Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Robotics: Forward and Inverse Kinem... by Damian Gordon 19792 views
- PID control dynamics of a robotic a... by popochis 9626 views
- Robot Manipulation Basics by Robots Alive India 17022 views
- Fundamental of robotic manipulator by snkalepvpit 15251 views
- Manipulator kinematics by Sudhir Reddy 2967 views
- Robot manipulator control_theory_an... by Sel Vam 3045 views

7,611 views

Published on

Published in:
Education

License: CC Attribution-ShareAlike License

No Downloads

Total views

7,611

On SlideShare

0

From Embeds

0

Number of Embeds

3

Shares

0

Downloads

250

Comments

0

Likes

3

No embeds

No notes for slide

- 1. 2 Link Planar Manipulator 2 1 a 1 a 2 O 2 O 1 O 0 x 1 x 0 x 2 y 1 y 2 y 0 Frame 0 – ground reference Frame 1 – link 1, distal end Frame 2 – link 2, distal end Length of Link 1 = a 1 Length of Link 2 = a 2 Note: coordinate systems are consistent with the Denavit-Hartenburg system
- 2. Forward Kinematics <ul><li>Find endpoint at 0 d 02 </li></ul><ul><ul><ul><li>(i.e. endpoint w.r.t. ground reference) </li></ul></ul></ul>
- 3. Homogeneous Transformations in a plane O 1 O 0 p 0 p 1 0 d 01 y 0 x 0 x 1 y 1 P
- 4. Composition of Homogeneous Transforms <ul><li>Coordinate transformations can be chained </li></ul><ul><ul><li>Forward: 0 T 2 = 0 T 1 1 T 2 </li></ul></ul><ul><ul><li>Inverse: 0 P = ( 0 T 1 ) -1 0 P </li></ul></ul>
- 5. Frame 1 is displaced from Frame 0 by rotation of 30 degrees and a translation of (1,1). Frame 2 is displaced from Frame 1 by a rotation of 60 degrees and translation of (1/2, 3/2) O 1 O 0 p 2 30 d 01 y 0 x 0 x 1 y 1 1 1 d 12 p 1 p 0 y 2 x 2 60 1/2 Sqrt(3)/2 1 1
- 6. O 1 O 0 p 2 30 d 01 y 0 x 0 x 1 y 1 1 1 d 12 p 1 p 0 y 2 x 2 60 1/2 Sqrt(3)/2 1 1
- 7. Homogeneous Coordinates <ul><li>In graphics HC used to represent: scaling, shear, translation, rotation. </li></ul><ul><li>Point denoted by set of coordinates </li></ul><ul><ul><li>A set of points in R 3 whose last coordinate1 is referred to as the standard affine plane in R 3 </li></ul></ul><ul><ul><li>A vector is denoted by 3 coordinate vector whose last component is 0 and lies in the affine plane </li></ul></ul>
- 8. P1 P2
- 9. Operators Note: in composing homogeneous transformations Translation matrix, then Rotation Matrix
- 10. Trans and Rot Operators <ul><li>Translate a point P 1 , represented relative to origin O 0 by p 1 , by displacement d to point P 2 , represented relative to origin O 0 by p 2 </li></ul><ul><li>The rotation operator rotates a point P 1 to P 2 by 1 </li></ul>
- 11. General Transformation Operator <ul><li>First rotates a point and then translates it </li></ul>
- 12. Two views of movement P1-> P2 <ul><li>Coordinate Transformation </li></ul><ul><ul><li>Change the position of the origin </li></ul></ul><ul><li>Point Transformation </li></ul><ul><ul><li>Move point relative to a fixed reference frame </li></ul></ul>
- 13. Composition of operators <ul><li>As a coordinate transformation </li></ul><ul><ul><li>Translate origin of frame 0 to (1,1/2) then rotates the axes by 30 degrees </li></ul></ul><ul><li>As an operator </li></ul><ul><ul><li>Rotate frame 1 by 30 degrees and then translate it to (1,1/2) all relative to frame 0 </li></ul></ul>
- 14. Poles of planar displacements <ul><li>Pole: a point that does not move under arbitrary planar operators except pure translation </li></ul>
- 15. Spatial Transformations and Displacements <ul><li>2D to 3D is straightforward for Linear displacements </li></ul><ul><li>Rotation in 3D is not Commutitave </li></ul><ul><ul><li>R 1 R 2 R 2 R 1 </li></ul></ul>

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment