BioLab - Biomechanics Teaching & Learning Tool Box
An Introduction to Linear
Kinematics
Linear Kinematics
Kinematic Analysis
• Linear Kinematics
– description of the motion of a body
– the appearance of a motion with respect to time
• Motion described in terms of (variables):
–
–
–
–
Distance, displacement, length (e.g. stride, stroke)
Time, cadence (e.g. stride frequency, stroke frequency)
Speed, velocity
Acceleration
• Single point models
– e.g. Centre of mass (CM) during running/jumping
• Multi-segment models
– e.g. Co-ordination of body segments during running/jumping
Distance & Displacement
• Distance:
– Length of path which a body covers during motion
– Units: metre (m), centimeter (cm), kilometer (km)
• Displacement:
– The change in position of a body during motion
– Units: metre (m), centimeter (cm), kilometer (km)
• Distance is a scalar, and displacement is a vector variable
Speed and Velocity
• Speed (scalar)
– Length of path (distance)
divided by change in time
(∆t)
Δp d
v=
=
Δt Δt
• Average velocity (vector)
– Change in position (∆p)
divided by change in time
(∆t)
– Displacement (d) divided by
change in time (∆t)
– Vector equivalent of linear
speed
If displacement = 50 m
If t = 5 s
v = 50 / 5
= 10 m·s-1
Velocity
• Units of velocity
Current
velocity
– m/s or m·s-1
• Velocity is a vector
– Magnitude and direction
calculated using Pythagoras
and trigonometry
– The velocity of a swimmer in
a river is the vector sum of
the velocities of swimmer
and current.
Swimmer’s
velocity
Resultant
velocity
Velocity
• For human gait, speed
is the product of stride
length and stride
velocity.
• Adults walk faster
using longer stride
lengths and faster
stride frequency.
• Stride length in
children has great
variability.
Velocity
• Runners traveling at a
slower pace tend to
increase velocity primarily
by stride ____?
• At faster running speeds,
runners rely more on
increasing stride ____?
• Most runners tend to
choose a combination of
stride length and stride
frequency that minimizes
physiological cost.
Best sprinters distinguished by high
stride ___ & short ground contact time.
Velocity
Men’s 100-m Dash 1988 Olympic Games
• Pace: rate of
movement, or
established rate of
locomotion.
• Pace = _time_
distance
– Men’s world record
marathon pace =
4:37 min/mile (2:03.38)
– Women’s world
record marathon
pace = 5:30 min/mile
Position
(m)
Ben Johnson
Elapsed time
Johnson
Pace
Carl Lewis
Interval time
Lewis
Pace
0
0
10
1.83 s
.183 s/m
1.89
.189 m/s
20
2.87 s
.104 s/m
2.96
.107 m/s
30
3.80 s
.093 s/m
3.90 s
.094 m/s
40
4.66 s
.086 s/m
4.79 s
.089 m/s
50
5.50 s
.084 s/m
5.65 s
.086 m/s
60
6.33 s
.083 s/m
6.48 s
.083 m/s
70
7.17 s
.084 s/m
7.33 s
.085 m/s
80
8.02 s
.085 s/m
8.18 s
.085 m/s
90
8.89 s
.087 s/m
9.04 s
.086 m/s
100
9.79 s
.090 s/m
9.92 s
.088 m/s
0
Velocity
• Average velocity
– Average velocity not
necessarily equal to
instantaneous velocity
• Instantaneous velocity
– Occurring at one instant in
time
– Like an automobile
speedometer
Winner of the Men's 100 m at the
2004 Athens Olympics in 9.85 s
Average velocity = 100 / 9.85
= 10.15 m·s-1
2004 Olympic Men's 100 m
Kinematic analysis of 100 m sprint
Kinematic analysis of 100 m sprint
Velocity during 100 m
Average velocity 0-10 m
v = d / ∆t = 10 / 2.2 = 4.5 m·s-1
10-20 m
= 10 / 1.2 = 8.3 m·s-1
20-30 m
= 10 / 0.8 = 12.5 m·s-1
30-40 m
= 10 / 0.7 = 14.3 m·s-1
40-50 m
= 10 / 0.8 = 12.5 m·s-1
50-60 m
= 10 / 0.8 = 12.5 m·s-1
60-70 m
= 10 / 0.7 = 14.3 m·s-1
70-80 m
= 10 / 0.8 = 12.5 m·s-1
80-90 m
= 10 / 0.9 = 11.1 m·s-1
90-100 m
= 10 / 0.9 = 11.1 m·s-1
Average Acceleration
• Change in velocity (∆v) divided
by change in time (∆t)
(v2 - v1 )
v
a=
=
t
t
• Units
– m/s/s or m/s2 or m·s-2
• Vector
– As with displacement & velocity,
acceleration can be resolved
into components using
trigonometry & Pythagorean
theorem
V1 = 4.5 m·s-1
V2 = 8.3 m·s-1
∆t = 1.2 s
a = (8.3 - 4.5) / 1.2 = 3.2 m·s-2
Acceleration during 100 m
Acceleration at start of race
a = (v2 - v1) / ∆t
= (8.3 - 4.5) / 1.2
= 3.2 m·s-2
Positive Acceleration
_________________________________________________________________________________________________________________________________
Acceleration during middle of race
a = (v2 - v1) / ∆t
= (12.5 - 12.5) / 0.8
= 0
Constant Velocity
_________________________________________________________________________________________________________________________________
Acceleration at end of race
a = (v2 - v1) / ∆t
= (11.1 - 14.3) / 0.9
= -3.5 m·s-2
Negative Acceleration
Acceleration and Direction of
Motion
• Complicating factor in understanding
acceleration is direction of motion of object.
• When object moving in same direction
continually, accelerate often used to indicate
an increase in velocity and decelerate to
indicate a decrease in velocity.
• If object changes direction, one direction is
positive, the opposite direction is negative.
Acceleration
Increasing velocity
Negative acceleration
Decreasing velocity
Positive acceleration
Motion in a negative direction
Increasing velocity
Positive acceleration
Decreasing velocity
Negative acceleration
Motion in a positive direction
Player running in negative direction increases negative
velocity results in negative acceleration.
Player begins to decrease velocity in negative direction has
positive acceleration.
Positive and negative accelerations can occur without
changing directions.
Summary
• Variables used to describe motion are either:
– Scalar (magnitude only: e.g. time, distance and speed)
– Vector (magnitude and direction: e.g. displacement,
velocity and acceleration)
• Displacement is the change in position of a body
• Average velocity is the change in position divided by the
change in time
• Average acceleration is the change in velocity divided by
the change in time
Recommended Reading
• Enoka, R.M. (2002). Neuromechanics of Human Movement
(3rd edition). Champaign, IL.: Human Kinetics. Pages 3-10
& 22-27.
• Grimshaw, P., Lees, A., Fowler, N. & Burden, A. (2006).
Sport and Exercise Biomechanics. New York: Taylor &
Francis. Pages 11-21.
• Hamill, J. & Knutzen, K.M. (2003). Biomechanical Basis of
Human Movement (2nd edition). Philadelphia: Lippincott
Williams & Wilkins. Pages 271-289.
• McGinnis, P.M. (2005). Biomechanics of Sport and Exercise
(2nd edition). Champaign, IL.: Human Kinetics.
Pages 47-62.