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Forward Kinematics

Forward Kinematics. Where is my hand ?. Examples. Denavit-Hartenberg. Specialized description of articulated figures (joints) Each joint has only one degree of freedom rotate around its z-axis translate along its z-axis What’s so interesting about 6 DOF ?. Denavit-Hartenberg.

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Forward Kinematics

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  1. Forward Kinematics • Where is my hand ?

  2. Examples

  3. Denavit-Hartenberg • Specialized description of articulated figures (joints) • Each joint has only one degree of freedom • rotate around its z-axis • translate along its z-axis • What’s so interesting about 6 DOF ?

  4. Denavit-Hartenberg • Compute the link vector ai and the link length • Attach coordinate frames to the joint axes • Compute the link twist αi • Compute the link offset di • Compute the joint angleφi • Compute the transformation (i-1)Ti which transforms entities from linki to linki-1

  5. Denavit-Hartenberg This transformation is done in several steps : • Rotate the link twist angle αi around the axis xi • Translate the link length ai along the axis xi • Translate the link offset di along the axis zi • Rotate the joint angle φi around the axis zi 5

  6. Denavit-Hartenberg 6

  7. Denavit-Hartenberg Multiplying the matrices : In DH only φ and d are allowed to change. 7

  8. Denavit-Hartenberg • Video

  9. Z3 Z1 Z0 Joint 3 X3 Y0 Y1 Z2 d2 Joint 1 X0 X1 X2 Joint 2 Y2 a0 a1 Example 1 D-H Link Parameter Table : rotation angle from Zi-1 to Zi about Xi : distance from intersection of Zi-1 & Xi to origin of i coordinate along Xi : distance from origin of (i-1) coordinate to intersection of Zi-1 & Xi along Zi-1 : rotation angle from Xi-1to Xi about Zi-1 http://opencourses.emu.edu.tr/file.php/32/lecture%20notes/Denavit-Hartenberg%20Convention.ppt

  10. Example 2 : rotation angle from Zi-1 to Zi about Xi : distance from intersection of Zi-1 & Xi to origin of i coordinate along Xi : distance from origin of (i-1) coordinate to intersection of Zi-1 & Xi along Zi-1 : rotation angle from Xi-1to Xi about Zi-1

  11. Example 3

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