# Concatenate Jacobian matrices

I have a manipulator A with known Jacobian matrix and manipulator B with also known Jacobian matrix. Now I want to chain them, B will be attached at the end of A. How do I get the Jacobian of this manipulator? Can I just multiply the both knwon Jacobian matrices?

## 2 Answers

Unfortunately is not as straightforward as multiplying them.

The Jacobian of B is considering that the first body is fixed to the plane. You would need to add the velocity at that point, which is the end-point of the first Jacobian.

Basically, you would have an intermediate point, which needs to have the precedent velocity and with some math manipulation, you could get to the full end Jacobian. q

• Certainly, the Jacobian cannot be multiplied together. The correct operation is concatenation, although some care needs to be taken at the "border" as you have pointed out. Jan 20 at 16:00

If you have the two Jacobian matrices, do you also have the two positional transformation matrices? If so, you could multiply these two matrices together, and take partial derivatives of the result to get the full Jacobian.

• True, but this holds only for the Analytic Jacobian, not for the Geometric Jacobian. Jan 20 at 22:30