quantity is objective and measurable.

Dimension System

Seven Fundamental Quantities

Unit Name Unit Symbol

Length (L) meter m

Mass (m) kilogram kg

Time (T) second s

Electric Current ampere A

Temperature degree of Klevin

Luminous Intensity candela cd

Amount of Substance mole mol

Derived Quantities

displacement (d) velocity (v) = dx / dt acceleration (a) = dv / dt angular velocity () =d/ dt force (F) = ma moment of force (M): torque = Fd work (W) = Fd power (P) = W / t energy (E)=mc2 momentum = mv area (A) volume (V) density (D) = m / V

pressure (P) = F / A

Dimensionless Quantities

percentage percentile

the 5th percentile the 25th percentile = 1st quartetile the 50th percentile = 2nd quartertile (median) the 75th percentile = 3rd quartetile the 95th percentile the 99th percentile the 100th percentile = 4th quartetile

Unit Conversion

System of Unit

metric system CGS system MKS system SI system (Systeme International d'Unites; the International System of

Units)for details: http://physics.nist.gov/cuu/Units/index.html

English System

Unit conversion of mass

1 lb = 0.454 kg 1 kg = 2.205 lb 1 ounce = 28.350 g = 1/16 lb

Unit conversion of length

Metric English Decimal miles

          1 m                             3 ft   3.5 in

          -

        1 km              1093 yd 1 ft 10 in         0.621

      10 km   6 miles 376 yd 0 ft   4 in         6.214

      50 km 31 miles 119 yd 2 ft 10 in       31.069

Standard Prefix

Name yotta tera giga mega kilo hecto deka

Symbol Y T G M k h da

Value 1024 1012 109 106 103 102 101

Name deci centi milli micro naro pico yocto

Symbol d c m n p y

Value 10-1 10-2 10-3 10-6 10-9 10-12 10-24

Review of Mathematics and Mechanics

Plane GeometryPlane TrigonometryVectorBasic StatisticsBasic Dynamics

Plane Geometry

angles, sides, and area of a triangle

where

angles, sides, and area of a polygon radius, diameter, circumference, and area of a circle arc length and area of a sector of a circle

Plane Trigonometry

define an angle between 2 lines units used to measure angles

o degree (deg) o radius (rad) = 57.9º

orthogonal projections of a line segment onto two perpendicular axes defintion  of sine (sin) definition of cosine (cos) definition of tangent (tan) inverse trigonometric relationship：

o if sin= a     then   = sin-1 a

o if cos= a     then   = cos-1 a o if tan= a     then   = tan-1 a

law of sine:

                      law of cosine:

                      solution of an arbitrary triangle knowing 3 sides to determine the angles knowing 2 sides and 1 angle to find the rest of the angles and sides knowing 2 angles and 1 side to find the rest of the angles and sides area of an arbitrary triangle

o

o      where       

Vector

scalar vs. vector scalar quantities： quantities with magnitude only, e.g. speed of 5 m/s vector quantities： quantities with magnitude and direction, e.g. velocity

of 5 m/s to right vector addition or subtraction vector decomposition expressed by unit vectors

Review of Basic Statics

External ForcesInternal ForcesMechanical AdvantageCentroid

Equilibrium of the Force SystemFree Body DiagramForce Couple

External Forces

Gravitational force (Force of Gravity)

g= 9.81 m/s2 W = mg 1 kg = 9.81 N

Ground reaction forces

force exerted on a body by the ground Fx     Fy     Fz     Mx     My     Mz

Friction force

resistance of two moving objects Fs = ms N     where ms = coefficient of static friction Fk = mk N     where mk = coefficient of kinetic friction

Air or Water resistance

Fa = Av2c

Internal Forces

1. muscle force 2. forces from tendon, ligament, and other connective tissues

Mechanical Advantage (MA) of the Lever

Definition

the ratio between the length of the force arm and the length of weight arm

Types of Lever

1. first-class lever 2. second-class lever: force advantage 3. third-class lever:

advantage for speed or distance; most in open-kinematic chain motion

Centroid

Definition

the point that defines the geometric center of an object If the material composing a body is homogeneous, the weight can be neglected.

Equilibrium of the Force System

Definition

a condition in which an object is at rest if originally at rest, or has a constant velocity if originally in motion

Newton’s Laws of Motion

Only used for a particle with a mass and negligible size moving in a non-accelerating reference frame

first law (law of inertia) o A particle originally at rest, or moving in a straight line with a constant

velocity, will remain in this state provided the particle is not subjected to an unbalanced force.

o If the resultant force acting on a particle is zero, then the particle is in equilibrium.ie.    If FR = 0    then v= constant

second law (law of acceleration) o A particle acted upon by an unbalanced force experiences an acceleration

that has the same direction as the force and a magnitude that is directly proportional to the force

o F= k (dmv/dt) = ma third law (law of action and reaction)

o the mutual forces of action and reaction between two particles are equal, opposite, and colinear

o Faction= -Freaction

Equation of equilibrium

requires both a balance of forces, to prevent the body from translating with accelerated motion, AND a balance of moments, to prevent the body from rotating

FR = 0     and     MR = 0

Free Body Diagram (FBD)

Definition

a sketch of the outlined shape of the body which represents it as being isolated from its surroundings and all forces and couple moments that the surroundings exert on the body

Review of Basic Dynamics

Definition of DynamicsLaw of AccelerationMechanical Analysis Methods Used in Dynamics

Definition of Dynamics

Dynamics： the study of the motion of bodies and the unbalanced forces that produce motion

Law of Acceleration

Newton's 2nd Law (Law of Acceleration)：A particle acting upon by an unbalanced force experiences an acceleration that has the same direction as the force and a magnitude that is directly proportional to the force

F = m a    for a single particle only valid on an inertial frame of reference

Mechanical Analysis Methods Used in Dynamics

direct dynamics (forward dynamics)：mechanical analysis of a system that determines movement from forces

F known acceleration displacement e.g. using force plate to record forces

inverse dynamics：mechanical analysis of a system that determines forces from movement

displacement acceleration F e.g. using video-based motion analysis

relationship between forces and movement o A defined set of forces results in a specific movement. o A specific movement can be the result of an infinite number of

combinations of individual forces acting on a system

Properties of Biological Materials

Objectives: After studying this series, the students will be able to

1. identify the functions of the musculoskeletal system and its relationship to mechanical properties

2. describe the mechanical properties of different viscoelastic materials in the musculoskeletal system

3. describe the adaptive response of the viscoelastic materials under different loading conditions

4. identify the factors that affect the mechanical properties of the viscoelastic materials in the musculoskeltal system

Biomechanics of Bone

About Skeletal System and BoneMechanical Properties of the BoneAdaptive Response of the Bone Under Different LoadingDegenerative Changes in BoneFailure of the Bone

Biomechanics of Collagenous Tissues

About Collagenous TissuesCollagen FiberStrength of Tendons and LigamentsFactors Affecting the Strength of Tendons and Ligaments

Biomechanics of Cartilage

About CartilageMechanical Properties of the Articular Cartilage

Lubrication MechanismFailure of the Cartilage

Biomechanics of Skeletal Muscles

About Skeletal MuscleStructural Organization of Skeletal MuscleFactors Affecting Muscle StrengthOther Properties of Skeletal MuscleMuscle Remodeling

Biomechanics of Bone

About Skeletal System and BoneMechanical Properties of the BoneAdaptive Response of the Bone Under Different LoadingDegenerative Changes in BoneFailure of the Bone

1. Frankel V.H. & Nordin M (2001): Biomechanics of Bone. In Nordin M. & Frankel VH (eds): Basic Biomechanics of the Musculoskeletal System. Philadelphia, PS, USA: Lippincott Williams & Wilkins. pp.26-58.

2. Hall SJ, 2003. Basic Biomechanics, 4th ed. Boston, MA, McGraw-Hill. pp. 87-116.

3. Whiting W.C. & Zernicke R.F. (1998): Biomechanics of Musculoskeletal Injury. Champaign, IL, USA: Human Kinetics. pp.87-100.

4. Chaffin & Andersson, 1999.

About Skeletal System and Bone

Functions of the Skeletal System

mechanical functions o to protect vital organs o to provide rigid kinematic links o to provide attachments sites for muscle o to facilitate muscle action and bone movement

physiological functions

o to produce blood cells (hematopioesis) o to maintain calcium metabolism (mineral hemeostasis)

Unique Characteristics of the Bone

the hardest structure in the body o high content (60-70% of dry weight) of mineral materials e.g. calcium and

phosphate

metabolically active throughout life o excellent capacity for self-repair o changes in properties and configuration in response to changes in

mechanical loads, systemic hormones, and serum calcium levels

Structure of the Long Bone

structures based on position o diaphysis o epiphysis o metaphysis

types of bone tissue： based on porosity o cortical bone (compact bone)

5-30% of porosity o cancellous bone (trabecular bone or spongy bone)

30-90% of porosity

Composition of the Bone Tissue

cells o osteoblast： located on bone surfaceo osteocyte：  located in lacunao osteoclast： located on bone surface

extracellular matrix o mineralized type I collagen fibers： 90% of the extracellular matrix and

25-30% of dry weight o ground substance： glycosaminoglycans (GAGs) o water： 25% of total weight and 85% in the organic matrix

Fundamental Unit： Osteon (Haversian System)

size： ~200  in diameter

component： o Haversian canal： a canal, in the center of the osteon, containing blood

vessels and nerves

o interstitial lamellae： concentric rings  of mineralized matrix surrounding the Haversian canal

o lacunae： the interface between lamellae, containing osteocyte and canaliculi

o cement line： boundary of the osteon

Bone Modeling and Remodeling

bone modeling： the process by which bone mass increased to alter the size, shape, and structure of the bone (new bone formation)

bone remodeling： the process through which bone mass adapts, with altering its size, shape, and structure, to the mechanical demands placed upon it (activation-resorption-formation process of bone)

o step I： activation of osteoclasts o step II： resorption the existing bone by osteoclasts o step II： new bone deposit by osteoblasts

differences between modeling and remodeling

Modeling Remodeling

process continuous cyclical

stimulus for activation not required required

coupling of formation and resorption system? local

Wolff's Law (1892)o static stress model o Bone is deposited where needed and resorbed where not needed. o current concept： Bone modeling and remodeling occurs in response to

the mechanical demands placed upon it.

Mechanical Properties of the Bone

Bone Strength

As the load increases, load and deformation increase in a relatively linear relationship, obeying Hooke's law and, after the yield point, smaller and smaller increases in load produce greater and greater deformation

ultimate stress the bone can sustain before failure o failure point in the stress-strain curve

ultimate strain the bone can sustain before failure energy the bone can store before failure

o size of the area under the entire curve

If the applied load is at the plastic region and removed later, the bone does not return to its original configuration (hysteresis)

Bone Stiffness

elastic modulus： the slope of the stress-strain curve in the elastic region metal >> glass > bone

Anisotropic Behavior of the Bone

anisotropy： the property of a material which exhibits different mechanical properties when loaded in different direction

Stiffness with respect to tension is maximal for axial loads and minimal for perpendicular loads.

for ultimate stress of cortical bone: compression > tension > shear

Adapted from Nordin M & Frankel VH (2001). Basic Biomechanics of the Musculoskeletal System.(p.54)

Bone Geometry

In tensile or compressive load, the load to failure and the stiffness are proportional to the cross-sectional area of the bone

moment of inertia o in a rectangular beam： I = BH3/12 o in a tube-like bone： I = mr2

Adaptive Response of the Bone Under Different Loading

Factors that affect the structure, composition, and quality of bone

external factors o mechanical loads：  gravity, physical activity, or immobilization

internal factors o systemic calcium level： nutrition o hormone level： gender, growth, menopause, or degeneration

Gravity

positive correlation between body weight and bone mass fast loss of bone mass in the weight-bearing joints of astronauts

Muscle Activity

contraction of muscle alters the stress

distribution in the bone

contraction of the gluteus medius

muscle produces great compressive

stress on the superior cortex of the

neck of the femur, neutralizing the

tensile stress and thereby allowing

the femoral neck sustain more load

Strain Rate Dependency

The stiffness of a bone changes with the rate of loading

when loads are applied at higher rate within the physiological limit, the bone o becomes stiffer o sustains a higher load to failure o stores more energy before failure

when a bone fractures, the stored energy is released. o single bone crack for a low-energy fracture o comminuted fracture of bone for a higher-energy fracture o severe destruction of bone before failure

Fatigue of Bone Under Repetitive Loading

Stress fracture may occur when a load of lower magnitude is applied repetitively. o march fracture

o spondylolithesis

Physical Activity

relationship between physical activity and bone mass o growing bone responds to low or moderate exercise through significant

increase in new cortical and trabecular bone o a threshold of physical activity exists above which some bone respond

negatively o moderate to intense physical training can generate modest increase in bone

density (1-3%) in men and premenopause women o the long-term effect of exercise are retained only by continuing to exercise o individuals with extremely low initial bone mass may have more to gain

from exercise than those with moderately reduced bone mass

effects o increase bone mass o increase cortical thickness o increase bone mineral content

Immobilization or Implantation

bed rest： ~ 1% of loss of bone mass per week

immobilization in body cast： a threefold decrease in load to failure and energy storage capacity in the vertebrae that have been immobilized in body cast for 60 days

immobilization with metal implant

o decrease in bone diameter and bone strength due to resorption of the bone under the metal plate

o increase in bone deposit at the bone-screw interface

Adapted from Nordin M & Frankel VH (2001). Basic Biomechanics of the Musculoskeletal System.(p.54)

Artificial Defects

stress raiser： defect length < bone diameter

o the stresses concentrate around the defect

o the weakening effect is marked under torsion loading (60% of decrease)

o example： compression hip screw

open section defect：  defect length > bone diameter

o only the shear stresses at the periphery of the bone resist the torsion

o the shear stresses at the interior of the bone run in the same direction of the

torsion.

