Jacobian Matrix Calculator (2R Manipulator)

An essential tool for robotics engineers and researchers to calculate the Jacobian matrix for a 2R manipulator. It helps in understanding the relationship between joint velocities and end-effector velocities.

Interactive Calculator

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Jacobian Matrix [0, 0; 0, 0]

Authoritative Data Source

All calculations are based on the standard kinematic equations for robotic manipulators. Consult the textbook "Robotics: Modelling, Planning and Control" (Siciliano et al., 2009).
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The Formula Explained

$$ J = \begin{bmatrix} -L_1 \sin(\theta_1) - L_2 \sin(\theta_1 + \theta_2) & -L_2 \sin(\theta_1 + \theta_2) \\ L_1 \cos(\theta_1) + L_2 \cos(\theta_1 + \theta_2) & L_2 \cos(\theta_1 + \theta_2) \end{bmatrix} $$

Glossary of Variables

How It Works: A Step-by-Step Example

Consider a 2R manipulator with arm lengths L1 = 1m and L2 = 0.5m. If Theta 1 is 30 degrees and Theta 2 is 45 degrees, the Jacobian matrix can be calculated using the given formula.

Frequently Asked Questions (FAQ)

What is the Jacobian Matrix?

The Jacobian matrix is a matrix that defines the relationship between the velocities of the joints and the velocity of the end effector in a robotic arm.

Why is the Jacobian Matrix important in robotics?

It is crucial for understanding how joint movements translate to end-effector movements, which is essential for control and planning in robotics.

Can this calculator be used for different types of manipulators?

Currently, this calculator is designed specifically for a 2R planar manipulator.

What are Theta 1 and Theta 2?

They are the angles of the first and second joints in a 2R manipulator, typically measured in degrees.

How do I determine the lengths L1 and L2?

They are predefined based on the physical dimensions of the manipulator and are crucial for accurate calculations.

Tool developed by Ugo Candido. Content reviewed by the Robotics Expert Team.
Last reviewed for accuracy on: October 15, 2023.

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