Notation of links, joints and coordinate frames
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The notation of the links and joints is shown in the figure below. A manipulator consists of links that are connected with
joints. The links correspond to the rigid parts of an arm and the joints are the flexible connections between them. A joint is always assigned to the proximate link. So a link
is connected with its joint
to the end of link
. The proximate link
is then mounted to the end of
via its joint
. The first link
is mounted on the base via joint
. So the base is actually link
but does not directly belong to the manipulator. The end of the last link
corresponds to the end-effector.
There are coordinate frames defined for the
links of a manipulator plus one base or reference frame, respectively. The coordinate frames are always attached to the end of the links at the distal joints. The first coordinate frame, indexed
, is the base or reference frame and attached to the base in joint
. The next frame is
at the end of link
in joint
followed by
at the end of
and so on. The coordinate frame
of the last link is finally attached to the end of of the manipulator and so to the end-effector.
![]() The left side of the figure below shows a manipulator with The joints are named Beginning with the base coordinate system |