o example： bone graft

Degenerative Changes of the Bone

progressive loss of bone density (osteoporosis) with normal aging process

structural changes with agingo marked reduction in amount of the cancellous bone o decrease in the diameter and thickness of the cortical bone due to resorbed

longitudinal trabeculae

changes in mechanical properties

o decrease in strength, deformation ability, and energy storage capacity

o the ultimate stress was approximately the same for the young and the old bones

o the old bone can withstand only 1/2 of

Adapted from Nordin M & Frankel VH (2001). Basic Biomechanics of the Musculoskeletal

the strain that the young bone can

aggravating factors o gender： Both men

and women lose cortical bone at the same rate but women lose trabecular bone more rapidly than men

o ageo post-menopause：

1.5-3% of loss per year after menopause

o endocrine abnormality o inactivity o disuse

o calcium deficiency

System.(p.54)

Failure of the Bone

Failure of bone may occur when the applied stresses exceed the ultimate strength limit, which may result from excessive stresses, or weak material, or both.

possible causes of bone failure o excessive acting forces o unfavorable acting moments o small bone dimension o excessive repetition of load application

osteoporosis o a disease or phenomenon marked by reduced bone mineral mass and then

changes in bone geometry o a function of normal aging process o the amount of bone mass at one site is not necessarily correlated to that at

the other sites

Procedure for drawing a free body diagram

1. imagine the body to be isolated from its surroundings and sketch its outlined shape

2. identify all the external forces and couple moments that act on the body, including applied loads, reaction occurring at the supports or at points of contact with other bodies, and the weight of the body

3. label all forces and couple moments with proper magnitudes and directions

Force Couple

two parallel forces that have the same magnitude, opposite directions, and are separated by a perpendicular distance

FR = 0    but

The only effect of a couple is to produce a rotation or a tendency of rotation in a specific direction

A couple moment is a free factor which act at any point since the couple moment depends only on the position vector directed between the forces and not the position vectors directed from the point O to the force

Biomechanical Measurements

Objectives: After studying this topic, the students will be able to 1. identify the commonly used biomechanical instruments 2. describe the parameters used in biomechanical studies 3. compare the differences among different instruments that have the same function

Measurements of Stress and Strain

Relationship Between Force and BodyStressStrainStress-Strain CurveMeasurements of Stress and Strain

Measurements of Muscle Strength

Evaluation of Muscle StrengthMuscle Strength Measurement SystemMeasurement of Muscle Activity

Kinematic Analysis

Rigid Body KinematicsMeasurement of Kinematic VariablesProcessing of Raw Kinematic DataDerived Kinematic Variables

Anthropometric Measurements

Application of Anthropometry in BiomechanicsMeasurement of Body Segment LengthMeasurement of Body Segment MassMeasurement of Center of MassMeasurement of Moment of Inertia

Kinetic Analysis

About KineticsMeasurement of Kinetic DataBiomechanical ModelsDerived Kinetic Variables

Measurements of Stress and Strain

Relationship between force and bodyStressStrainApplication of Stress-Strain CurveMeasurements of Stress and Strain

1. Frankel V.H. & Nordin M (2001): Biomechanics of Bone. In Nordin M. & Frankel VH (eds): Basic Biomechanics of the Musculoskeletal System. Philadelphia, PS, USA: Lippincott Williams & Wilkins. pp.26-58.

2. Chaffin & Andersson, 1999: 101-124, 146-158, 167-170

Relationship Between Force and Body

Force

an action that changes the state of rest or motion to which it is applied external force vs. internal force strength： maximum force that a body can be loaded stress： load per unit

Body

an object that may be real or imaginary but represents a definite quantity of matter (mass), with certain dimensions, occupying a definite position in space

rigid vs. deformable body o rigid body： no relative displacement can occur between the particles

when forces are applied to the body o deformable body： the adjacent particles can be displaced relative to one

another when the forces are applied to the body

Effect of forces on a body

in dynamic sense o linear motion (translation) in the direction of net force o rotary motion (rotation) in the direction of net moment

in static sense o static equilibrium if the body is rigid or if the stress is low or if the

duration is short o deformation (shape and size changes) if the body is deformable

long-term biological changes o growth o injuries o degeneration

Mechanics of Materials

a branch of applied mechanics that develops relationship between the external loads applied to a deformable body and the internal forces acting within the body

o deformation of the body o body's stability when it is subjected to external loads

Stress

Definition of stress

the intensity of force per unit area of the tissue o normal stress： the intensity of internal force acting perpendicular to a

plane = F / Aassumptions：

1. the material is homogeneous 2. the cross-sectional area at each point is the same3. the strain is even 4. the resultant load is passing through its centroid

o shear stress： the intensity of internal force acting tangent to a plane = V / A

SI unit：  Pa (Pascal) = N/m2 USCS unit： psi = lb/in2 tensile stress is positive while compressive stress is negative

Types of stress

tensile stress (tension) o one kind of normal stress that is applied perpendicular to the body and

taks it apart o the body tends to be elongated in the direction of the applied forces

compressive stress (compression) o one kind of normal stress that is applied perpendicular to the body and

puts it together o the body tends to be shrink in the direction of the applied forces

shear stress o the force acting in directions tangent to the area resisting the force o also named as tangential force

bending stress

o failure under bending stress three point bending: failure at the point of the middle force four point bending: failure at the weakest point

torsion stress： loads parallel to the surface of the structure and in the same direction, resulting in the tensile stresses and strains at one side and compressive stresses and strains at the other side of the structure; there are no stresses and

strains along the neutral axis

combined stress

Strain

Definition of stain

the extent of deformation relative to its initial condition o normal strain： the ratio of the change in length to the original length

= L / L o shear strain： the intensity of internal force acting tangent to a plane

= d / h

unit  normal strain = % (dimensionless quantity) or mm/m        shear strain = rad

tensile strain is positive while compressive strain is negative

Factors affecting the extent of deformation

mechanical properties size of the body shape of the body temperature humidity magnitude, direction, and duration of applied forces

Application of Stress-Strain Curve

Stress-Strain curve

elastic region： When the magnitude of the stress is small, the elastic force can be represented by the relation for an ideal spring (Hooke's law), i.e., the elastic force exerted by the viscoelastic material is proportional to the amount of deformation

o F = k xwhere F = elastic force            k = spring stiffness which is a constant            x = amount of deformation

plastic region yield point failure point

Strength

maximum stress that a body can be loaded (ultimate stress) maximum strain that a body can be deformed (ultimate strain) maximum energy stored

Stiffness

modulus of elasticity (Young's modulus)： for both tensile and compression stress

o the ratio of the stress to strain in the elastic region of the stress-strain curve

E =

o named after Thomas Young (1773-1829, English scientist) o SI unit： Pascal o USCS： psi

Hooke's law ： only for tensile stress o for an elastic material, the strain is a linear function of the stress applied o named after Robert Hooke (1653-1703, English scientist)

modulus of rigidity (shear modulus of elasticity)

G =       where = d / h

SI unit： Pascal USCS： psi

Poisson's ratio

When a material is under a tensile stress, the tensile strain and the lateral contraction is proportional.

= lateral / longitudinal

o assumptions： the material is homogeneous the material is isotropic

o named after Simeon Denis Poisson (1781-1840)

unit： dimensionless 0 ½ relationship between the modulus of elasticity and that of rigidity

G = E / 2(1 + )

Brittle vs. Ductile materials

brittle material： the material whose failure occurs at a very low strain, e.g. ceramic or glass ductile material： the material that is able to resist a very high strain before failure, e.g. aluminum alloys

Creep Phenomenon (潛變現象)

progressive deformation of a material with time as the amount of load remains constant

Load Relaxation Phenomenon (鬆弛現象)

progressive decrease in load with time as the deformation of the structure remains constant

Hysteresis (遲滯現象)

Energy stored in a viscoelastic material when a load is given and then relaxed.

aged heel pad： poor ability to absorb the shock

Elastic vs. Plastic materials

elasticity： the ability of a body to resume its original size and shape on removal of the applied loadsNOTE： the elastic material is not necessary to have a linear relationship on the stress-strain curve plasticity： When a tissue is stretched to the plastic region and then released, the tissue will assume a new resting length that is longer than the initial length because of plastic changes in its structure. clinical application： flexibility exercise or joint mobilization 

Allowable stress

When a structural member or mechanical element is designed, the stress must be restricted in a material to a level that will be safe. This is the allowable stress. factor of safety (F.S.)： the ratio of a theoretical maximum load that can be carried by the member until it fails in a particular manner divided by an allowable load

F.S. = Ffail / Fallow

the factor of safety is chosen to be greater than 1 to 10 in order to avoid the potential for failure

Measurements of Stress and Strain

Tension test

to apply a tensile load on the material to be tested and measure the strain using extensometer

nominal strain： L / initial L natural strain： L / final L

Compression test

to apply a compressive load on the material to be tested and measure the strain using extensometer

ASTM

American Society for Testing and Materials

Biomechanics of Collagenous TissuesAbout Collagenous TissuesCollagen FiberStrength of Tendons and LigamentsFactors Affecting the Strength of Tendons and Ligaments

1. Nordin M, Lorenz T, Campello M (2001): Biomechanics of tendons and ligaments. In Nordin M & Frankel VH (eds): Basic Biomechanics of the Musculoskeletal System, 3rd ed. Philadelphia, PA, USA: Lippincott Williams & Wilkins. pp.102-125.

About Collagenous Tissues

Classification of collagenous tissues

dense connective tissue o ligament： withstanding tensile stress

to augment capsule function for joint stability to guide joint motions to check excessive motion (static restraint)

o tendon： withstanding tensile stress to attach muscles to bone to transit tensile loads from muscle to bone (dynamic restraint)

loose connective tissues o capsule： withstanding tensile stress

to augment joint stability to check excessive motion

o skin： withstanding tensile stress to protect internal structures to check excessive motion

o heel pad： withstanding shear stress to provide shock absorption due to abundant adipose tissue inside to resist shear stress

cartilage o articular cartilage： withstanding compressive/ shear stress

to absorb the compressive loads to allow motions between joint surfaces with minimal friction to resist shear stress

o fibrocartilage： withstanding compressive/ shear stress to link two bony structure to resist the compressive and/or shear loads

Components of Collagenous Tissues

cell： ~20% of total volume o fibrobalst o chondrocyte

extracellular matrix： ~80% of total volume o fiber

collagen fiber： for strength elastin fiber： for flexibility retin fiber： for mass

o ground substance： PGsGAG bonded to a core protein, bind to a long hyaluronic acid (HA) chain

o water： ~70% of extracellular matrix

Collagen Fibers

Structure of collagen fiber

the most abundant protein in the body (~1/3 of total protein in the body)

tropocollagen： 3 procollagen polypeptide chains ( chains) coiled about each other into a left-handed triple helixes

collagen molecule：length: ~280 nmdiameter: ~1.5 nm

collagen fibril：parallel packing of several collagen molecules with cross-linksdiameter：110-120 nm in young adults

Types of collagen fiber

Type I： found in bone, tendon, ligament, and skin Type II： found in articular cartilage, nasal septum, and sternal cartilage Type III： found in loose connective tissues, the dermis of the skin, and blood vessel walls

Tensile strength of collagen fiber

closely associated with the number and quality of the cross-links within and between the collagen molecules

stress-strain curve for an ideal collagen fiber o When the magnitude of the tensile strength is relatively small, a toe region

is present because the relaxed, wavy collagen fiber is straightenedo When the magnitude of the tensile strength is small, the elastic behavior of

the collagen fiber follows Hooke's law

o rupture as the tendon of the extensor digitorum longus is stretched by about 15% of its initial length or as the medial collateral ligament is stretched by about 20%

sources of tensile stress o for ligament： distraction of articular surfaces from mechanical actions o for tendon

passive increasing joint angle active shortening of muscle fibers

Compressive Strength

only able to resist low compression loads buckle under compression load slenderness ratio

ratio of length to thickness

Strength of Ligaments and Tendons

Components of Connective Tissue

cell： 20% o fibroblast

matrix： 80% o water： 60-70% for ligaments o collagen： 70-80% of dry weight; molecular cross-link

Components of Connective Tissue

cell： 20% o fibroblast

matrix： 80% o water： 60-70% for ligaments o collagen： 70-80% of dry weight; molecular cross-link

Factors Affecting Strength of Tendons and Ligaments

Age-Related changes

before adolescent： ligament strength < bone strength maturation

o increase in # and quality of cross-links o increase in diameter of collagen fibril o increase in tensile strength and stiffness

aging o decrease in # of collagen fibers o collagen fibril concentration in the collagen fibers： controversial o decrease in tensile strength and stiffness

Pregnancy and the postpartum period

increase in laxity of the tendons and ligaments in pubic area decrease in tensile strength of tendons and ligaments during later stages of

pregnancy and the postpartum period decrease in stiffness during the early stage of postpartum period

Mobilization vs. immobilization

remodeling in response to the mechanical demands placed upon it physical activity

o mechanical strength： becomes stronger and stiffer o the diameters of the collagen fibers： increase

immobilization o mechanical strength： weaker and less stiff o the diameters of the collagen fibers： controversial

reconditioning after immobilization o do not return to normal at one year after injury

adapted from Noyes FR (1997). Clin Orthop 123, 210-242.

