biomechanics 2
TRANSCRIPT
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.