Difference between revisions of "Assigning coordinate frames"
| Line 5: | Line 5: | ||
===Notation=== | ===Notation=== | ||
| − | The notation of the links and joints is shown in the figure below. A manipulator consists of <math>n</math> links that are connected with <math>n</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_i</math> is connected with its joint <math>J_i</math> to the end of link <math>L_{i-1}</math>. The proximate link <math>L_{i+1}</math> is then mounted to the end of <math>L_i</math> via its joint <math>J_{i+1}</math>. The first link <math>L_1</math> is mounted on the base via joint <math>J_1</math> | + | The notation of the links and joints is shown in the figure below. A manipulator consists of <math>n</math> links that are connected with <math>n</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_i</math> is connected with its joint <math>J_i</math> to the end of link <math>L_{i-1}</math>. The proximate link <math>L_{i+1}</math> is then mounted to the end of <math>L_i</math> via its joint <math>J_{i+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> that does not directly belong to the manipulator. The end of the last link <math>L_n</math> corresponds to the end-effector. |
| + | |||
| + | 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_n</math> of the last link is finally attached to the end of of the manipulator and so to the end-effector. | ||
[[File:links.png|left|850px]] | [[File:links.png|left|850px]] | ||
Revision as of 16:24, 30 October 2015
| ← Back: Denavit-Hartenberg Convention | Overview: Denavit-Hartenberg Convention | Next: Denavit-Hartenberg parameters → |
To be able to determine the spatial relationship or transformation, respectively, between the links of a manipulator, local coordinate frames have to assigned to them first. There are several rules that have to be observed when assigning coordinate frames following the Denavit-Hartenberg convention.
Notation
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 
that does not directly belong to the manipulator. The end of the last link 
corresponds to the end-effector.
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.
