<s>
In	O
mechanical	O
engineering	O
,	O
a	O
kinematic	B-Application
chain	I-Application
is	O
an	O
assembly	O
of	O
rigid	O
bodies	O
connected	O
by	O
joints	O
to	O
provide	O
constrained	O
(	O
or	O
desired	O
)	O
motion	O
that	O
is	O
the	O
mathematical	O
model	O
for	O
a	O
mechanical	O
system	O
.	O
</s>
<s>
Kinematic	O
pairs	O
model	O
the	O
hinged	O
and	O
sliding	O
joints	O
fundamental	O
to	O
robotics	O
,	O
often	O
called	O
lower	O
pairs	O
and	O
the	O
surface	O
contact	O
joints	O
critical	O
to	O
cams	B-Data_Structure
and	O
gearing	O
,	O
called	O
higher	O
pairs	O
.	O
</s>
<s>
A	O
kinematic	O
diagram	O
is	O
a	O
schematic	O
of	O
the	O
mechanical	O
system	O
that	O
shows	O
the	O
kinematic	B-Application
chain	I-Application
.	O
</s>
<s>
The	O
modern	O
use	O
of	O
kinematic	B-Application
chains	I-Application
includes	O
compliance	O
that	O
arises	O
from	O
flexure	O
joints	O
in	O
precision	O
mechanisms	O
,	O
link	O
compliance	O
in	O
compliant	O
mechanisms	O
and	O
micro-electro-mechanical	B-Architecture
systems	I-Architecture
,	O
and	O
cable	O
compliance	O
in	O
cable	O
robotic	O
and	O
tensegrity	O
systems	O
.	O
</s>
<s>
The	O
degrees	O
of	O
freedom	O
,	O
or	O
mobility	O
,	O
of	O
a	O
kinematic	B-Application
chain	I-Application
is	O
the	O
number	O
of	O
parameters	O
that	O
define	O
the	O
configuration	O
of	O
the	O
chain	O
.	O
</s>
<s>
Specifically	O
,	O
hinges	B-Operating_System
and	O
sliders	O
each	O
impose	O
five	O
constraints	O
and	O
therefore	O
remove	O
five	O
degrees	O
of	O
freedom	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
a	O
hinge	B-Operating_System
or	O
slider	O
,	O
which	O
are	O
one-degree-of-freedom	O
joints	O
,	O
have	O
and	O
therefore	O
.	O
</s>
<s>
The	O
constraint	O
equations	O
of	O
a	O
kinematic	B-Application
chain	I-Application
couple	O
the	O
range	O
of	O
movement	O
allowed	O
at	O
each	O
joint	O
to	O
the	O
dimensions	O
of	O
the	O
links	O
in	O
the	O
chain	O
,	O
and	O
form	O
algebraic	O
equations	O
that	O
are	O
solved	O
to	O
determine	O
the	O
configuration	O
of	O
the	O
chain	O
associated	O
with	O
specific	O
values	O
of	O
input	O
parameters	O
,	O
called	O
degrees	O
of	O
freedom	O
.	O
</s>
<s>
The	O
constraint	O
equations	O
for	O
a	O
kinematic	B-Application
chain	I-Application
are	O
obtained	O
using	O
rigid	B-Algorithm
transformations	I-Algorithm
to	O
characterize	O
the	O
relative	O
movement	O
allowed	O
at	O
each	O
joint	O
and	O
separate	O
rigid	B-Algorithm
transformations	I-Algorithm
to	O
define	O
the	O
dimensions	O
of	O
each	O
link	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
a	O
serial	O
open	O
chain	O
,	O
the	O
result	O
is	O
a	O
sequence	O
of	O
rigid	B-Algorithm
transformations	I-Algorithm
alternating	O
joint	O
and	O
link	O
transformations	O
from	O
the	O
base	O
of	O
the	O
chain	O
to	O
its	O
end	O
link	O
,	O
which	O
is	O
equated	O
to	O
the	O
specified	O
position	O
for	O
the	O
end	O
link	O
.	O
</s>
<s>
Kinematic	B-Application
chains	I-Application
of	O
a	O
wide	O
range	O
of	O
complexity	O
are	O
analyzed	O
by	O
equating	O
the	O
kinematics	O
equations	O
of	O
serial	O
chains	O
that	O
form	O
loops	O
within	O
the	O
kinematic	B-Application
chain	I-Application
.	O
</s>
<s>
The	O
complexity	O
(	O
in	O
terms	O
of	O
calculating	O
the	O
forward	O
and	O
inverse	B-General_Concept
kinematics	I-General_Concept
)	O
of	O
the	O
chain	O
is	O
determined	O
by	O
the	O
following	O
factors	O
:	O
</s>
<s>
Its	O
topology	B-Architecture
:	O
a	O
serial	O
chain	O
,	O
a	O
parallel	O
manipulator	O
,	O
a	O
tree	O
structure	O
,	O
or	O
a	O
graph	O
.	O
</s>
<s>
The	O
constraint	O
equations	O
of	O
a	O
kinematic	B-Application
chain	I-Application
can	O
be	O
used	O
in	O
reverse	O
to	O
determine	O
the	O
dimensions	O
of	O
the	O
links	O
from	O
a	O
specification	O
of	O
the	O
desired	O
movement	O
of	O
the	O
system	O
.	O
</s>
<s>
His	O
use	O
of	O
the	O
newly	O
developed	O
computer	O
to	O
solve	O
Freudenstein	O
's	O
equation	O
became	O
the	O
prototype	O
of	O
computer-aided	B-Application
design	I-Application
systems	O
.	O
</s>
