Biomechanics 1

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Introduction to Biomechanics Review of Mathematics and Mechanics Properties of Biological Materials Methodology in Biomechanical Studies Clinical Biomechanics Sports Biomechanics Occupational Biomechanics 2003 Huei-Ming Chai at School of Physical Therapy, National Taiwan University, Taipei All Right Reserved

Introduction to BiomechanicsObjectives: After studying this topic, the students will be able to 1. 2. 3. 4. describe the definition of Biomechanics understand the development of Biomechanics identify the scope of biomechanical studies and their applicaton explain the common used physical quantities and their symbols

About Biomechanics Definition of Biomechanics Development of Biomechanics Scopes of Biomechanics Physical Quantity

1. Chaffin & Andersson, 1999: Chap 1 2. Luttgens, K. & Hamilton, N., 2002 Chap 1

About Biomechanics

Who should take this 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, staff, spy..... entertainment specialist/ actor or actress dancer/ painter

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 (Movement science) Arts o performance arts o fine arts o entertainment arts

Definition of BiomechanicsBoard Definition of Biomechanicsthe application of the principle of the physics and mechanical engineering sciences to the problem in the context 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

Scopes of Musculoskeletal Biomechanical ResearchResearch directions of musculoskeletal biomechanical research

structure and/or physical properties of muscle, tendon, ligament, capsule, cartilage, and bone effect of load and underload of speciifc strutures

factors influencing performance

Subjects for human biomechanical studies

elderly vs. young kids vs adults women vs. men disable vs. able people athelets vs. sedentary people workers vs. non-workers

Methodology in Biomechanical Studies

anthropometric method performance limit evaluation kinesiology method o kinematic method o kinetic method biomechanical modelling method task analysis method

Physical Quantities

When you can measure what you are speaking out and express it in numbers, you know something about it!! -- Lord Kelvin Physical Quantity the quantity that can be used in the mathematical equations of science and technology Physical quantity is objective and measurable.

Dimension SystemSeven Fundamental Quantities Length (L) Mass (m) Time (T) Electric Current Temperature Luminous Intensity Amount of Substance Unit Name meter kilogram second ampere degree of Klevin candela mole Unit Symbol m kg s A cd 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 ConversionSystem of Unit

metric system

CGS system MKS system

SI system (Systeme International d'Unites; the International System of Units) for details: English System

Unit of Mass 1 foot (lb) = 0.454 kg 1 kg = 2.205 lb 1 ounce = 28.350 g = 1/16 lb

Unit of Mass 1 foot (ft) = 0.305 m 1 m = 3.281 ft 1 inch = 25.4 mm = 1/12 ft

Standard PrefixName Symbol Value yotta Y 1024 tera T 1012 giga G 109 Name Symbol Value deci d 10-1 centi c 10-2 milli m 10-3 micro 10-6 naro n 10-9 pico p 10-12 yocto y 10-24 mega M 106 kilo k 103 hecto h 102 deka da 101

Review of Mathematics and Mechanics

Plane Geometry Plane Trigonometry Vector Basic Statics

Basic Dynamics

Plane Geometry

angles, sides, and area of a triangle


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) = 57.9 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 owhere


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 StaticsExternal Forces Internal Forces Mechanical Advantage Centroid Equilibrium of the Force System Free Body Diagram Force Couple

External Forces

Types of external forces gravitational force ground reaction force friction force air or water resistance

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 resistanceFa = Av2c

Internal Forces1. muscle force 2. forces from tendon, ligament, and other connective tissues

Mechanical Advantage (MA) of the Lever


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

Types of Lever1. first-class lever 2. second-class lever: force advantage 3. third-class lever: advantage for speed or distance; most in open-kinematic chain motion


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 SystemDefinition

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

Newtons Laws of Motion

Only used for a particle with a mass and negligible size moving in a nonaccelerating 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)

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= -Freactiono

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

Procedure for drawing a free body diagram1. 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 directio