Download Introduction to Biomechanics 2001

國立台灣大學九十學年度第二學期生物力學
REVIEW OF MECHANICS
教學目標：學生在修習本課程後，應能
1. 闡述牛頓定律及其運用
2. 了解靜力平衡與動作的產生之關係
3. 描述物理運動時，作用力與動作之關係
參考書籍：
1. Chaffin, 1999: Chap 1
2. Luttgens, K. & Hamilton, N., 1997
Review of Basic Statics
A. Mechanical force (loads)
1. definition
a. an entity that changes the state of motion of a body
b. not necessary to be in contact
2. unit of force
a. 1 newton (N)
- a force that causes linear acceleration of a free body of 1 kg at 1 m/s2
- 1 N = 1 kg·m/s2
b. 1 dyne = 1 g·cm/s2 = 10-5 N
c. 1 lb·ft/s2 = 0.138 kg·m/s2= 0.138 N
F
d
O
Mo = Fd
3. external forces (loads)
a. gravitational force (force of gravity)
g = 9.81 m/s2
HC\BioMech\IntroBM2.doc
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Feb 11,
2002
國立台灣大學九十學年度第二學期生物力學
REVIEW OF MECHANICS
W = mg

1 kg = 9.81 N
b. ground reaction forces: force exerted on a body by the ground
Fx
F y F z Mx My
Mz
c. friction force
-- resistance between two objects
Fs = s N where s = coefficient of static friction
Fk = k N where k = coefficient of kinetic friction
d. air or water resistance
Fa = Av2c
4. internal forces
a. muscle force
b. forces from tendon, ligament, and other connective tissues
c. joint reaction force
FJR = W
MJR = W·dcos
FJR
MJR

d
W
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國立台灣大學九十學年度第二學期生物力學
REVIEW OF MECHANICS
B. Mechanical advantage (MA) of the lever
1. the ratio between the length of the force arm and the length of weight arm
AL( force)
MA 
AL( weight )
2. types of lever
a. first-class lever
b. second-class lever: force advantage
c. third-class lever: advantage for speed or distance; most in open-kinematic
chain motion
C. Centroid
1. definition: the point that defines the geometric center of an object
2. if the material composing a body is homogeneous, the weight can be neglected.
D. Equilibrium
1. definition: a condition in which an object is at rest if originally at rest, or has a
constant velocity if originally in motion
2. Newton’s three laws of motion: used for a particle with a mass and negligible
size moving in a non-accelerating reference frame
a. first law (law of inertia): 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
If F = 0 then v = constant
b. 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
F = k (dmv/dt) = ma
c. third law (law of action and reaction): the mutual forces of action and reaction
between two particles are equal, opposite, and colinear
Faction = -Freaction
3. 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
4. equation of equilibrium
FResultant = 0
HC\BioMech\IntroBM2.doc
MO = 0
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國立台灣大學九十學年度第二學期生物力學
REVIEW OF MECHANICS
E. Free body diagram (FBD)
1. 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
2. procedure for drawing a free body diagram
a. image the body to be isolated from its surroundings and sketch its outlined
shape
b. 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
c. label all forces and couple moments with proper magnitudes and directions
F. Force couple
1. definition: two parallel forces that have the same magnitude, opposite directions,
and are separated by a perpendicular distance
2. FR = 0

 M  (r
A

 rB ) F
3. The only effect of a couple is to produce a rotation or a tendency of rotation in a
specific direction
4. 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
F1
r1
r2
F2
HC\BioMech\IntroBM2.doc
F1 ·r1=F2 ·r2
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國立台灣大學九十學年度第二學期生物力學
REVIEW OF MECHANICS
Basic Concepts in Dynamics
A. Law of acceleration
1. F = ma for a single particle
2. only valid on an inertial frame of reference
B. Mechanical analysis methods used in dynamics
1. direct dynamics (forward dynamics): mechanical analysis of a system that
determines movement from forces
2. inverse dynamics: mechanical analysis of a system that determines forces from
movement
3. relationship between forces and movement
-- 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
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