文档介绍：MECH572A Introduction To Robotics
Lecture 7
Dept. Of Mechanical Engineering
Review
Basic Robotic Kinematic Problems
Direct (forward) Kinematics
Inverse Kinematics
DH Notation
Oi-1
Oi
Oi+1
Zi-1
Zi
Zi+1
i-1
i
i+1
Xi-1
Xi
Xi+1
Revolute joints
bi-1
bi
i
ai-1
ai
i
i-1
i-1
Review
Transformation Between Neighboring Links
Fi to Fi+1
Orientation:
Position:
Review
Forward Kinematics
Known joint angles
End Effector Position + Orientation
Inverse Kinematics
Overview
- Problem description:
Known EE position and orientation, find joint angles (inverse process)
Direct Kinematics Problem (DKP) -> Solution unique
Inverse Kinematics Problem (IKP) -> May have multiple solutions,
not always solvable (Kinematic Invertibility)
Equations in IKP are usually highly nonlinear, analytically solvable (closed form solution available) only for certain types of manipulators, examples:
PUMA (6R decoupled)
Stanford Arm (5R-1P)
Canadarm 2 (7R with 3 parallel pitch joint axes)
other types of manipulator rely on numerical methods for solution
Inverse Kinematics
Overview (cont'd)
- PUMA – 6R decoupled (Arm + Wrist)
Inverse Kinematics
Overview (cont'd)
- Canada Arm 2 – 7R (Off-pitch Joints + Pitch joints)
3 parallel pitch joints
4 off-pitch joints
Inverse Kinematics
Overview (cont'd)
Scope of this course – Decoupled manipulators
Have Special architecture that allows the decoupling of position problem from orientation problem. . PUMA
Analytical IKP solution available
Inverse Kinematics
6-R Decoupled Manipulator
Arm (Position)
Wrist (Orientation)
C: wrist centre
Inverse Kinematics
6-R Decoupled Manipulator
Position Problem
Recall ai =Qibi - eq()