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Two-Link Planar Robot Arm Inverse Kinematics Joint Angles Calculator

Easily calculate and compute two-link planar robot arm inverse kinematics joint angles calculator with accurate equations, live formulas, and expert guidance.

Desired Cartesian horizontal position.

Desired Cartesian vertical position.

Length of first proximal arm link.

Length of second distal arm link.

1 for positive theta2, 2 for negative theta2.

Calculated Result
-1.7 deg

Base Joint θ₁

Base Joint θ₁

-1.7 deg

Joint Angle Theta1 Deg

-1.7

Joint Angle Theta2 Deg

71.2

Radial Target Distance Mm

367.2

Maximum Reachable Workspace Mm

450

-1.7 — deg

Calculation Breakdown

  1. Applied FormulaSolves the analytical closed-form inverse kinematics for a 2-DOF planar articulated robotic arm, providing joint angles (θ1, θ2) for elbow-up and elbow-down configurations.\cos\theta_2 = \frac{x^2 + y^2 - L_1^2 - L_2^2}{2 L_1 L_2}, \quad \theta_1 = \operatorname{atan2}(y, x) - \operatorname{atan2}(L_2 \sin\theta_2, L_1 + L_2 \cos\theta_2)

Two-Link Inverse Kinematics Metric Output

Interactive visualization based on your current inputs

Calculated Value
-1.7-1.0-0.30.31.0Base Joint θ₁

What Is the Two-Link Planar Robot Arm Inverse Kinematics Joint Angles Calculator?

This tool computes two-link planar robot arm inverse kinematics joint angles calculator with high precision arithmetic.

How Does the Two-Link Planar Robot Arm Inverse Kinematics Joint Angles Calculator Work?

Solves the analytical closed-form inverse kinematics for a 2-DOF planar articulated robotic arm, providing joint angles (θ1, θ2) for elbow-up and elbow-down configurations.

Two-Link Planar Robot Arm Inverse Kinematics Joint Angles Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

cos⁡θ2=x2+y2−L12−L222L1L2,θ1=atan2⁡(y,x)−atan2⁡(L2sin⁡θ2,L1+L2cos⁡θ2)\cos\theta_2 = \frac{x^2 + y^2 - L_1^2 - L_2^2}{2 L_1 L_2}, \quad \theta_1 = \operatorname{atan2}(y, x) - \operatorname{atan2}(L_2 \sin\theta_2, L_1 + L_2 \cos\theta_2)

Solves the analytical closed-form inverse kinematics for a 2-DOF planar articulated robotic arm, providing joint angles (θ1, θ2) for elbow-up and elbow-down configurations.

How to Use the Two-Link Planar Robot Arm Inverse Kinematics Joint Angles Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Two-Link Planar Robot Arm Inverse Kinematics Joint Angles Calculator Example

Input Values:

targetCartesianXMm:320
targetCartesianYMm:180
link1LengthMm:250
link2LengthMm:200
elbowConfiguration:1
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required deg.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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