Difference between revisions of "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 <math>k</math> links that are connected with <math>k</math> 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 <math>L_n</math> is connected with its joint <math>J_n</math> to the end of link <math>L_{n-1}</math>. The proximate link <math>L_{n+1}</math> is then mounted to the end of <math>L_n</math> via its joint <math>J_{n+1}</math>. The first link <math>L_1</math> is mounted on the base via joint <math>J_1</math>. So the base is actually link <math>L_0</math> but does not directly belong to the manipulator. The end of the last link <math>L_k</math> corresponds to the end-effector. | + | The notation of the links and [[Types of joints|joints]] is shown in the figure below. A manipulator consists of <math>k</math> links that are connected with <math>k</math> 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 <math>L_n</math> is connected with its joint <math>J_n</math> to the end of link <math>L_{n-1}</math>. The proximate link <math>L_{n+1}</math> is then mounted to the end of <math>L_n</math> via its joint <math>J_{n+1}</math>. The first link <math>L_1</math> is mounted on the base via joint <math>J_1</math>. So the base is actually link <math>L_0</math> but does not directly belong to the manipulator. The end of the last link <math>L_k</math> corresponds to the end-effector. |
There are <math>k</math> '''coordinate frames''' defined for the <math>k</math> 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 <math>K_0</math>, is the base or reference frame and attached to the base in joint <math>J_1</math>. The next frame is <math>K_1</math> at the end of link <math>L_1</math> in joint <math>J_2</math> followed by <math>K_2</math> at the end of <math>L_2</math> and so on. The coordinate frame <math>K_k</math> of the last link is finally attached to the end of of the manipulator and so to the end-effector. | There are <math>k</math> '''coordinate frames''' defined for the <math>k</math> 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 <math>K_0</math>, is the base or reference frame and attached to the base in joint <math>J_1</math>. The next frame is <math>K_1</math> at the end of link <math>L_1</math> in joint <math>J_2</math> followed by <math>K_2</math> at the end of <math>L_2</math> and so on. The coordinate frame <math>K_k</math> of the last link is finally attached to the end of of the manipulator and so to the end-effector. | ||
Revision as of 17:48, 10 November 2015
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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.
