Inverse Kinematics (2-DOF)

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advanced

Calculate joint angles from end-effector position.

Formula

q2 = acos((x2+y2-L12-L22)/(2xL1xL2))

Compare two scenarios side-by-side

Target X

Target Y

Link 1 Length

Link 2 Length

Joint 1 Angle

—

Joint 2 Angle

—

Reachable (1=yes)

—

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About This Calculator & Guide

About the Inverse Kinematics (2-DOF)

The Inverse Kinematics (2-DOF) is a dedicated tool in our Engineering category designed to help you calculate joint angles from end-effector position in seconds. By automating the underlying mathematics, this utility eliminates manual calculations and provides reliable, instantaneous estimations.

Mathematical Principles & Calculation Steps

To compute the results, the calculation engine processes your custom inputs: Target X (m), Target Y (m), Link 1 Length (m), Link 2 Length (m). Specifically, the calculations are evaluated using the standard relationship: q2 = acos((x2+y2-L12-L22)/(2xL1xL2)). All computations are performed locally within your secure browser session, ensuring absolute data privacy and instantaneous updates without any network delay.

Worked Step-by-Step Calculation Example

Worked Example Sandbox

For illustrative purposes, consider the following calculation using our default values. When we initialize the input fields with Target X = 0.7 m, Target Y = 0.3 m, Link 1 Length = 0.5 m, Link 2 Length = 0.4 m, the client-side calculator processes the numbers to resolve the formula and produce the final outputs: Joint 1 Angle = -5.189 ° and Joint 2 Angle = 64.849 ° and Reachable (1=yes) = 1.

How to Use This Calculator

Set Inputs: Adjust the input values: Target X, Target Y, Link 1 Length to match your scenario.
Verify Outputs: The outputs: Joint 1 Angle, Joint 2 Angle, Reachable (1=yes) are updated in real-time on your screen.
Iterate: Change values and compare alternative scenarios to find your optimal result.

Frequently Asked Questions

What does the Inverse Kinematics (2-DOF) calculator do?+

Calculate joint angles from end-effector position. It is part of the Engineering category on WebCalcSys and provides instant, accurate results. Simply enter your values and the calculator computes the answer in real time — no downloads or sign-ups required.

How do I use the Inverse Kinematics (2-DOF) calculator?+

Enter the required values (Target X, Target Y, Link 1 Length, Link 2 Length) into the input fields. The calculator processes your data instantly and displays Joint 1 Angle, Joint 2 Angle, Reachable (1=yes) in real time. You can adjust any input to run what-if scenarios.

What formula does the Inverse Kinematics (2-DOF) calculator use?+

This calculator uses the formula: q2 = acos((x2+y2-L12-L22)/(2xL1xL2)). It is based on standard engineering principles and is trusted by students, professionals, and educators worldwide.