Introduction to Biomechanics
Assigned Reading:
Jenkins: pp. 17-30.
Definitions
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biomechanics - application of the principles of mechanics / physics to biological
organisms
muscle action vs. function
o action - motions produced by a muscle's shortening; described in reference
to axes and planes of body
 - determined by architecture of joint and position of muscle around
it
 - pure mechanics which can be inferred
o function - how the organism chooses to use a muscle
 - can involve positive, negative or non- work (see below)
agonists (Gr., contestant)- muscles with an identical action; usually restricted to
single axis or plane of reference
antagonists (Gr., against + contestant; lit. enemy) - muscles with opposite action;
usually restricted to single axis or plane of reference
synergist (Gr., together + work) - muscles which act together to perform a
function; can involve both agonists and antagonists
work (W) - the mechanical definition
o - occurs when a force moves its point of application
o - e.g., muscles work by moving myosin heads along actin filament
o - thus W = (F) (X), where
 F= force (newtons; N)
 X = distance moved (meters; m); can be positive or negative
relative to line of action of force
o - work is measured in joules [J = (N)(m)]
o - muscles generate tension to perform positive, negative or non- work
 - positive work - muscle shortens while generating tension (i.e.,
X > 0)
 - negative work - muscle lengthens while generating tension (i.e.,
X < O)
 - non-work - muscle generates tension without changing length
(X=0)
Some Physiology (gag!)
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isometric and isotonic contractions
o - limited to experimental conditions in which mechanical properties (either
tension or change in length) of muscle are measured; i.e., not possible in
vivo
o - isometric contraction - muscle length is fixed and tension is measured
 - used to generate length/tension curves (see below)
o
- isotonic contraction - muscle tension (load) is fixed and change in length
(shortening) measured
 - used to generate force (tension)/velocity curves (see below)
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sliding filament theory and length/tension curve
o - theory proposed by biophysicist Jean Hanson (1919-73) and physiologist
Hugh Esmor Huxley (1924- ) in 1954
o - states that during contraction thin filaments slide past thick filaments
with no change in the length of either type of filament
o - force for producing sliding of thin filaments is generated by the crossbridges (formed by myosin heads)
o - theory predicts that force output will be proportional to the degree of
overlap between thick and thin filaments or, more specifically, the number
of cross-bridges formed
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biomechanical implications of the sliding filament theory:
o 1. for maximum force output (total tension) muscle should be positioned
below its optimal length so that work (either positive or negative) will
occur over peak of length/tension curve
o 2. muscles which produce the same action across a joint are typically
arranged such that their optimal lengths occur at different joint positions
thus permitting a nearly constant level of force output at all joint positions
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velocity-force curves
o - generated from series of isotonic contractions
o - force and velocity are inversely related such that at zero (0) velocity
maximum force is generated, and at maximum velocity zero (0) force is
generated
o - power output = force x velocity (rate of doing work)
 - measured in watts (1N x 1m/s)
 - is maximized at about 30% of maximum force
Preliminary concepts
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1. Force output is proportional to cross-sectional area
o - specifically F = total CSA x Specific Tension of muscle (N/cm2)
o - thus muscles that differ in length but have equal CSA generate equal
amounts of force
2. Excursion (distance a muscle can shorten) is proportional to fiber length (see
o - maximum sarcomere excursion = 50% of resting length
o - thus longer fibers will contract a greater distance
3. Velocity (distance of shortening/unit of time) is proportional to fiber length
(assuming equal load)
o - muscles of different fiber length will contract to 50% in same amount of
time
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- since excursions distances differ but time is constant, velocity is greater
in muscles with longer fibers
Muscle Architecture
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Muscle architecture refers to arrangement and length of muscle fibers w/i a
muscle
o - variation in muscle architecture can affect:
 (1) excursion (distance a muscle can contract)
 (2) velocity
 (3) force, and
 (4) line of action
o - variety of classification schemes exist; none perfect (except mine); many
primarily descriptive
o - functionally 3 general types: parallel, triangular and pinnate based on
fiber arrangement
 1) triangular - muscle fibers radially arranged
