Jacobian Matrix

Question 1

What is the velocity Jacobian matrix used for?

Answer 1

• Relation between joint velocities and cartesian velocities and inverse problem
• Analysis of kinematic singularities
• Inverse position kinematics
• Inverse dynamics

Question 2

Derive the Jacobian matrix from a simple mechanism (2 links).

Answer 2

1. x = L1cos(theta1) + L2cos(theta1+theta2)
   y = L1sin(theta1) + L2sin(theta1 + theta2)
2. derivation

Question 3

Singularity analysis.

Answer 3

Is a particular condition of the robot.

• Infinite solutions for the inverse kinematic problem
• High speeds of motors

Det(J) = 0

Question 4

Principle of the virtual work.

Answer 4

dW = F*dx
….
{r} = [J]^T * {F}