8 Computers and Automation Engineering – “Robotic Systems”
Robotic Systems
Inverse Kinematics of Manipula
Case Study
,Forward kinematics VS. Inverse kinematics
X end-effector
(Tool)
Z Position and Orientation
Y
(𝒙 , 𝒚 , 𝒛 , 𝑹𝒙 , 𝑹𝒚 , 𝑹𝒛 )
Object (Goal)
IK
Y
FK
Base
X
Z Manipulator’s
,𝜽𝟏 , 𝜽𝟐 , ⋯ , 𝜽𝒏 , 𝒅𝟏 , 𝒅𝟐 , ⋯ , 𝒅𝒎 -
Parameters
Robotic 20-21 / Dr. Aghiad Kh. (email: )
, DENAVIT-HARTENBERG PARAMETERS FOR JOINT ( 𝒊 )
a i the distance
from Zˆ to Zˆ measured along Xˆ
i i 1 i 𝑨𝒙𝒊𝒔 𝒊 − 𝟏
𝑱𝒐𝒊𝒏𝒕 𝒊
𝒍𝒊𝒏𝒌 𝒊 − 𝟏
i the angle 𝑱𝒐𝒊𝒏𝒕 𝒊 − 𝟏
from Zˆ i to Zˆ i 1 measured about Xˆ i 𝒁𝒊−𝟏
𝒁𝒊
𝒀𝒊−𝟏 𝒀𝒊
d i the distance
𝑿𝒊
from Xˆ to Xˆ measured along Zˆ
i 1 i i *𝒊 − 𝟏+ 𝑿𝒊−𝟏 *𝒊+
𝒂𝒊−𝟏 𝒅𝒊
i the angle 𝜶𝒊−𝟏 𝜽𝒊
from Xˆ i 1 to Xˆ i measured about Zˆ i
Robotic 20-21 / Dr. Aghiad Kh. (email: )
Robotic Systems
Inverse Kinematics of Manipula
Case Study
,Forward kinematics VS. Inverse kinematics
X end-effector
(Tool)
Z Position and Orientation
Y
(𝒙 , 𝒚 , 𝒛 , 𝑹𝒙 , 𝑹𝒚 , 𝑹𝒛 )
Object (Goal)
IK
Y
FK
Base
X
Z Manipulator’s
,𝜽𝟏 , 𝜽𝟐 , ⋯ , 𝜽𝒏 , 𝒅𝟏 , 𝒅𝟐 , ⋯ , 𝒅𝒎 -
Parameters
Robotic 20-21 / Dr. Aghiad Kh. (email: )
, DENAVIT-HARTENBERG PARAMETERS FOR JOINT ( 𝒊 )
a i the distance
from Zˆ to Zˆ measured along Xˆ
i i 1 i 𝑨𝒙𝒊𝒔 𝒊 − 𝟏
𝑱𝒐𝒊𝒏𝒕 𝒊
𝒍𝒊𝒏𝒌 𝒊 − 𝟏
i the angle 𝑱𝒐𝒊𝒏𝒕 𝒊 − 𝟏
from Zˆ i to Zˆ i 1 measured about Xˆ i 𝒁𝒊−𝟏
𝒁𝒊
𝒀𝒊−𝟏 𝒀𝒊
d i the distance
𝑿𝒊
from Xˆ to Xˆ measured along Zˆ
i 1 i i *𝒊 − 𝟏+ 𝑿𝒊−𝟏 *𝒊+
𝒂𝒊−𝟏 𝒅𝒊
i the angle 𝜶𝒊−𝟏 𝜽𝒊
from Xˆ i 1 to Xˆ i measured about Zˆ i
Robotic 20-21 / Dr. Aghiad Kh. (email: )