Steroids vs. nonsteroidal anti-inflammatory drugs (NSAID)

steroid o inhibit collagen synthesis o decrease in stiffness, ultimate stress, and energy absorption ability o time- and dosage-dependent

NSAID o increase tensile strength o increase cross-linkage of collagen molecules

Reconstruction surgery

tendon graft ： not the same as normal in mechanical properties

Pathological conditions

diabetes mellitus

pathology proportion in DM

tendon contracture 29%

tenosynovitis 59%

joint stiffness 40%

capsulitis 16%

hemodialysis

pathology proportion in hemodialysis

tendon rupture 36%

hyperlaxity of tendons or ligaments

74%

patellar tendon elongation 49%

articular hypermobility 51%

Biomechanics of CartilageAbout CartilageMechanical Properties of the Articular CartilageLubrication MechanismFailure of the Cartilage

1. Mow VC & Hung CT (2001). Biomechanics of articular cartilage. In Nordin M & Frankel VH (eds): Basic Biomechanics of the Musculoskeletal System, 3rd ed. Philadelphia, PA, USA: Lippincott Williams & Wilkins. pp.60-100

2. Chaffin DB, Andersson GBJ,  Martin BJ (1999). Occupational Biomechaincs, 3rd ed.  New York, John Wiley & Sons.

About Cartilage

Types of the Cartilage

hyaline cartilage (articular cartilage) fibrocartilage

Characteristics of articular cartilage

1-5 mm hyaline cartilage： dense connective tissue

translucent： no blood vessels, lymphatic channel, or nerve innervation

How does the cartilage obtain nutrition and remove metabolites?

components： low cellular density o condrocyte： < 10% o extracellular matrix

collagen fibers ground substance： proteoglycans water： 65-80%： interstitial fluid movement is important in mechanical property

and joint lubrication

Functions of articular cartilage

spread load over a wide area allow movement of two articulating bones with minimal friction and wear deformed under loading, exuding synovial fluid

Collagen fibers in articular cartilage

biological unit： tropocollagen mechanical properties: tensile stiffness and strength distribution of collagen in articular cartilage

o superficial tangential zone： parallel to the articular surface o middle zone： randomly distributed o deep zone： perpendicular to cartilage-calcified cartilage interface (tidemark)

Proteoglycans in articular cartilage

basic unit：glycosaminoglycans (GAGs)

mutually repelled between neighboring GAGs

proteoglycan o hyaluronic acid o link protein

o GAG chains：200-400 nm in length

protein core chondroitin sulfate chains (CS)：  decrease with aging keratan sulfate chains (KS)： increase with development and aging

CS/KS ratio：  10：1 at birth and 2：1 in adult 

Mechanical Properties of the Articular Cartilage

Biphasic creep response

exudation of fluid： up to 50% of the fluid can be squeezed out creep phenomenon of the collagen fiber

Biphasic load relaxion phenomeon

stress increased as fluid exudation stress decreased as fluid redistribution

Non-linear permeability

Rate dependency of the material behavior

rapid loading： like elastic material slow loading： like viscoelastic

Lubrication Mechanism

Boundary lubrication

the chemical adsorption of a monolayer of lubricant molecules onto the articular surfaces depends on the chemical property of lubricants

Fluid film lubrication

a much thicker film of lubricant causing a relatively large separation of the two bearing surface Elastohydrodynamic fluid films of both the sliding and the squeeze type probably play an

important role in lubricating the joint With high load and low speeds of relative motion, the fluid film will decrease in thickness as the

fluid is squeezed our from between the surfaces. Under very high loading conditions, the fluid film may be eliminated, allowing surface-to-surface

contact

Failure of the Cartilage

mechanical loading and unloading prevent cartilage degeneration

limited ability to remodel itself if articular cartilage is damaged

types of failure interfacial wear： wear resulting from the direct interaction of bearing surfaces

adhesion or abrasion wear only takes place in an impaired or degenerated joint traumatic arthritis

fatigue wear： wear resulting from bearing deformation under repetitive loads failure of collagen-PG matrix + loss of PG e.g. chondromalacia patella

damage from a high impact

loads leading to wear

acute injury： active loading or impact loading chronic injury： interfacial or fatigue loads

Biomechanics of Skeletal Muscle

About Skeletal MuscleStructural Organization of Skeletal MuscleFactors Affecting Muscle StrengthOther Properties of Skeletal MuscleMuscle Remodeling

Objectives: After studying this topic, the student will be able to

1. explain the relationships of fiber types and fiber architecture to muscle function 2. describe the effects of the length-tension and force-velocity relationships 3. identify the factors affecting the mechanical properties of the skeletal muscles

1. Hall SJ, 2003. Basic Biomechanics, 4th ed. Boston, MA, McGraw-Hill. Chapter 6, pp.145-182

2. Lorenz T & Campello M: Biomechanics of skeletal muscle. In Nordin M & Frankel VH, 2000.  Basic Biomechanics of the Musculoskeletal System, 3rd ed. Philadelphia, PA, USA: Lippincott, Williams & Wilkins. Chapter 6

3. Chaffin, D.B., Andersson, G. B., Martin, D.J., 1999.  Occupational Biomechanics, 3rd ed.  John Wiley & Sons.

About Skeletal Muscle

Please review the basic concepts of muscle in Kinesiology class.

Functions of skeletal muscle

To move the body limb by creating motion To provide strength by generating active force To protect joints by absorbing shock specific functions of connective tissues within muscle

To provide gross structure to muscle To generate passive tension against stretch To transmit force to the bone and across the joint

Basic behaviors of skeletal muscle

muscle fiber extensibility： the ability to be stretched or to increase in length elasticity： the ability to return to the original length after a stretch irritability： the ability to respond to a stimulus e.g. action potential or mechanical force contractility： the ability to develop tension* NOTE： Increase in tension does not imply decrease in muscle length.

tendon, fascia, or aponeurosis viscoelasticity non-contractility

NOTE： Contractile tissue described by J. Cyriax  indicates muscle fibers and tendons although tendons do not have any contractibility.

Mechanical model of a muscle

The musculotendinous unit behaves as a contractile component in parallel with one elastic component and in series with another elastic component

contractile component： muscle fiber series elastic component (SEC)： tendon

parallel elastic component (PEC)： muscle membrane or fascia The viscoelasticity of skeletal muscle is primarily from SEC

Structural Organization of Skeletal Muscle

Muscle fiber

Motor unit

Types of muscle fibers

Fiber architecture

parallel fiber arrangement： parallel to the longitudinal axis of the muscle longitudinal： sartorius quadrate or quadralateral： rhomboid triangular or fan-shaped： pectoralis major fusiform or spindle-shaped：biceps brachii

pennate fiber arrangement： at an angle to the longitudinal axis of the muscle, unipenniform： extnesor digitorum longous bipenniform： flexor hallucis longus multipenniform： middle deltoid

effect of the angle of pennation the greater the angle of pennation, the smaller the amount of effective force transmitted to the tendon the angle of the pennation increases as tension progressively increases in the muscle fibers

The pennate arrangement will allow the packing of more fibers given the same space.

Factors Affecting Muscle Strength

Muscle strength

the force generation capability of an entire muscle group at a joint torque = the production of force and the moment arm stabilization component vs. distraction component

dependent on cross-sectional area and training state

Length-Tension Relationship

Force-Velocity Relationship

Force-Time Relationship

Stretch-Shortening Cycle (SSC)

a pattern of muscle contraction which is characterized by eccentric contraction followed immediately by concentric contraction When a muscle is stretched just prior to contraction, the resulting contraction is more forceful than in the absence of the pre-stretch. possible contributors to forceful tension development

elastic recoil effect of the series elastic component of the actively stretched muscle stretch reflex of the forced lengthening muscle

example: wind-up during baseball pitching or jumping

Electromechanical Delay (EMD)

time interval between arrival of neural stimulus and tension development by the muscle, usually approximately 20-100 ms

EMD in FT fibers < that in ST fibers EMD in kids > that in adults EMD in a resting muscle > that in an activated muscle not related to muscle length, contraction type, contraction velocity, and fatigue

is needed for the contractile component of the muscle to stretch the SEC

compared with anticipatory postural adjustment

Body Temperature

Muscle function is most efficient at 38.5°C (101°F). elevated muscle temperature shift in force-velocity curve

increased maximum isometric tension nerve conduction velocity frequency of stimulation muscle force enzyme activity efficiency of muscle contraction elasticity of collagen extensibility of muscle muscle force

increased maximum velocity of muscle shortening requiring less motor unit to sustain a given load

body temperature too high heat exhaustion or heat stroke

Other Properties of Skeletal Muscle

Muscle power

the product of muscle force and contraction velocity maximum power at ~1/3 of maximum velocity and ~1/3 maximum concentric force peak power productiontype IIb ： type IIa ： type I = 10 ： 5 ： 1

Muscle endurance

the ability of the muscle to exert tension over a period of time the longer the time tension is exerted, the greater the endurance

Muscle fatigue

reduction of muscle force production capability and contraction velocity, as well as prolonged relaxation of motor units between recruitment dependent on muscle itself, exercise duration, fiber type composition, and/or pattern of motor unit activation for a single muscle fiber, fatigue indicates an inability to develop tension when it is stimulated Causes： reduction in the rate of intracellular calcium release and uptake by sacroplasmic reticulum

Muscle Remodeling

Muscle Hypertrophy

by physical training cross-sectional area of muscle fibers number of muscle fibers change in proportion of muscle fiber types

by electric stimulation

Muscle Atrophy

cross-sectional area of fibers number of muscle fibers aerobic capacity by changing the proportion of muscle fiber types

sedentary people：# of type I fibers athletes： fiber type affected by that sport

Measurements of Muscle StrengthEvaluation of Muscle StrengthMuscle Strength Measurement SystemMeasurement of Muscle Activity

1. Chaffin, D.B., Andersson, G. B., Martin, D.J., 1999.  Occupational Biomechanics, 3rd ed.  New York, John Wiley & Sons. pp. 101-124, 146-158

2. Nigg B.M. & Herzog W., 1999. Biomechanics of the Musculo-Skeletal System. New York, John Wiley & Sons. pp.349-371

Evaluation of Muscle Strength

Force generated by human body

muscle force： the active force generated by muscle contraction in response to resist the external forces or other internal forces connective tissue tension： the passive forces generated from the tension of the connective tissues, such as tendons, ligaments, fasciae, capsule, or skin

Related terminology

muscle strength： the force generation capability of an entire muscle group at a joint

tnesile strength： maximum force that a body can be loaded to resist a tensile stress

muslce power： the product of muscle force and contraction velocityNOTE： This term is also used by clinicians to indicate muscle strength

muscle endurance： the ability of the muscle to exert tension over a period of time

Types of muscle exertion

Classification of Muscle Strength

Type of Muscle Contraction

Definition

static strength e.g. holding or carrying

isometric contraction muscle contraction without changing its length

dynamic strength e.g. lifting or push-and-pull

isotonic contraction muscle contraction with a constant  tension (??)

isokinetic strength muscle contraction in a constant speed

isoinertial strength muscle contraction in response to a constant, external load

Variables used to represent muscle strength

peak force at maximum isometric contraction： static strength to maintain 6 sec and average the middle 3-sec data at least > 2 min resting interval between contractions in order to prevent

fatigue closely related to verbal commands and/or visual feedback

peak torque at isokinetic or isoinertial contraction： dynamic strength closely related to type and velocity of contraction

rate of tension development： static strengtho slope of force-time curve before the maximum strength reaches o ~ 3 times faster for the maximum contraction compared to the 25%

submaximum contraction

o closely related to verbal command o maximum and hold o as fast as possible

muscle activity at maximum voluntary exertion level： static strength

Muscle Strength Measurement System

Localized static strength measurement systems

hand-held dynamometer o electronic strain

gauges o measuring peak

force during isometric contraction

o advantages： safe, reliable, and practical

seated strength tester

Localized dynamic strength measurement systems

Cybex isokinetic system measured by dynamometer measuring muscle moment

(torque)

Kin-Com isokinetic system measured by load cell

measuring muscle force

Whole-body static strength measurement systems

position of load cell can be adjusted to different heights position of load cell can be adjusted to different directions load cell can be attached with different handles

Whole-body dynamic strength measurement systems

isokinetic lift strength tester o Using simple electromechanical measuring system for performing a lifting

task o components of the system

o electronic load cell and velocity transducer connected to a readout device

o constant-velocity motor with adjustable speed control Isoinertial strength test (Liftest test)

o lifting loads with different weights until one’s psychophysiological limit is reached

o used for personnel selection in US military department

Factors affecting muscle strength

gender static strength: female = 65-85% of male knee isokinetic strength: 70-75% of male

age greatest around late 20’s at 40 y/o, 5% loss of young at 60 y/o, 20% loss of young

anthropometric data body height lean body weight cross-sectional area of muscle

pain physical training immobilization or bed-ridden

Measurement of Muscle Activity

Muscle activities and EMG signals

EMG signal： changes in electrical potential across the muscle fiber membrane resting membrane potential of a muscle fiber = -90mV action potential of a muscle fiber = 30-40 mV motor unit action potential (MUAP)： electric potential from the depolarization

of a motor unit

Electromyography

types of EMG o surface electrode o needle electrode： indwelling electrode o wire electrode： indwelling electrode

variables obtained from EMG raw EMG： firing pattern integrated EMG (IEMG)

o amplitude: RMS (root mean square) o frequency analysis

Relationship between EMG activity and muscle force

an increase in tension results from an increase in myoelectric activity not a linear relationship EMG records the recruitment of motor unit

Relationship between EMG signals and muscle fatigue

increase in amplitude but decrease in frequency with fatigue mean frequency of EMG activity when the muscle is at rest is twice that found

when the muscle is fatigue

Kinematic Analysis

Rigid Body KinematicsMeasurement of Kinematic VariablesProcessing of Raw Kinematic DataDerived Kinematic Variables

1. Winter, D.A., 1990. Biomechanics and Motor Control of Human Movement, 2nd ed. New York, Wiley & Sons. pp. 11-50

2. Chaffin, D.B., Andersson, G. B., Martin, D.J., 1999.  Occupational Biomechanics, 3rd ed.  New York, John Wiley & Sons.  pp. 131-146. 

