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Planar Two-Link Robot Arm Inverse Kinematics Joint Angle Calculator

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

Calculated Result
-5.6 degrees

Shoulder Angle θ₁

Shoulder Angle θ₁

-5.6 degrees

Shoulder Angle Theta1 Elbow Down Deg

-5.6

Elbow Angle Theta2 Elbow Down Deg

90.6

Shoulder Angle Theta1 Elbow Up Deg

74.6

Elbow Angle Theta2 Elbow Up Deg

-90.6

-5.6 — degrees

Calculation Breakdown

  1. Applied FormulaSolves the closed-form analytical geometric inverse kinematics for a two-degree-of-freedom planar robotic arm producing both elbow-up and elbow-down solutions.\cos\theta_2 = \frac{x^2 + y^2 - L_1^2 - L_2^2}{2 L_1 L_2}, \quad \theta_1 = \text{atan2}(y, x) - \text{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
-5.6-3.9-2.3-0.71.0Shoulder Angle θ₁

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

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

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

Solves the closed-form analytical geometric inverse kinematics for a two-degree-of-freedom planar robotic arm producing both elbow-up and elbow-down solutions.

Planar Two-Link Robot Arm Inverse Kinematics Joint Angle 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 = \text{atan2}(y, x) - \text{atan2}(L_2\sin\theta_2, L_1 + L_2\cos\theta_2)

Solves the closed-form analytical geometric inverse kinematics for a two-degree-of-freedom planar robotic arm producing both elbow-up and elbow-down solutions.

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

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

Step-by-Step Example Calculation

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

Input Values:

link1LengthMm:300
link2LengthMm:250
targetPositionXMm:320
targetPositionYMm:220
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required degrees.

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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