What Is the Planar 2R Robot Arm Inverse Kinematics Calculator?
Inverse kinematics is the mathematical problem of calculating actuator joint variables from desired end-effector spatial coordinates.
In a 2R robot arm, there exist up to two distinct joint configurations that achieve the exact same tool position.
How Does the Planar 2R Robot Arm Inverse Kinematics Calculator Work?
Calculates radial distance r = √(x² + y²) to ensure target lies within the reachable annular workspace.
Applies the law of cosines to find the elbow flexion angle θ₂.
Uses atan2 trigonometry to determine the shoulder base angle θ₁.
Planar 2R Robot Arm Inverse Kinematics Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Applies law of cosines and geometric vector decomposition to extract joint angles.
How to Use the Planar 2R Robot Arm Inverse Kinematics Calculator
- Input link lengths L₁ and L₂.
- Provide desired Cartesian coordinate (x, y).
- Select preferred elbow posture branch (up or down).
Step-by-Step Example Calculation
Planar Reach Coordinate
Input Values:
Understanding Your Result
The primary output provides the shoulder joint angle θ₁ in degrees.
Summary displays both joint angles and workspace verification.
Factors That Affect the Result
- Link length ratios.
- Proximity to workspace boundary singularities.
When Should You Use This Calculator?
- Pick-and-place robot programming.
- Trajectory tracking and motion controller setpoint generation.
Assumptions & Limitations
- Targets outside the workspace circle cannot be reached and throw an error.
- Joint angle limits are not applied.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Analytical closed-form trigonometric solution.