3. Hall, 2003：Chapter 2, 10 (pp.318-329), and 11

Rigid Body Kinematics

Application of Rigid Body Kinematics

rigid body kinematics： the study of motion of a rigid body without concerning its causes (e.g. forces) using 2D or 3D markers to determine limb segment positions and orientation

assumptions 1. body segment acts like a rigid body 2. the human body is a system of mechanical links 3. each link has known physical size, mass, and form

examples： reach forward movement can be regarded as a 3-segment movement

contributors

Marrey Eadweard Muybridge： a British landscape photographer

Reviews of kinematics terminology

types of motion： linear vs. angular motion reference system： relative vs. absolute reference system plane of motion：3 cardinal planes axis of motion：3 axes

Kinematic variables

variable linear kinematics angular kinematics

position r (x, y, z) displacement s = r

velocity v = dr /dt = d  /dt

acceleration a = dv /dt = d  /dt

Total description of a body segment in space

position (x, y, z) of segment COM or center of rotation of the joint

linear velocity ( ) of segment COM or center of rotation of a joint

linear acceleration ( ) of segment COM or center of rotation of the joint angle of segment in two planes (xy, yz) angular velocity of segment un two planes (xy, yz) angular acceleration of segment un two planes (xy, yz)

Source of errors in application of rigid body kinematics

not always represent true skeletal locations relative errors： the relative movement of two markers with respect to each other

resources： skin movement and movement of underlying bony structure error reduction：

invasive marker placement mathematical algorithms: smoothing techniques marker attachment system

absolute errors： the movement of one specific marker with respect to specific bony landmarks of a segment errors from inadequate placement of markers

Measurement of Kinematic Variables

Direct measurement techniques

universal goniometer： a protractor with two long arms source of errors： the location of the goniometer, the palpation of landmarks, and the estimation during reading

electric goniometer (elgon) first developed by Karpovich in the late 1950's a goniometer with an electrical potentiometer at its axis continuous graphic recording of relative joint angle advantages

inexpensive immediate output planar rotation is recorded independent of the plane of movement of the joint

disadvantages relative data time consuming to fit and align too many straps and cables if a large number are fitted most joints do not move as a hinge cost for recorder or analog-to-digital converter

inclinometer： a gravity-based goniometer source of errors

the location of the inclinometer the different shape of muscles

accelerometer： a continuous recording of segment acceleration advantages

inexpensive immediate output

disadvantages relative data cost for recorder or analog-to-digital converter too many straps and cables if a large number are fitted sensitive to shock and easily broken noises increase during rapid movement or movement involving impact

system combining photocells, light beams, and timer： two or more records of time when each photocell is intercepted by the light beam and then the motion velocity can be calculated as the distance between two photocells divided by the recorded time.

Optoelectric Image Measurement Techniques

types of marker LED (light-emitting diode) reflective markers

sampling frequency of camera 60 Hz 120 Hz 240 Hz 1000 Hz

advantages both absolute and relative reference system data unlimited markers minimal movement encumbrance able to be re-played frame by frame saving storage

disadvantages expensive need well-trained persons time consuming laboratory used only

considerations the clarity of the captured image the number of cameras used： more than 2 cameras are needed for a 3-D image the placement of cameras

commercialized video spot locator system ViconTM, Peak PerformanceTM, Motion Analysis SystemTM, Visual3DTM, MacReflexTM, etc. selection criterion： the time required to accurately track sequences of markers from multiple cameras

Other image measurement techniques

cinematography： 8/ 16 mm movie camera television-based  video system： 50/ 60Hz video camera

advantages： widespread availability, durability, and easy in use photogrammetric system multiple exposure ultrasound-based image system

Zebris advantages

relatively inexpensive good reliability

limitations low sampling frequency encumbrance of control wires to the motion

electromagnetic-based image system Flock of Birds (144 Hz) advantages

no marker occlusion acquisition of position and orientation (6 dimensions) accuracy  1.8 mm for position and 0.5º for orientation

limitations sensitive to ferrous and conductive metals in the environment more variability in angular displacement (~ 6º) and velocity encumbrance of control wires to the motion

electromechanical body suits

Processing of Raw Kinematic Data

Source of noises

electronic noise in optoelectric devices spatial precision of the TV scan or film digitization system human error in film digitizing

Time-domain analysis

the signals are expressed as a time-dependent waveform an alternating signal is one that is continuously changing with time types of alternating signal (AC component)

periodic random a combination of periodic and random

Frequency-domain analysis

the signals are expressed as a frequency-dependent waveform, which can be the sum of a number of sine and cosine wave V(t) = VDC + V1sin(0t + 1) + V2sin(20t + 2) + + Vnsin(n0t + n) where 0 = 2 f0            n = the phase angle of the nth harmonic

Fourier series： the sum of the proper amplitudes of the harmonics Harmonic analysis (Fourier Transformation)： the mathematic process to transform  given time-varying data to their frequency components

Digitization

Why needs digitalization? Continuous signal measurement is the most desirable because no data are lost. However, computer-based systems require periodic measurements since by their nature, computers can only accept discrete numbers at discrete intervals of time

analog to digital converter Analog signals are continuous in time and amplitude. Digital signals are discrete in time and amplitude.

Sampling Theorem

the process signal must be sampled at a frequency at least twice as high as the highest frequency present in the signal itself If the signal is sampled at a too-low frequency, the aliasing error are obtained.

Data Smoothing

assumption: the trajectory signal has a predetermined shape equation:

Data Filtering

Most of the signals from daily human movements are contained in the lower 12-14 harmonics. source of noises

electronic noise in optoelectric devices spatial precision of the TV scan or film digitization system error in film digitizing

purposes of filtering： to remove the high-frequency noises choice of cutoff frequency： residual analysis

Derived Kinematic Variables

Displacement

the change of position that an object moves from one place to another a vector quantity that represents the straight-line distance and direction from point A to point B displacement vs. distance： distance magnitude of displacement, why? distance may be equal or greater than the magnitude of displacement

Velocity

change in position divided by change in time the first derivative of linear displacement

assumptions the raw displacement data have been smoothed by digital filtering the line joining xi+1 to xi-1 has the same slope as the line drown tangent to the curve at xi

velocity vs. speed

Acceleration

the rate of change in velocity i.e. the change in velocity in a given time interval the second derivative of linear displacement

           or           assumptions

the raw displacement data have been smoothed by digital filtering the line joining xi+1 to xi-1 has the same slope as the line drown tangent to the curve at xi

Angle

a vector quantity that is composed of two sides which intersect at a vertex

segment angle (absolute angle)：

the angle of one body segment which is measured in a counter-clockwise

direction starting with the horizontal plane equal to 0°

the absolute angle

in space

joint angle (relative

angle)：

the angle between 

longitudinal axes of

two adjacent

segments

joint angle at the

anatomical position is

defined as zero

How to calculate angular velocity or angular acceleration??

What is the relationship between linear and angular kinematic variables?

Anthropometric Measurements

Application of Anthropometry in BiomechanicsMeasurement of Body Segment LengthMeasurement of Body Segment MassMeasurement of Center of MassMeasurement of Moment of InertiaMeasurement of Physiological Cross-sectional Area

1. Winter, D.A., 1990. Biomechanics and Motor Control of Human Movement, 2nd ed. New York, Wiley & Sons. pp. 11-50

2. Chaffin, D.B., Andersson, G. B., Martin, D.J., 1999.  Occupational Biomechanics, 3rd ed.  New York, John Wiley & Sons. Chapter 3, pp. 65-130. 

3. Hall, 2003：Chapter 3

Definition of anthropometry

the study investigating the physical dimensions or other properties of the human body to determine the differences in the individuals and groups the science that deals with the measure of size, mass, shape, and inertia properties of the human body (Chaffin & Andersson, 1999, p.65)

Examples in movement science

length of body segment trajectory of joint center of rotation angle of pull of tendons length and cross-sectional area of muscles

Knowledge needed in anthropometry

mathematics physics biomechanics biostatistics

Materials used in anthropometric research

living body cadaver： fresh or frozen fossil

Measurement of One Body Segment

Length of body segment link

assumption in motion analysis： the human body is a system of mechanical links, with each link of known physical size and form the center of rotation of each joint can be easily identified by bone landmark

determination of link： the line draw along the longitudinal axis of the segment determination of center of rotation： the intersection of two segment links during motion link length = the distance between two centers of rotation error： < 5%

Estimation of link length using bony landmark

Dempster, 1955 identification of bony landmark located near the joint center of rotation link length = the distance between two bony landmarks R2 >0.9

segment linklink-to-length ratio

(%)

humerus acromion to laterl humeral epicondyle 89.0%

radiuslateral humeral epicondyle to ulnar styloid

process 107.0%

handulnar styloid process to knuckle of 3nd

metatarsal head 20.6%

femur greater trochanter to lateral femoral condyle 91.4%

tibia lateral femoral condyle to lateral melleolus 110.0%

foot lateral malleolus to 2nd metatarsal head 30.6%

Expressed segment length as a percentage of body height

Drillis and Contini, 1966

grouped link % of BH single link % of BH

total arm 44%

upper arm 18.6%

forearm 14.6%

hand 10.8%

total leg at stance 53.0%

thigh 28.5%

low leg 24.6%

foot 3.9%

Note: real foot length=15.2%

Measurement of Body Segment Mass

Definition of mass

a physical quantity of matter composing a body symbol： m unit： kg (kilogram) in SI unit Can you distinguish mass from weight ?

Measurement of whole body density

The human body consists of many types of tissue, each with a different density cortical bone > 1.8

muscle = ~1.0 fat < 1.0

average whole body density： a function of somatotype

d = 0.69 + 0.9 (h / w 1/3)      where the unit = kg/ l

Measurement of segment density

density of distal segment > density of proximal density immersion techniques

Di = mi / Vi

Measurement of segment mass

If the location of the center of mass of the segment is known, then the weight of each segment can easily be calculated. Please see the next section segment mass： expressed by the percentage of the total mass (%M)

grouped segment% of total body

weightindividual segment

% of grouped segment

head and neck 8.4%head 73.8%

neck 26.2%

torso 50.0%

thorax 43.8%

lumbar 29.4%

pelvis 26.8%

total arm 5.1%

upper 54.9%

forearm 33.3%

hand 11.8%

total leg 15.7%

thigh 63.7%

shank 27.4%

foot 8.9%

Measurement of Center of Mass

Definition of Center of Mass (COM)

the point where the entire weight of the body is concentrated the point in a body about which all the parts exactly balance each other Note：Can you distinguish the center of mass from the center of gravity (COG) or from the center of pressure (COP)? its precise location depending on

individual's anatomical structure habitual standing posture current position external support

NOTE： Location of COM remains fixed as long as the body does NOT change the shape

methods to estimate the COM of an object suspension method moment subtraction method segment zone approach weighed average of every segment of the entire body kinetic method： double integration of shear forces from the force platform clinical method： measurement of the PSIS (posterior superior iliac spine) level in the sagittal plane

Suspension Technique

A body segment is suspended in a frame from only one point and then the point where the gravity effect is equaled is the location of the center of mass

Moment Subtraction Method

developed by Williams & Lissner, 1977 example I： to measure the location of COM of a segment composed of the low leg and foot

given： segment weight W1. have the subject lie prone on

a scale

2. measure the length from head

to scale, L

3. measure the weight on the

scale S

4. then have the subject bend

one leg

5. measure the length from head

to knee, X'

6. read the value on the scale, S'

7. the location of the COM of

the low leg and foot is equal

to (X-X') from the knee joint

example II： to measure the mass of the segment composed of the low leg and foot given： location of the COM of the segment composed of the low leg and foot the mass of the low leg and foot is

Kinetic AnalysisAbout KineticsMeasurement of kinetic dataBiomechanical ModelsDerived Kinetic Variables

1. Nigg B.M. & Herzog W., 1999. Biomechanics of the Musculo-Skeletal System. New York, John Wiley & Sons. pp.349-371

2. Chaffin & Andersson, 1999： Chapter 5-2

About Kinetics

Application of kinetics

kinetics： the study that concerns with forces that produce, arrest, and modify motions of bodies force： an action that changes the state of rest or motion to which it is applied

external force： force generated by something outside the body internal force： 2 definitions

force generated by the human body itself reaction force

effect of forces on a rigid body in dynamic sense

linear motion (translation) in the direction of net force rotary motion (rotation) in the direction of net moment

in static sense static equilibrium

Types of external force

gravitational force g = 9.81 m/s2 W = mg 1 kg = 9.81 N

ground reaction force friction force： the resistance of two moving objects, e.g. friction force between feet and ground

Fs = s N where s = coefficient of static friction Fs = k N where k = coefficient of kinetic friction

air or water resistance Fa = Av2c

Types of internal force

force generated by the human body muscle force connective tissue tension

reaction force

Newton's Law of Motion

first described by Newton including

Law of inertia： A body continues in its states of rest or of uniform motion unless an unbalanced force acts on it. Law of acceleration： The acceleration of an object is directly proportional to the force causing it, is in the same direction as the force, and is inversely proportional to the mass of the object (F = ma) Law of action and reaction： For any action there is an equal and opposite reaction.

