Inverse Kinematics Calculator (2R Manipulator)

This calculator is designed for robotics enthusiasts and engineers to determine the joint angles of a 2R manipulator required to achieve a specific end effector position. Simply input the desired coordinates, and the calculator will provide the necessary angles.

Input Parameters

Results

Joint Angle 1 (θ1)
Joint Angle 2 (θ2)

Data Source and Methodology

All calculations are based on standard formulas from robotics kinematics. For further reading, see the reference article. All calculations are rigorously based on the formulas and data provided by this source.

The Formula Explained

To calculate the joint angles for a 2R manipulator:

\[\theta_1 = \arctan2(y, x) - \arccos\left(\frac{x^2 + y^2 + L_1^2 - L_2^2}{2 \cdot L_1 \cdot \sqrt{x^2 + y^2}}\right)\]

\[\theta_2 = \arccos\left(\frac{x^2 + y^2 - L_1^2 - L_2^2}{2 \cdot L_1 \cdot L_2}\right)\]

Glossary of Variables

How It Works: A Step-by-Step Example

For a target position of (3, 4), the calculator will compute the joint angles θ1 and θ2 required to position the end effector at this location using the 2R manipulator inverse kinematics equations.

Frequently Asked Questions (FAQ)

What is inverse kinematics?

Inverse kinematics is a method in robotics to calculate joint parameters that provide a desired position of the end of a robotic arm.

How is this calculator used?

Enter the desired end effector position and the calculator will output the joint angles needed to achieve that position.

What are the limitations of a 2R manipulator?

A 2R manipulator can only operate within a specific workspace defined by the lengths of its two arms.

Can I use this calculator for different robots?

This calculator is specifically designed for 2R manipulators. Different robots may have different kinematics.

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