DefinitionsKinematics is the science of motion. In human movement, it
is the study of the positions, angles, velocities, and accelerations of body
segments and joints during motion.
It's important to define these terms
Body segments are considered to be rigid bodies for
the purposes of describing the motion of the body. They include the foot, shank
(leg), thigh, pelvis, thorax, hand, forearm, upper-arm and head.
Joints between adjacent segments include the ankle (talocrural
plus subtalar joints), knee, hip, wrist, elbow and shoulder.
Position describes the location of a body segment or joint in
space, measured in metres. A related measure called displacement refers
to the position with respect to a starting position. In two dimensions, the
position is given in Cartesian co-ordinates, with horizontal followed by
In three dimensions all three directions must be defined:
e.g. (1.5, 6.2, 3.2), (2.8, 9.6, 7.8) etc.
(also called inter-segmental angle) is the simply the angle between the two
segments on either side of the joint, usually measured in degrees and often
converted to clinical notation. Since joint angles are relative to the segment
angles, they don't change with the body orientation.
Segment angle is
quite different. It is the angle of the segment with respect to the right-hand
horizontal. Note that it is an absolute measure, meaning that it changes
according to the orientation of the body.
another word for speed. Velocity may be linear (change in position)
measured in metres per second (m/s or ms-1), or angular (change in
angle), measured in degrees per second (deg./s or deg.s-1). Normally, velocity
is derived from position or angle data by the process of differentiation.
Velocity = distance moved / time taken
Thus if the knee moves
from a horizontal position of 1.5 m to a position of 1.6 m in 1/50 of a second,
it has a velocity of
Velocity = (1.6 - 1.5) / (1/50)
= 0.1 x 50
= 5 ms-1.
Acceleration is change in velocity. Again, it may be
linear (change in linear velcocity) measured in metres per second per
second (m/s2 or ms-2), or angular (change in angular velocity), measured
in degrees per second per second (deg./s2 or deg.s-2). Acceleration, too, is
usually calculated from the position data by differentiating twice. It can also
be measured directly by an instrument called an accelerometer.
Use of kinematic measurementsKinematic measurements are limited in what
they can tell us about the causes of motion is - for this we need to look at the
kinetics. However, they do provide a description of the motion
which can be valuable for certain purposes.
Stance-phase kinematicsOne important observation we can make from
looking at the kinematics is the amount of up-down and sideways motion. In
actions such as walking and running, the body is attempting to move horizontally
across the ground - any other motion, especially vertical, does not help this
objective, and uses up precious energy.
If the body had wheels it could
avoid vertical motion all together, but since we have legs, there must be some
vertical motion. The reason for this is that at heel-strike and toe-off the two
legs make up the sides of a triangle, while during mid-stance the stance leg is
Mid-stance -----------------> Toe-off
This has the effect of
lowering the upper-body (often called the HAT segment for Head-Arms-Trunk) at
heel-strike and toe-off (which together make up the phase known as double
stance, when both feet are in contact with the ground), and raising it
Mid-stance -------------> Toe-off
By the way, the funny
cross-like sign means the body centre of mass (CoM), which is located in the HAT
segment (in the pelvis). In order for the CoM to rise up between heel-strike and
mid-stance, energy must be expended, which is not gotten back when it drops back
down again at toe-off. This up-down motion of the CoM is therefore inefficient,
and we will see the locomotor system has several methods to try to reduce its
The Determinants of GaitAfter the second-world war, there were a large
number of limbless ex-servicemen in the United States. The Government realised
that a major effort was needed to develop improved prostheses, particularly
lower-limb prostheses, to get these people walking again. As part of this large
research project, the University of Calfornia at Berkely was requested to
perform comprehensive studies on normal and disordered locomotion. Out of this
research came much of our present understanding of the biomechanical mechanisms
used in walking and running.
Several of these key mechanisms relate to
the methods used by the body to reduce the up-down and side-to-side motion of
the body CoM, and because of their fundamental importance to walking
biomechanics, they have been called the Determinants of Gait. The determinants
have two main goals: to reduce the maximum height of the body CoM during
mid-stance, and to increase the minimum height of the body CoM at heel-strike
a) Pelvic rotation
The pelvis rotates
anteriorly at heel-strie, and posteriorly at toe-off to increase the effective
leg-length at these times:
The pelvis lists downward (obliquity) to increase the effective
leg length at toe-off and heel-strike:
c) Stance Phase knee
A slight flexion of the knee lowers the CoM during stance:
The ankle is dorsiflexed at heel-strike and
plantar-flexed at toe-off. Both these actions increase the length of the leg(see
e) Transverse rotation of leg
The lower-limb is lengthened by external rotation, and shorted
by internal rotation.
In the foot, these rotations are facilitated by the
torque-converter effect, whereby pronation at heel-strike is converted to
internal tibial (and subsequently femoral) rotation, and external rotation of
the femur at toe-off is converted into supination of the foot. These actions are
a consequence of the axes of the talo-crural and talo-calcaneal (subtalar)
f) Genu valgum The anatomical valgus at the knee permits a
narrower walking base, and thus a smaller lateral shift, than would otherwise be
All these actions in themselves contribute very small reductions in the
amplitude of the CoM (pelvis) motion, but added together, they reduce it
considerably, to around 50 mm (up-down and side-to-side) in normal gait.
Swing-phase kinematicsAn essential pre-requisiste for gait is to be
able to shorten the swing leg before propelling it foward. The main way
this is achieved is by flexion of the knee. This amount of swing-phase
knee-flexion is proportional to the stride length, and thus the gait velocity
(Kirtley et al, 1985):
Many gait pathologies (e.g hemiplegia, diplegia,
knee osteoarthrosis) impair swing-phase knee flexion, causing compensatory
mechanisms to be used, such as hip-hiking, lateral-tilting and
Summary of sagittal-plane joint anglesSo, basically, you can think of
the actions of the knee and ankle joints as compensating for the
flexion-extension motion of the hip. At extreme flexion of the hip (at
heel-strike and toe-off) the knee is extended, while during stance knee flexion
and ankle dorsiflexion help to reduce the effective height of the body.
Other useful kinematic measuresOther useful kinematic measures relate
to the risk of falling. In general, there are two types of fall: the
trip, and the skid. The former is a result of the low foot
clearance during mid-swing, typically about 1.5 cm, while the latter is
caused by a high forward velocity at heel-strike. Moreover, it is
possible that the vestibular organ may be disorientated by high accelerations
from the lower-limbs if they are not (as is usually the case) attenuated by the
spine. Thus, the head to hip forward acceleration ratio has been used to
gauge the efficiency of this spinal damping mechanism.
ReferencesKirtley C, Whittle MW & Jefferson RJ (1985) Influence of
Walking Speed on Gait Parameters Journal of Biomedical Engineering 7(4):
Inman & Saunders, Human Walking (2nd Edition).
DA (1991) The biomechanics and motor control of human gait: normal, elderly and
pathological. University of Waterloo press, Ontario.
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