Kinetic variables

variable name formula SI unit

force F = ma

linear moment M = Fd

angular moment M = I

Measurement of Kinetic Variables

Force transducer

a force measuring device that gives an electric signal proportional to the applied force types of force transducer

capacitive sensor： F 1/Q conductor sensor： F 1/R

strain gauze electrical resistant transducer： wire

piezoelectic sensor

non-conducting crystal that exhibits the property of generating an electrical charge when subjected to mechanical strain, e.g. quartz

selection of force transducer capacitive or conductor sensors

for measuring forces on soft or uneven surfaces or pressure distribution less accurate (20% of error)

strain gauze or piezoelectic sensor for measuring forces on rigid body more accurate (5% of error)

Force plate system

four-corner type force plate a rectangular flat plate with 4-triaxial force transducers mounted at each corner

Fx-total = Fx1 + Fx2 + Fx3 + Fx4 Fy-total = Fy1 + Fy2 + Fy3 + Fy4 Fz-total = Fz1 + Fz2 + Fz3 + Fz4 Mx-total = Mx1 + Mx2 + Mx3 + Mx4 My-total = My1 + My2 + My3 + My4 Mz-total = Mz1 + Mz2 + Mz3 + Mz4

central-support type force plate one centrally instrumented pillar which supports an upper flat plate

quiet stance vs. forward bending

given an individual stands on a force place, what happens if leaning backward leaning to the right rotating to the right jumping vertically

Electromyography

muscle force connective tissue tension

Mechanical analysis methods from Kinematic analysis

direct dynamics (forward dynamics)： mechanical analysis of a system that determines movement from forces inverse dynamics： mechanical analysis of a system that determines forces from movement relationship between forces and movement

F = ma A defined set of forces results in a specific movement A specific movement can be the result of an infinite number of combinations of individual forces acting on a system

Biomechanical Models

Definition of modeling

an attempt to represent reality, which is used for actual or theoretical situations

Purposes of modeling

to facilitate understanding of knowledge and insights of reality to estimate and predict variable of interest

Importance of making a scientific model

an attempt to represent reality, which is used for actual or theoretical situations conflicts

all important aspects must be included all unimportant aspects must be neglected

Making assumptions and simplifications lead to a simple model What to include, what to neglect, and what assumptions to be made should be decided. Evidence and reasons why these assumption are reasonable must be applied.

Types of model

analytical models based on knowledge and insight advantages

to have a unique solution independent of the selected mathematical procedures

critical points： selection of assumptions and simplification semi-analytical model

based on knowledge and insight, but more unknowns than equations in it mathematical description need more assumptions

black box model A set of mathematical functions are used to determine the input-output relations advantages

to estimate quantities that cannot be measured to provide insight into possible functional relationships between input and output

conceptual model consisting of hypotheses and procedures capable of accepting or rejecting the tested hypothesis advantage： larger concepts smaller steps disadvantage： a hypothesis can never be proved several pieces of evidences must be accumulated to provide enough support for a concept

Steps of modeling

mechanical system of interest assumptions free body diagram equation of motion mathematic solution

Example of a 2D kinematic model

Following Newton’s 2nd law, the following equation of motion must be satisfied

Fx = m ax

Fy = m ay

MG = IG

Derived Kinetic Variables

Center of pressure (COP)

the point where the resultant of all ground reaction forces act

               Fz-total = Foo + Fxo +Fxy + Foy

If all forces are equal, then COP = (x/2, y/2) unit： mm

Mechanical energy

a measure of the state of a body at an instant in time as to its ability to do work unit： joules the segment energy at every instant is composed of potential (translational) and kinetic (rotational) energy

M.E. = P.E. + K.E.

potential energy (P.E.) the potential of doing work due to the position or configuration of a rigid body P.E. = mgh for a rigid body which is elevated to a height of h P.E. = ½k x2 for a spring which is stretched x length beyond its neutral position

kinetic energy (K.E.) the work required to stop a moving body at velocity v or to move a body from rest to the velocity v K.E. = ½mv2-- product of the force along the direction of displacement and the displacement of a rigid body in motion

e.g. a body which has 200 J potential energy and 300 J kinetic energy is capable of doing 500 J of work on another body

Law of conservation of energy： the total energy of a body at position 1 is equal to that of position 2

energy balance： the sum of all the flows of energy into and out of the segment equals the energy change of that segment power balance： the sum of all the rate of flow of energy into and out of the segment equals the rate of change of energy of that segment

the only source of mechanical energy generation in the human body is muscles energy absorption： by muscle energy dissipation： into heat as a result of joint friction and viscoelasity of connective tissues

Work

a measure of energy flow from one body to another (Winter, 1990) product of the force along the direction of displacement and the displacement of a rigid body in motion W = F d unit： joules e.g. muscle A can do work on segment B if energy flows from the muscle to the segment

Power

the work done per unit of time P = W / t = Fd / t unit： joules / s

Momentum

product of the mass and its velocity of a rigid body in motion L = mv unit： kg·m / sec

Impulsive force (Impulse)

a large force applied to a rigid body through a small period of time (impact) the product of impulse force and the time period impulse = F t unit： N·s

Moment of inertia

physical property of matter, which resists any change in the state of motion (e.g. rotation or translation) depends on magnitude of the mass and its geometrical distribution I = M /

I = I0 + mr2 developed by Miller & Nelson, 1976 Please check Chaffin's book for details

For a multisegment in 3D expression

Ratios of Location of COM to Segment Length

Different values have been reported form different studies due to variations in the definition of segment length and different measurement techniques. Please check Chaffin's book for details

segment % from proximal end

upper arm 43.6%

forearm 43.0%%

hand 49.4%

thigh 43.3%%

shank 43.3%

foot 42.9%%

Measurement of Moment of Inertia

Definition of moment of inertia

physical quantity that an object resists to change or to action in response to angular velocity

or

where   mi = mass of the ith segmentri = perpendicular distance that the mass is located from a

given axis of rotation of the ith segment

Calculaiton of moment of inertia

moment of inertia acting around the axis of a joint

moment of inertia acting around the COM

Radius of gyration

definition: the radial distance from the axis of rotation at which the mass of the segment can be concentrated without altering the moment of inertia of the segment

I = m 2 moment of inertial around a joint axis

where I0 = moment of inertia about COM            x = distance between COM and center of rotation           m = mass of segment

Physiological Cross-Sectional Area

Physiological cross-sectional area of a paralleled muscle

where m = mass of muscle fibers (g)            d = density of muscle (g/cm3) = ~1.056g/cm3

             l = length of muscle fibers (cm)

Physiological cross-sectional area of a pwnnate muscle

definition of pennation angle: the angle between the long axis of the muscle and the fiber angle of a pennate muscle

where m = mass of muscle fibers (g)             d = density of muscle (g/cm3) = ~1.056g/cm3

              l = length of muscle fibers (cm) = pennation angle

Clinical BiomechanicsObjectives: After studying this topic, the students will be able to

identify the center of mass, center of gravity, and center of pressure of human body and distinguish their differences identify different types of locomotion and a typical gait cycle

understand ground reaction forces and how it works on the body during different types of stance and level walking describe methods to measure limit of stability, gait pattern, and the factors that affect them explain the changes in center of mass and center of pressure at quiet stance, different perturbed tasks, and level walking

Stance and Stability

Stability and BalanceQuiet StanceExternally-Perturbed StanceSelf-Perturbed Stance

Level Walking

Review of Locomotion and GaitKinematics of Level WalkingKinetics of Level Walking

Sit to Stand

Wheelchair Propelling

Stance and Stability

Posture and BalanceQuiet StanceExternally-Perturbed StanceSelf-Perturbed Stance

1. Hamilton, N., & Luttgens, K. 2002. Kinesiology, Scientific Basis of Human Motion, 10thed. Boston: McGraw-Hill. Chapter 14, pp. 371-394 and Chapter 15, pp. 399-411

2. Chaffin & Andersson, 1999： Chapter 17 3. Hall, 2003：Chapter 13

Posture and Balance

Terminology

posture： a term to describe the

orientation of any body segment relative to

the gravitational vector

balance： a term to describe the dynamics

of body posture to prevent falling

center of mass (COM)： the point where

the entire mass of the body is concentrated

center of gravity (COG)： the vertical

projection of the center of mass to the ground

center of pressure (COP)： the point

where the resultant of all ground reaction

forces act

centroid： the point that defines the

geometric center of a body

base of support (BOS)： the area

underneath and between both feet

Location of center of pressure (COP)

COP parameters absolute position of the COP in the AP and ML directions excursion of the COP (COPE) safety margin

measurement of the position of the COP

single-force-platform method

two-force-platform method： measurement the COP with one foot standing on one force plate and the other foot on the second force plate

Location of center of mass at erect posture

methods to estimate the COM at quiet stance segment zone approach： weighed average of every segment of the entire body kinetic method： double integration of shear forces from the force platform clinical method： measurement of the PSIS (posterior superior iliac spine) level in the sagittal plane

COM parameters absolute position of the COM in the AP and ML positions excursion of the COM linear acceleration of the COM equals to the difference between the COP and COM

COP - dCOM = kawhere k = constant           a = linear acceleration of the COM

since and,

get,

so

Classification of equilibrium

stable equilibrium occurs when an object is placed in such a position that any disturbance effort would raise its COM tend to fall back its original position, e.g. BOS or COM

unstable equilibrium occurs when an object is placed in such a position that any disturbance effort would lower its COM tend to fall into a more stable position

neutral equilibrium occurs when an object is placed in such a position that any disturbance effort would not change the level of its COM tend to fall into a more stable position

Major sensory systems involved in posture and balance

sensory input visual vestibular system proprioception other somatosensory system

Factors affecting stability

size and shape of base of support (BOS) wide-base stance tandem stance: standing with one foot ahead the other

stance with crutches

height of COM relationship of COG to BOS

Pai et al., 1997： effects of velocity and position of COM on base of support

mass of body friction segmental alignment psychological or mental status muscle activities

postural muscle： the muscle that acts to prevent collapse of the skeleton

slow twitch fatigue resistant

phasic muscle： fast muscle physiological and pathological factors

Tasks used to study the stability of erect posture

quiet stance stand still with both feet apart naturally necessary to maintain static stability

perturbed stabce

self-perturbed stance： necessary to maintain dynamic stability externally-perturbed stance： necessary to regain dynamic stability

Quiet Stance

Postural sway

the body sways back and forth like an inverted pendulum, pivoting about the ankle, at quiet stance

AP sway (anteroposterior sway) sway in the sagittal plane ~ 5-7 mm at quiet stance in young adults

ML sway (mediolateral sway) sway in the frontal plane ~ 3-4 mm at quiet stance in young adults

inverted pendulum model the trunk sways around the ankle joint like an inverted pendulum (GRF) (dCOP) = (BW) (dCOG) + I assumptions

1. BW = GRF 2. body sway around ankle only

3. ankle acts as a hinge joint

postural sway at quiet stance In the case if the COP ahead the COG (see the sketch below), a counter-clockwise moment (I) is present at the ankle joint, resulting in backward rotation of the trunk and the balance is regained. In the case if the COP behind the COG, a clockwise moment is present at the ankle joint, resulting in forward rotation of the trunk and the balance may be lost and possibly fall forward.

postural sway strategy strategy： the timing and amplitude of the coordinated motor patterns at many joints in order to adjust (reactive or proactive) posture and balance ankle strategy vs. hip strategy no matter what kind of the strategy is used, the dynamic range of the COP must be somewhat greater than that of the COG for preventing falling

CNS regulates COG by controlling the net ankle moment the difference between the COP and COM is proportional to the horizontal linear acceleration of the COM

dCOP - dCOM = ka where k = constant and a = linear acceleration of the COM

factors affecting postural sway strategy age： highly correlated to falls in the elderly fatigue injury bracing obesity stability of the external environment

Externally-Perturbed Stance

Definition

externally-perturbed stance： a stance posture that an individual is subject to a perturbation from the external environment, such as a moving force plate stability during externally-perturbed stance

one kind of dynamic balance the ability that the body regains balance at the moment of giving any externally-perturbed situation

Methods of external perturbation

changes in direction of perturbation by standing on a moving platform horizontal translation sagittal plane translation

changes in surrounding environment

Horizontal translation on a moving platform

Nashner (1977)： first researcher to study the effect of a moving platform COM sways backwards when the platform moves backwards

NOTE： Actually, what he did is to measure the COP rather than the COM.

bottom-up sequence of activities of the participating muscles

Platform tilting up and down

Nashner 1982 tilting-upward

both gastrocnemius and hamstring muscles are strectched backward sway of the COM

titling downward stretched muscles? COM motion ?

Self-Perturbed Stance

Definition

self-perturbed stance： a stance posture that an individual is subject to a perturbation from his/her changing posture stability during self-perturbed stance

one kind of dynamic balance the ability that the body maintains balance during a functional task

Methods of self perturbation

stance with external support using crutches using canes

change in base of support wide-base stance tandem stance one-leg stance

moving one of body parts fast arm raise reach leaning

closing eyes

Relationship of COG and COP during forward reach movement

CNS regulates COG by controlling the net ankle moment that is expressed by COP (Fung and Winter, 1996)

Biomechanics of Level Walking

Review of Locomotion and GaitKinematics of Level Walking Kinetics of Level Walking

1. Simoneau G.G., 2002. Kinesiology of Walkign. In: Neumann, D.A. (ed). Kinesiology of the Musculoskeletal System: Foundations for Physical Rehabilitation. St. Louis, Missouri: Mosby. pp. 523-569.

2. Hamilton, N., & Luttgens, K., 2002. Kinesiology, Scientific Basis of Human Motion, 10thed. Madison, WI, Brown & Benchmark. Chapter 19, pp. 467-494.

