1. بسم الله الرحمن الرحیم

2. رباتیک
جلسه هشتم

3. Kinematic relations X=FK(θ) θ =IK(X) Task Space Joint Space
Location of the tool can be specified using a joint space or a cartesian space description

4. Velocity relations
Relation between joint velocity and cartesian velocity.
JACOBIAN matrix J(θ)
Task Space
Joint Space

6. Jacobian
Suppose a position and orientation vector of a manipulator is a function of 6 joint variables: (from forward kinematics)
X = h(q)

7. Jacobian Matrix

8. Jacobian Matrix
Jacobian is a function of q, it is not a constant!

9. Jacobian Matrix
Linear velocity
Angular velocity
The Jacbian Equation

10. Example 2-DOF planar robot arm 2 1 Given l1, l2 , Find: Jacobian
(x , y) l2 l1

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