 -specialized for altering line of action assuming nonuniform distribution of motor units
 2) parallel - muscle fibers are arranged parallel to line of action
(muscle pull)
 - specialized for excursion and/or velocity
 3) pinnate - muscle fibers lie at an angle to line of action (muscle
pull)
 - specialized for force production
 - N.B. Relationship between angle of pinnation (parallel fibers
have an angle of pinnation = 0 degrees), fiber length and excursion
is not simple; in fact in some situations pinnation actually can
increase excursion
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Advantage of pinnation / Disadvantage of parallel
o - maximum force produced by a muscle is proportional to the sum of the
cross-section of all its fibers
o - for muscles of equal volume, more muscle fibers can be packed into a
pinnate arrangement than a parallel arrangement
o - since axis of contraction of muscle fibers not parallel to pull of muscle
(line of action) some muscle force dissipated perpendicular to line of
action
o - thus force output = # of fibers x cosine of angle of insertion
o - thus advantage of pinnation is to increase force output of a muscle by
packing more fibers in a given volume of space
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Cost of pinnation / Advantage of parallel
o - excursion = length a muscle fiber can contract; function of fiber length
o - for muscles of equal length, pinnate muscles have decreased excursion
relative to parallel
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- max. sarcomere shortening = 50% of resting length; thus max. excursion
of muscle = 50% of fiber length
- parallel fibers can shorten to their maximum
- pinnate fibers cannot shorten to their maximum w/o dislodging
themselves from their tendons
- thus pinnate muscle has shorter excursion
Lever mechanics
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Muscles generate forces and skeletal elements apply these forces and thus serve a
machines
o - machine - device for transmitting forces from one point to another
o - majority (but not all) of skeletal elements function as type of machine
known as lever
o - lever is a rigid bar (regardless of shape) which rotates about a fixed point
(fulcrum)
o - in levers forces work by creating rotational forces about the joints
(fulcrum) known as moments; i.e.,
 m = F x L, where
 m = moment or torque
 F = force; in this case muscle tension
 L = Lever (or moment) arm; distance between force and
fulcrum; lies perpendicular to line of action of force
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Lever systems are most easily analyzed under the conditions of equilibrium Force
equilibrium: Fi x Li (in-torque) = Fo x Lo (out-torque)
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- solving for Fo:
 Fo = Fi x (Li/Lo)
- thus to maximize force-output of a lever system for a given
muscle force (Fi):
 1) increase Li
 2) decrease Lo
- Li/Lo = lever advantage
Velocity equilibrium: Vo x Li = Vi x Lo
 - solving for Vo
 Vo = Vi x (Lo/Li)
 - thus to maximize velocity-output of a lever system for a given
muscle velocity (Vi):
 1) decrease Li
 2) increase Lo
 - Lo/Li = gear ratio
Note that for a given muscle input (Fi) a muscle lever system can either:
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a) maximize lever advantage (Li/Lo) and produce a stronger but
slower force (Fo)
 b) maximize gear ratio (Lo/Li) and produce a faster but weaker
force (Vo)
- it cannot maximize both (inverse relationship)
- thus, there is a trade off between velocity and force in any lever system
Muscle fiber types
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Quality of force production can be varied by using different types of muscle fibers
o - vertebrate muscles can be broadly divided into slow and fast based upon
speed of contraction
o - slow fibers - specialized for prolonged tension generation
 - typically generate small forces (due to small fiber CSA and low
innervation ratio) at low metabolic cost (aerobic respiration)
 - fatigue resistant due to high density of mitochondria and
myoglobin
 - 2 subtypes
 1) tonic - multi-terminal fibers; membrane cannot
propagate an AP thus contraction is graded; limited to
extra-ocular muscles in mammals
 2) slow twitch - single terminal fibers; widely distributed
o - fast [twitch] fibers - specialized for generating tension rapidly
 - typically generate larger forces (due to larger fiber CSA and high
innervation ratio) at high metabolic cost (use both aerobic and
anaerobic respiration)
 - different sub-types (2A, 2B, 2X) differ in myosin isoforms and
fatigue resistance
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Majority of muscles are of mixed fiber type composition being a combination of
fast and slow fibers occurring in two arrangements
 1) mosaic - fast and slow fibers uniformly distributed
 2) compartmentalized - fiber types non-uniformly distributed into
intramuscular compartments
o - however, some muscles which are used for repetitive or constant tasks
(e.g., posture) can be comprised nearly entirely of slow fibers
 - e.g., soleus