Review of Locomotion and Gait

Locomotion

the act or power of moving from place to place by means of one’s own mechanisms or power the result of the action of the body levers propelling the body Please review more details in Kinesiology web page

Typical gait cycle

the duration that occurs from the time when the heel of one leg strikes the ground to the time at which the same leg contacts the ground again 2 phases

stance phase (62%)： initial contact, midstance, and propulsive periods swing phase (38%)： acceleration, midswing, and deceleration periods

Please review more details in Kinesiology web page

Gait parameters during level walking

time variables： stance time, single support time, double support time, swing time, stride or step time, etc. distance variables： stride length, step length, wide of base, degree of toe-out, etc. velocity variables： cadence, walking speed, walking velocity, etc. kinematic variables：

center of mass： linear or angular change of displacement and/or velocity, etc each joint： angle change, linear displacement of joint center, etc each body segment： linear or angular displacement and/or velocity, linear or angular acceleration, etc.

kinetic variables： ground reaction forces： displacement, anteroposterior and/or mediolateral excursion, etc. COP： anteroposterior and/or mediolateral excursion, path, displacement and velocity, etc.

impulse muscle activity

Recording the gait cycle

pneumatic switch (Marey, 1873)： 1st person to record the duration of sole contact electric switch (Scherb, 1927)： using 3 separate switches interrupted-light photography (Murray et al., 1964) pressure transducer (Andriachi et al., 1977) motion analysis system

Kinematics of Level Walking

Displacement of body COM

Walking is a translatory motion of the body that is accomplished by the alternating rotary motions of both lower extremities COM moves forward COM beyond anterior edge of BOS the other foot moves forward to BOS

Vertical displacement of body COM

path： 2 sinosoid curves during 1 gait cycle amplitude： ~5 cm at the average walking speed highest point: immediately after COM passes over the WB leg (30% and 80% of gait cycle) lowest point: at the termination of the swing phase of the other leg (5% and 55% of gait cycle)

Lateral displacement of body COM

path： a sinosoid curve amplitude： ~4 cm at the average walking speed to keep the COM over the weight-bearing foot

Transverse rotation of lower extremity

Eberhart et al, 1947 pelvis rotation < femur rotation < tibia rotation internal rotation of the pelvis, femur, and tibia as well as foot pronation in the initial contact period of stance phase external rotation of the pelvis, femur, and tibia as well as foot supination in the propulsive period of stance phase various largely between individuals

Kinetics of Level Walking

Forces that control walking

gravity (body weight) air resistance internal muscle forces ground reaction forces

normal component： vertical forces shear component： anterior-posterior and medial-lateral friction forces

Ground reaction forces

definition： the forces applied to the body by the ground, as opposed to those applied to the ground, when an individual takes a step

in Cartesian ayatem： Fx, Fy, Fz, Mx, My, Mz vertical component

o double peaks 1st peak at heel

strike： the action of body momentum

2nd peak at push-off： contraction of calf muscle

o amplitude： 100-120% BW

o peak value = 120% BW

o lower than BW during midstance as a result of balancing the upward momentum of the COM

anterior-posterior component (fore-and-aft shear) o the magnitude and direction of the

anterior-posterior shear force depends on the position of the COM relative to the location of the foot

in the posterior direction at heel strike for slowing the forward progression of the body

in the anterior direction at toe off for propelling the body forward

the larger the step length, the greater the shear forces because of the greater angle of between the lower extremity and the floor

o peak value = 20% BW o sufficient friction force between foot and ground is necessary for preventing

slipping down

o the propulsive force of one limb is applied simultaneously to the braking force of the other limb when the weight is transferred from one limb to the other

medial-lateral component

o the magnitude of the medial-lateral shear force depends on the position of the COM relative to the foot

in the lateral direction at heel strike

in the medial direction at the rest of stance phase

the larger the step width, the greater the shear forces because of the greater angle of between the lower extremity and the floor

o peak value = ~5% BW

o wide variety depending on different foot types

Trajectory of center of pressure

At heel strike, the COP is located lateral to the midpoint of the heel At midstance, the COP moves more laterally From heel off to toe off, the COP moves medially from the metatarsal heads to the big toe

Joint moment

At heel strike, the line of action of the ground reaction forces passes posterior to the ankle joint, posterior to the knee joint, and anterior to the hip joint, leading to promote ankle plantarflexion, knee flexion, and hip flexion. To prevent collapse of the lower extremity, these external moments are counterbalanced by internal joint reaction moments that are created by ankle dorsiflexors, the knee extensors, and the hip extensors. net moment： the summation of the external and internal moments

do NOT indicate the direction of motion e.g. cocontraction of agonists and antagonists e.g. quadriceps avoidance

Joint power

definition

the rate of work performed by controlling muscles

the product of the net joint moment and the joint angular velocity

significance： indicating the net rate of generating or absorbing energy by all

muscles and other connective tissues crossing the joint

positive value indicates power generation, reflecting a concentric

contraction

negative value indicates power absorption, reflecting an eccentric

contraction

Sports BiomechanicsRunning

Characteristics of Running CycleBiomechanical Analysis of RunningSpecial Considerations in SprintingSpecial Considerations in Jogging

Throwing, Striking, and Kicking

Sequential Movements of the Body SegmentsBiomechanics of ThrowingBiomechanics of Striking

Swimming

Biomechanics of Running

Characteristics of Running CycleBiomechanical Analysis of RunningSpecial Considerations in SprintingSpecial Considerations in Jogging

1. Hamilton, N., & Luttgens, K. 2002. Kinesiology, Scientific Basis of Human Motion, 10thed. Boston, MA: McGraw-Hill. Chapter 19, pp. 480-484.

2. Adelaar, R.S. 1986. The practical biomechanics of running. American Journal of Sports Medicine  14:497-500.

3. Cavanagh P.R. 1987. The biomechanics of the lower extremity action in distance running. Foot and Ankle 7:197-217.

Characteristics of Running Cycle

Running cycle

contact phase (support phase; drive phase)： one foot is in contact with the ground, i.e., from foot strike to toe-off

foot strike midsupport take off

swing phase： the lower extremity is swinging through the air, i.e., from toe-off to foot strike

follow through forward swing

foot descent

Characteristics of running

stride length and frequency tend to increase with increased running speed stride length depends on leg length, range of motion of hip, and strength of leg extensors stride frequency depends on speed of muscle contraction and the skill of running for speeds over 7 m/s, a increment in stride length is small but the stride frequency is significantly greater

Both feet tend to fall on the same line along the path of progression. With increasing running speed, duration of contact period decreases but that of swing phase increases. As the foot strikes on the ground, the foot is in front of the COM of the body but the distance from foot contact to the COG is shorter in running as compared to walking. This distance becomes shorter with the increase of the speed.

In barefoot running, the degree and duration of maximum foot pronation are increased as compared to that in running with shoes and/or foot orthoses.

Comparisons of running with walking

to distinguish walking from running a double swing phase during running while a double support phase during walking

the body is totally airborne for a period of time during running whereas at least one part of the body (usually indicating foot) contact the ground for the whole gait cycle during walking

comparisons of kinematic and kinetic parameters of running with those of walking

running walking

entire cycle swing phase longer stance  phase longer

duration of stance phase shorter longer

double support period absent present

duration of swing phase longer shorter

floating period present absent

stride length longer shorter

stride freqency higher lower

position of body COM lower higher

vertical oscillation of body COM

less more

linear and angular velocity of lower extremity

faster slower

required ROM greater less

muscle activities greater less

leg drive during swing phase

muscular momentum (pendulum)

foot progression line 1 line along midline of body

2 parallel lines

ground reaction force 2.5~3 times body weight ~90% of body weight

Biomechanical Analysis of Running

Foot strike

patterns of foot strike heel strike： better for long-distance running because the heel pad has a better ability to absorb high impact force midfoot strike or whole-foot strike forefoot strike

only can be used in sprinting metatarsalgia or stress fracture of the central metatarsal bones commonly occurs in the jogger with forefoot strike because of repetitive large loads onto the central metatarsal heads

At the moment of foot strike, the foot is slight supinated with the tibia in some external rotation. The most important event during foot strike is to absorb the initial impact of the foot striking the ground through

rapid extension of the hip flexion of the knee internal rotation of the tibia pronation of the subtalar joint shoes and/or orthoses

initial impact (impulse) impulse = F t initial ground reaction force = 2.5~3 times body weight, depending on the running speed heel pad has better ability to absorb initial impact than other adipose tissues in human body improvement in materials of shoes (e.g. air-cushioned shoes) or ground surface (e.g. PU or wooden surface) may decrease the initial impact

effect of lateral flare common used in jogging shoes because the heel flare increases base of support of the heel, resulting in decreased impact force per unit area at the moment of initial contact Heel flare shifts the initial contact point laterally, which increases length of the moment arm (lever arm) and then increase amount of ankle moment.   This increase in ankle moment facilitates rapid pronation of the subtalar joint at the moment of landing, decrease the possibility of lateral ankle sprain

Takeoff

the greater the power of the leg drive, the greater the acceleration of the runner (F = ma) to make the foot act as a rigid lever to propel the body forward through

supination of the subtalar joint locking of the midtarsal joint dorsiflexion (extension) of the MP joint of the big toe

impulse = F t = m a t = m v = momentum since running is a forward motion of the entire body, the horizontal component of the momentum is much more important than the vertical component

momentum： a product of mass and velocity momentum = mv impulse-momentum relationship： any changes in momentum equals to the impulse that produced it

concentric contraction of the gastrocnemius muscle

the moment arm of the Achilles tendon increases during takeoff

moment of inertia is greatest at take-off during the entire running cycle the larger distance the body will move during swing phase depends on

less angle of takeoff higher speed of body projection at takeoff less difference in the height of COM at the moment of takeoff and landing

Swing phase

reduce the moment of inertia by lifting the knee and the hip close to the body increase ROM of the lower extremity to bring the mass of the swing leg close to the hip and increase the angular velocity of the swinging leg

moment of inertia

definition： the property of an object that causes it to remain in its state of either rest or motion (Hamilton & Luttgens, 2002) I = I0 + Ar2

where I0 = I about centroid axis           A = area           r = distance moment of intertia about centroid axis at different fixed-shape objects

circular area:： I0 = (1/4) r2 rectangular area：I0 = (1/12) b h3 traingular area： I0 = (1/36) bh3

example： determine moment of inertia around centroid axis of a T-shaped beam

I = I0 + Ar2

  = [(1/12)(2)(10)3(2)(10)(8.55-5)2] +      [(1/12)(8)(3)3(8)(3)(4.45-1.5)2]=645.6

According to Newton's first law of motion, force is needed to change the velocity (amplitude and direction) of an object. moment of inertia is greatest at take-off and least after acceleration has ceased

clearance of the foot from the ground is completed by ankle dorsiflexion knee flexion hip flexion

distance of a body moving in the air depends on the angle of take-off i.e. ths distance of the body COG ahead of take-off point the speed of the body projection at take-off the height of the COM at take-off and landing

muscle activities of the lower extremity during swing phase

joint motion force for movement muscle used

hip flexion muscleiliopsoas + rectus femoris (concentric)

kneefirst 2/3： flexionlast 1/3：extension

first 2/3： momentumlast 1/3： muscle

first 2/3： --last 1/3： hamstrings (eccentric)

ankle dorsiflexion muscle tibialis anterior + toe extensors

(concentric)

Special Considerations in Sprinting

Definition

running distance < 400 m stance phase of sprinting is only 22% of the running cycle

Efficiency of running -- to get maximum horizontal velocity without falling

increase in stride length speed = stirde length stride frequency stride length is dependent on leg length, angle of hip raising, and strength of the leg extensors stride frequency is dependent on speed of muscle contraction and the skill of runner During the acceleration phase of the race, the trunk is more erect so that the length of the stride increase dependent on the angle that the hip joint raises

decrease in vertical displacement of the COM Given the same ground reaction force, the smaller the vertical component of the leg drive, the the greater the horizontal component of running velocity

foot strike close to center of gravity better to use midfoot or forefoot strike in order to have line of gravity passing through the ankle joint If the foot strikes ahead the line of gravity, the ground reaction force creates a upward and backward moment that will retard forward motion.  Therefore, as the running speed increases, the distance between the contact point of foot strike and the center of gravity decreases in order to reduce the stance and facilitate propulsion.

If the foot strikes behind the line of gravity, the ground reaction force create a upward and forward moment that will make the body fall forward

decease in lateral movements motions occurring in the entire lower extremity should be in the sagittal plane the arm movement is used to counterbalance rotation of the pelvis only

shortening of swing leg the shortening of swing leg shortens the moment arm to decreases moment of inertia and increase forward velocity the higher the knee lifts, the greater the velocity is created.

decrease internal resistance from the viscosity of the soft tissues warm-up and stretching exercises can reduce the viscosity of the soft tissues of the participating limbs

Sprint start

crouching start (蹲踞起跑) the greater the power of the leg drive, the greater the acceleration of the runner (F = ma)

assistance of starting block (起跑架) make it possible that trunk inclines forward without overstretching the Achilles tendon provides a tilting surface against which the foot pushes horizontally while using total hip, knee, and ankle extension the horizontal push-off force (impulse) results in an increased horizontal velocity (momentum)

Biomechanics of Jogging

Definition

running > 1500 m classification of long-distance runners (Brody, 1980)

jogger： run 3-20 miles per week at a rate of 9-12 minutes per mile sports runner： run 20-40 miles per week and participate in "fun runs" or races of 3-6 miles long-distance runner： run 40-70 miles a week at a pace of 7-8 minutes per mile and may compete in 10,000 m races or marathons elite marathoner： run 70-200 miles a week with a pace of 5-7 minutes per mile

Characteristics of jogging

stance phase decreases to 31% should prevent repetitive impact stresses

heel strike or midfoot strike medial and lateral flares better material for heel pad

Throwing and Striking

Sequential Movements of Body SegmentsBiomechanics of ThrowingBiomechanics of Striking

1. Hamilton, N., & Luttgens, K. 2002. Kinesiology, Scientific Basis of Human Motion, 10thed. Chapter 18, pp. 450-466.

Objectives: After studying this topic, the students will be able to

identify the sequential movement and give examples classify sports activities involving sequential movements according to the nature of force application identify the mechanical factors that affecting to throwing, striking, or kicking

Sequential Movements of Body Segments

Definition of sequential movement

the movement that involves a sequential action of a chain of body segments, leading to a high-velocity motion of external objects (Hamilton & Luttgens, 2002, p.451)

results in the production of a summated velocity at the end of the chain of segment used the path of the external object motion is curvilinear in nature

examples a pitcher throws a baseball a young adult spikes a volleyball a batter hits a baseball an elderly drives a golf ball a tennis player serves a tennis

Modification of sequential movement

objectives of sequential movements skill speed accuracy distance

components that are used to modify movement according to different objectives

numbers of body segment used range of motion (ROM) used lever length used

Classification by nature of force application

momentary contact

force imparted to an object through temporally contact with that object by a moving part of the body segment or by implement held or attached on the body segment the object may be either stationary or moving examples：

on moving object： baseball striking, soccer heading or kicking, volleyball set, or tennis driving on stationary object： golf

projection force imparted to an object through the end of a chain of body segments in order to develop kinetic energy, followed by a high-velocity motion of that object the object may be held in one hand or hands examples：

for distance： shot put, javelin, or volleyball serving for accuracy： baseball pitching or dart throw

continuous application force imparted to an object with the force continuously applying to that object examples：

against large resistance： pushing a desk or lifting weight maintain a position while waiting for a release： archery

Biomechanics of Baseball Throwing

Patterns of throwing

overarm (overhead) sidearm underarm

Kinematics of Overarm Throwing

windup (cocking) phase shoulder horizontal abduction and fully external rotation (closed-packed position) trunk left rotation prone to have shoulder impingement syndrome

acceleration phase shoulder internal rotation

deceleration phase checked by shoulder external rotators

follow-through phase trunk rotation

Kinematics of sidearm throwing

preparation phase shoulder horizontal abduction only trunk right rotation

acceleration phase shoulder horizontal adduction

deceleration phase checked by deltoid posterior

follow-through phase opposite hip internal rotation

Kinematics of underarm throwing

preparation phase shoulder extension elbow extension

acceleration phase shoulder flexion (arm flexion)

deceleration phase checked by shoulder extensors

follow-through phase trunk rotation

Mechanical Factors of Throwing

ballistic movement of one segment imparting force must overcome the inertial of an object

mass of object internal resistance friction between object and supporting surface resistance to surrounding medium

force needed dependent on

speed of object distance of throwing accuracy of target： related to direction of the object after its release

direction of the object after release dependent on

direction of the object at the moment of release： path tangential to the arc of motion gravity air or water resistance spin of the object

timing pattern of movement part The slowest or heaviest part must start to move first, and the quickest and lightestone last

to facilitate use of stretch reflex

Biomechanics of Striking

Forehand drive in tennis

action： the player takes the racket to hit the ball and send it into the opponent's court

type of movement： ballistic movement participating lever： racket, racket-side arm, and trunk location fulcrum： the hip joint at non-racket side skill requirement： high speed and moderate accuracy

motion description back swing phase

the player pivots his body to have the non-racket side face forward the racket is taken back at the shoulder level the body weight is over the foot of the racket side the head of the racket is kept above the wrist

forward swing phase the player lowers down his body by flexing the knee to have the racket below the intended contact point the trunk rotates forward to shift the weight to the foot of the non-racket side the racket is perpendicular to the ground at the moment of impact

follow-through phase the body continues forward the racket arm swings across the body and up toward the chin

the effect of body spinning mechanical factors contributing the impact to the ball： the greater impart force will impart more momentum to the ball, leading to speed up the ball on its return flight

increase the lever-arm length by using a long-arm racket, keeping the arm straight

firmness of grip depends on muscle strength of wrist and finger flexors

the angle of the racket face at ball hitting because the angle of rebound is highly correlated to the angle of incidence

actually, the ball is not a rigid body so that the angle of rebound is slightly less than the angle of incidence

Occupational Biomechanics

Occupational Biomechanics

the study of the physical interaction of workers with their tools, machines, and materials so as to enhance the worker’s performance while minimizing the risk of musculoskeletal disorders (Chaffin, 1994) applications

to improve working performance and efficiency to prevent occupational injuries to make industrial robots for high-risk or high-structured or repetitive works

Pushing and Pulling

Push-and-Pull MotionsForce ImpartBiomechanics of Pushing a Cart

Load Lifting

NIOSH Manual Materials Handling LimitsMulti-Segment Biomechanical ModelBiomechanics of Symmetrical Load Lifting

Seated Work

Sitting PostureAnthropometric Dimensions of Seated WorkersSeated Work Place and LayoutVideo Display Terminal Users

Application of Biostatistics

Hazard LevelsNormal DistributionInferences from Sampling Distribution

Design of Hand Tools

Vibration Environment

Pushing and Pulling

Push-and-Pull MotionsForce ImpartingBiomechanics of Pushing a Cart

1. Hamilton, N., & Luttgens, K. 2002. Kinesiology, Scientific Basis of Human Motion, 10thed. Boston: McGraw-Hill. Chapter 17, pp. 435-449.

2. Chaffin, D.B, & Andersson G.B.J., 1999. Occupational Biomechanics, 2nd ed.

Objectives: After studying this topic, the students will be able to

1. define push and pull patterns of motion 2. identify the the activities that involves push and pull patterns and give examples 3. analyze mechanical factors that affecting to push-and-pull activities

Push-and-Pull Motions

Definition

broad definition： a segment motion that involves moving an object, either directly by part of the body or by means of implement, in pushing and pulling pattern (Hamilton & Luttgens 2002, p.436)

a pitcher throws a baseball a tennis player serves a tennis a worker lifts a box from the floor onto an overhead rack an archer shoots an arrow from a bow

limited definition： a segmental motion that all forces are continuously applied onto an external object (continuous application pattern of sequential movement)

an individual pushes a desk across the room a traveler pulls his suitcase

Joint action patterns

simultaneous and opposite movement pattern in the upper extremity flexion in elbow with extension in shoulder

extension in elbow with flexion in shoulder

simultaneous movement pattern in the lower extremity simultaneous extension in the hip, knee, and ankle joints simultaneous flexion in the hip, knee, and ankle joints

at the distal end of the movement chain, a rectilinear path of motion is present. All forces produced by segmental motion are applied directly to the object and applied in the direction of motion. (Hamilton & Luttgens 2002, p.436) results： maximum forces and/or maximum accuracy but no tangential forces

trade-off in velocity and accuracy

Force Imparting

Mechanical factors to be considered

source of force by hand by foot by head by trunk by implement

force magnitude of force direction of force point of force application

stability of the body at the moment of giving motion the interaction between the body and the surface that supports it characteristics of the moving object

Magnitude of force

The force to move an object must be greater enough to overcome the resultant of the following forces

internal resistance (moment of inertia) friction between the object and the supporting surface resistance of the surrounding medium, such as air or water

For maximum force production, the maximum number of segments should be used through the largest safe range of motion. For maximum force accuracy, the minimum number of segments should be used through the smallest possible range of motion.

Direction of force

The direction the object moves is determined by the direction of the resultant of all forces imparting on it For maximum force production, the segments involved should be aligned with the intended direction. If the object is subject to move along a preset path (e.g. a sliding door), any component of force not in this direction will be wasted and may act to increase resistance. If that force is greater enough, then some destructions will occur.

Point of force application

Force applied in line with the COM of an object will result in linear motion of that object, provided the object is freely movable; otherwise, it will result in rotary motion.

Biomechanics of Pushing a Cart

Economy of effort

use lower extremities ( friction) force applied in line with the object’s COM and in desired direction

Load Lifting

NIOSH Manual Materials Handling LimitsMulti-Segment Biomechanical ModelBiomechanics of Symmetrical Load Lifting

1. Chaffin, D.B, & Andersson G.B.J., 1999. Occupational Biomechanics, 2nd ed.

Objectives: After studying this topic, the students will be able to

1. understand the NIOSH standards2. identify the the activities that involves lifting patterns3. analyze mechanical factors that affecting to lifting activities

NIOSH Manual Materials Handling Limits

About NIOSH

full name： National Institute for Occupational Safety and Health reported statistics of overexertion injuries

~ 1/4 of all reported occupational injuries is overexertion injuries < 1/3 of the patients with low back pain returned to their previous work ~ 2/3 of overexertion injury claims involves lifting loads and ~ 1/5 involves pushing or pulling loads

Manual material handling (MMH)

types of manual materials handling lifting： to move a load from a lower place to a higher place press down： to press a load in a downward direction pushing/ pulling： to move a material with continuous force application carrying： to move a material horizontally from one place to another holding： to hold a material without any motion

characteristics of major components affecting manual materials handling system (Herrin et al., 1974)

worker： physical measures, sensory processing capacities, motor capacities, psychomotor (interface for mental and motor processing), personality, training/ experience, health status, and leisure time activities material/ container characteristics

load： weight, pushing/pulling force requirements, and mass moment of inertia dimensions： size of unit workload, e.g. height, width, breadth, and form distribution of load： location of COM of the unit workload respect to the worker couplings： simple devices used to aid in grasping and manually manipulating the unit load, e.g. texture, handle size, shape, and location stability of load： consistency of COM location, especially for handling

liquids or bulk material task/ workplace： workplace geometry, time dimension of the task (frequency, duration, and pace), complexity of the load, and environmental factors work practices： operating practices under the control of the individual worker, work organization, and administration of operating practices

1981 NIOSH Lifting Guide for evaluation and control of symmetric, sagittal plane lifting includes both biomechanical spinal compression force limits and psychological limits in order to predict incidence and severity of  overexertion injuries factors would lead to a hazardous lift

weight of object lift (L) location of object COM horizontally from the ankle (H) location of object's COM at the beginning of lift (V) vertical traveling distance of hands from origin to destination of object (D) frequency of lifting duration of the period which lifting takes place

Lifting hazard levels

Action Limit (AL) epidemiological data indicates that some workers would be at increased risk of injury on jobs exceeding the AL biomechanical studies indicates that L5/S1 disc compression forces can be tolerated by most people, but not all, at about 3400 N level, which would be created by conditions at AL physiological studies indicates that the average metabolic energy requirement would be 3.5 kcal/min for jobs performed at the AL Psychological studies indicates that > 75% of women and 99% of men could lift the load at the AL

Maximum Permissible Limit (MPL) = 3AL epidemiological data indicates that musculoskeletal injury rates and severity reates are significantly higher for most workers placed on jobs exceeding the MPL biomechanical studies indicates that L5/S1 disc compression forces cannot be tolerated over the 6400 N level in most people, which would be created by conditions at AL physiological studies indicates that the average metabolic energy requirement would exceed 5.0 kcal/min for most workers frequently lifting loads at the MPL Psychological studies indicates that only <1% of women and ~25% of men could lift the load above the MPL

categories of lifting hazard level above MPL： unacceptable between AL and MPL： unacceptable without administrative or engineering controls below AL： appropriate for most workers

Multi-Segment Biomechanical Model

Biomechanical Model

definition model is a representation of a system, based on some simplifications and assumptions, to make it easily understand (Chaffin & Andersson, 1999)

purposes of biomechanical modeling to understand easily about a complex system e.g. beam model of the plantar fascia to explore each component of a complex system and their interactions to simulate some conditions that are rare, dangerous (e.g. ultimate strength of biological tissues), hard to be measured (e.g. intradiscal pressure), or time- and/or cost-consuming tasks (e.g. zero-g conditions) to predict some outcomes or potential hazards without real practice, e.g. prediction of maximum allowable load

Single body segment static model

The force to move an object must be greater enough to overcome the resultant of the following forces

internal resistance (moment of inertia) friction between the object and the supporting surface resistance of the surrounding medium, such as air or water

Example： An anthropometrically averaged-sized worker holds a even-distributed load in both hands, with forearm in the horizontal position, at waist height in front of his body.Question： What rotation moments and forces are acting on his elbow?Model used： static model since the task is only holdingAnswer：

Single segment dynamic model

As a body segment is rotated about a joint center, inertial forces act at the COM of the segment

o tangential force： force tangent to the arc of motion

o contrifugal force： force along the radius of the arc of motion to pull away from the center of rotation

o centripetal force： the reaction force of centrifugal force to hold the structures together

o moment at the joint is equal to the sum of the moment from the weight of the segment (the static gravity effect), the instantaneous acceleration effect due to the tangential force, and the rotation acceleration effect due to the mass distribution

Biomechanics of Load Lifting

Joint reaction forces and moments -- Static model

load lifting can be simplified and regarded as a 5-link static model if the velocity is minimum.

For each joint, the resultant force and moment should be equal to zero. force component： weight of each limb, load, and reaction force of the adjacent joint

moment component： the moment produced by the weight of each segment, the moment produced by the load, and the moment produced by the reaction force of adjacent joint

what would happen about the reaction forces and moments if the posture is changed? when the lifting is completed with both knees keeping straight when the lifting is completed with both elbows keeping straight

Reaction forces are only affected by the load. for each joint, reaction force Rloaded = Rload=0 + load

Reaction moments are largely affected by both the load and lifting postures, e.g. arm reaching out trunk leaning forward knee bending for each joint, reaction moment Mloaded = Mload=0 + (load)(disanceload-to-joint)

exercise： please try to set up a 3D model for lifting

Dynamic lifting strength

highly correlated to the posture as the lifting task is performed major errors in earlier lifting research

using static strength to measure the capacity for a dynamic task basic assumption： to move a maximum load in a very slow speed can be regarded as a static task may be under-predicted by as much as 54% because the effect of acceleration is not considered

using vertical lift type of test instead of actual lift pathway in reality, when a load is lifted, the path of motion is a combination of vertical lift and toward body pulling

Multi-segment dynamic model of load lifting

highly correlated to the acceleration of lifting first peak： at first 200-400 ms 2nd peak： for accuracy

larger moment are present at th hip joint as compared to the moments at upper extemity

Low back biomechanical model

use the load moment at lumbosacral disc (L5/S1) as the basis for settig limits for lifting and carrying loads since 85-95% of disc herniation occurs at the L5/S1 and L4/L5 levels Morris, Lucas, and Bressler (1961) using static sagittal-plane model

extensor errector spinae： exerting force at 5 cm posterior to the center of L5/S1 IVD (intervertebral disc) abdominal pressure： in front of the L5/S1 IVD resulting on large disc compression force that was confirmed by Machemson and Elfstrom (1970)

Chaffin 1975 using add hip-sacral link and lumbar-thoracic link to refine the above model length of the hip-sacral link is approximately 20% of that of the shoulder-hip link pelvic angle from the horizontal is approximately 45 deg. estimation of compression force estimation of force of erector spinae at the L5/S1 level

estimation of abdominal muscle forceFabd = PabdAdiagram

where average Adiagram = 465 cm2 estimation of moment at the L5/S1 level

Asymmetrical lifting

isometric lifting strength decreases 20% for the task requiring left/ right trunk rotation and decreases 26% for the task requiring trunk backward rotation

Seated WorkSitting PostureAnthropometric Dimensions of Seated WorkersSeated Work Place and LayoutVideo Display Terminal Users

1. Chaffin, D.B, & Andersson G.B.J., 1999. Occupational Biomechanics, 3rd ed. New York: John Wiley & Sons. pp.355-392.

Objectives: After studying this topic, the students will be able to

1. understand the biomechanics of sitting posture 2. identify the anthropometric measurements for the seated workers 3. understand the guideline for seated work place design and layout 4. understand the common problems and solutions for VDT users

Sitting Posture

Definition

a body position in which the weight of the body is transferred to a supporting area, mainly by the ischial tuberosities of the pelvis and their surrounding tissues (Schoberth, 1962)

body weight transferring through the ischial tuberosity to the seat and then to the floor the foot directly to the floor the forearm to the armrest and then to the floor the back and pelvis to backrest and then to the floor

comparisons of sitting posture with standing posture

Sitting posture provides stability required on tasks with high visual and motor control. Sitting posture is less energy consuming than standing posture. Sitting posture places less stresses on lower extremities than standing posture. Sitting posture lowers hydrostatic pressure on lower extremity circulation. The pelvis rotates backward and the lumbar spine flattens when standing to sitting.

Advantages of seated work

sitting posture provides stability required in the tasks that involve high visual and motor control sitting posture is less energy consumption than standing sitting posture places less stresses on the lower extremities sitting posture lowers the hydrostatic pressure on the lower extremity circulation Although seated work provides some advantages for the workers, it is obvious that the work place should be assessed carefully so as not to introduce musculoskeletal problems.

Types of sitting posture

middle sitting COM of the upper body directly above ischial tuberosity floor support ~25% subtypes：

relaxed middle sitting with the lumbar spine straight or slight kyphosis supported middle sitting： with the lumbar spine straight or slight lordosis

forward sitting (forward leaning sitting) COM of the upper body in front of ischial tuberosity floor support >25% subtypes：

forward rotation of the pelvis with the lumbar spine straight or slight kyphosis little rotation of the pelvis but with large kyphosis of the lumbar spine sitting on a chair with a forward sloping seat： with the lumbar spine slight lordosis

backward sitting (backward leaning sitting) COM of the upper body behind ischial tuberosity floor support <25% subtypes：

backward sitting without lumbar support： backward rotation of the pelvis and kyphosis of the lumbar spine backward sitting with a lumbar roll support： backward rotation of the pelvis and lordosis of the lumbar spine

Standard sitting posture

chin in neck flexion 5-10 º keep lumbar lordosis hip： 85-100 º tibia： perpendicular to the floor foot flat on the floor

Sitting on a high chair

should have a foot support without foot support, the weight of leg will form a moment at the hip joint to create anterior tilt of the pelvis, and then increase lumbar lordosis that might result in low back pain

Semi-sitting posture

good for ‘active’ workere.g. grocery check-out person

to encourage mobility to allow rapid changes between sitting and standing to preserve lumbar lordosis

inclination of the seat starts just in front of the ischial tuberosity to have full support of the trunk and the thigh

Anthropometric Dimensions of Seated Workers

Vertical anthropometric measurements

All of the anthropometric measurements are based on the position when an individual sits with the popliteal fold 3-5 cm above the seat, with knee flexion of 90º, and with the foot flat on the floor.

sitting height： the vertical distance from the floor to the posterior aspect of the mid-point of the thigh shoulder height： the vertical distance from the sitting height to the superior aspect of the acromion elbow height： the vertical distance from the sitting height to the tip of the olecranon with the elbow being flexed to 90º and the upper arm being vertical thigh height： the vertical distance from the floor to the highest point of the thigh patellar height： the vertical distance from the floor to the superior aspect of the patella orbital height： the vertical distance from the floor to the orbit

Sagittal anthropometric measurements

abdominal depth： the sagittal distance from the posterior aspect of the buttocks to the anterior aspect of the abdomen external sitting depth： the sagittal distance from the posterior aspect of the buttocks to anterior aspect of the patella internal sitting depth： the sagittal distance from the posterior aspect of the buttocks to the posterior aspect of the popliteal fold

Transverse anthropometric measurements

shoulder width： the transverse distance between the tips of both acromion processes buttocks width： the maximum transverse distance at the buttocks external elbow width： the transverse distance between the tips of both olecrani when the arms are placed at shoulder abduction of 90º

Seated Work Place and Layout

Dimensions of the seat

seat height = sitting height 3-5 cm below the knee fold when the low leg is vertical; otherwise it will cause compression of the posterior aspect of the thighs 3-5 cm above popliteal level if the chair is tiltable or the seat slope is forward (Bendix, 1987)

seat width

seat depth (length)： 10 cm less than the internal sitting depth in order to facilitate rising from the chair

seat slope backward slope of 5º adjustable seat slope： better used in the office forward slope of 20º

shape of the seat： Front part of seat should be contoured so that the edges of the seat should not be detectable during seated work.

friction properties

softness： pressure should be avoided on the posterior aspect of lower thigh

adjustability

climatic comfort

Dimension of the backrest

Either with backrest or with lumbar support will decrease the pressure under the ischial tuberosity.

Backrest should not restrict trunk or arm movements

backrest top height = backrest bottom height + backrest height backrest bottom height

backrest center height

backrest height

backrest width

backrest horizontal radius： concave from side to side to conform the body contour

backrest vertical radius： convex from the top to the bottom to conform to the lumbar lordosis

backrest-seat angle

pivoting and recline possibility

softness

adjustability： adjustable in the vertical and/ or horizontal planes

climatic comfort

Dimension of the Armrest

Armrest can reduce the loading on the spine and facilitate the rising from the chair armrest length armrest width

armrest height = elbow height shoulders shrug if the armrests are too high trunk slumps or leans to one side if the armrests are too low

armrest-to-armrest width distance from armrest front to seat front

Dimension of the chair base

number of feet base diameter use of caster or wheel

Dimension of the Workbench

Not necessarily the same for all types of work factors affecting workbench dimensions

size of the workpiece motions required by the task performer overall work layout

workbench top height 3-4cm above the elbow level (Bendix, 1987) Key board height = workbench top height if the computer is used

workbench bottom height： greater than the thigh height in order to ensure sufficient space for the thigh workbench surface

size large enough to accommodate work objects but not too far to reach friction high enough to prevent sliding of work

inclination of workbench surface The influence on lumbar posture from inclined table surfaces was actually greater than the influence of the seat slope. (Bendix, 1987) for reading： a slope of 45° for writing: a flat desk

field of vision VDT must be placed to prevent forward head or trunk flexion of the user focal distance: 20-40 cm

Video Display Terminal Users

Definition

maintaining the same posture > 2 hours for one specific computer work repeated using the same key(s) or mouse NOTE： In most developed countries, approximately ¾ of labors is sedentary workers (Reinecke et al. 1992)

Cumulative traumatic syndromes in VDT users

Hultgren & Knave1st, 1974 1streporter about soft tissue problems among VDT users Muscle fatigue, soreness, stiffness, cramps, numbness, and/or pain were frequently found in VDT users associated with the frequency of key strikes

More than half of computer users have reported local pain. (1991 US statistics) location of pain

neck and shoulder pain: 67% low back pain: 40% wrist pain: 29%

resulting in increase in medical expenditure Increase in work compensation decrease in productivity

Possible causes

physiological factors Endurance time decreases significantly when the posture required more than 30% of the strength of back muscles (Jorgensen, 1970)

intradiscal pressure changed during various sitting postures

If the trunk leans forward, the moment loaded on the lumbar disc increased as the sine of . For example, if the trunk leans forward at an angle of 30º, then the moment is Wd(sine30º), i.e., 0.5 Wd.

flextion of the neck depends on the visual demand and the height of work surface.

environmental or task factors malposture or maintaining the same posture for a long period of time improper workplace repetitive motions

psychological factor work stress time stress

social factors

prevention of cumulative traumatic syndromes

to decrease the sustained duration muscle cannot sustain contractions over ~15-20% of their maximum strength without fatigue

to decrease the frequency to increase muscle strength in the posture where the task requires

Biomechanical considerations in VDT workplace design

chair chair with armrest

seat slope

chair base better to have 5-foot support radius = 30-35cm use of casters or wheels

computer desk to provide sufficient space for the legs i.e. work bench bottom height thigh height If the desk is too low, an individual tends to lean forward and lower and protract the shoulder joints. If the desk is too high, an individual tends to elevate and shrug the shoulder joint which is susceptible to muscle fatigue.

keyboard keyboard height (from middle row to floor): 70-85 cm keyboard distance (from middle row to table edge): 10-26 cm in the position to have minimum wrist extension, flexion, and ulnar deviation

screen screen height (from center of screen to floor): 90-115 cm screen inclination: 88-105° screen distance (screen to table edge): 50-75 cm

body posture visual distance (from eyes to center of screen) viewing angle (from eyes to center of screen)： < 20º trunk-seat angle： most people uses the backward leaning posture that causes in a decrease in lumbar lordosis and is susceptable to herniation of the intervertebral disc. elbow angle： ~ 90º shoulder flexion angle： as small as possible

Application of Biostatistics

Hazard LevelsNormal DistributionInferences from Sampling Distribution

1. Chaffin, D.B, & Andersson G.B.J., 1999. Occupational Biomechanics, 3rd ed. New York: John Wiley & Sons.

Objectives: After studying this topic, the students will be able to

1. understand the classification of hazard levels 2. identify the normal distribution and its related statistics 3. understand the sampling distribution and its applications

Hazard Levels

Action Limit (AL)

epidemiological data indicates that some workers would be at increased risk of injury on jobs exceeding the AL biomechanical studies indicates that L5/S1 disc compression forces can be tolerated by most people, but not all, at about 3400 N level, which would be created by conditions at AL physiological studies indicates that the average metabolic energy requirement would be 3.5 kcal/min for jobs performed at the AL

psychological studies indicates that > 75% of women and 99% of men could lift the load at the AL

Maximum Permissible Limit (MPL) = 3AL

epidemiological data indicates that musculoskeletal injury rates and severity rates are significantly higher for most workers placed on jobs exceeding the MPL biomechanical studies indicates that L5/S1 disc compression forces cannot be tolerated over the 6400 N level in most people, which would be created by conditions at AL physiological studies indicates that the average metabolic energy requirement would exceed 5.0 kcal/min for most workers frequently lifting loads at the MPL psychological studies indicates that only <1% of women and ~25% of men could lift the load above the MPL

Categories of lifting hazard level

above MPL： unacceptable between AL and MPL： unacceptable without administrative or engineering controls below AL： appropriate for most workers

Normal Distribution

Definition of normal distribution (Gaussian distribution)

a distribution followed the curve of

a symmetrical bell-shaped curve with the mean value of and the standard deviation of standardized normal distribution： given = 0 and =1

68.3% of population fall within 1 standard deviation from the mean 95.0% of population fall within 1.96 standard deviation from the mean 95.4% of population fall within 2 standard deviations from the mean 99.0% of population fall within 2.58 standard deviation from the mean 99.7% of population fall within 3 standard deviations from the mean

Central tendency of a distribution

mean (： the average value of all observations in a population

for example： a population of 18 observations as follows

observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

value 6.8 5.3 6.1 4.3 5.0 7.1 5.5 3.8 4.6 6.0 7.2 6.4 6.0 5.5 5.8 8.8

mean = (6.8 + 5.3 + 6.1 + ... + 5.9)/ 16 = 94.2 / 16 = 5.89

median (Md)： the middle observation in a populationin the above example, the values in rank-order are

observation 8 4 9 5 2 7 14 15 10 13 3 12 1 6 11 16

value 3.8 4.3 4.6 5.0 5.3 5.5 5.5 5.8 6.0 6.0 6.1 6.4 6.8 7.1 7.2 8.8

the middle observation is somewhere between #14 and #15,so median = 0.5 (5.5 + 5.8) = 5.65

mode： the value that occurs most frequently in a distributionin the above example, mode = 5.5 and 6.0.

Variability of a distribution

range = maximum - minimumin the above example, range = 8.8-3.8 = 5

variance (²)：

standard deviation ()： 

Percentiles

definition： a number that indicates the percentage of a distribution that is equal to or below that number method

1. to rank all observations in an ascending order 2. to divide them into 100 subgroups, and then 3. to assign one subgroup as a percentile

mean = median = 50th percentile for a normal distribution In occupational Biomechanics, we usually report

1st percentile = - 2.326 5th percentile = - 1.645 25th percentile = - 0.67 50th percentile = 75th percentile = + 0.67 95th percentile = + 1.645 99th percentile = + 2.326

Inferences from Sampling Distribution

Central limit theorem

sampling distribution： select many samples from the target population, compute the mean in each sample, and then the distribution of all these means is the sampling distribution

the mean of the sampling distribution of means is equal to the population mean

the standard deviation of the sampling distribution of means is called as standard error of the mean (SEM)

If the population distribution is normal, then the sampling distribution is normal, too.