What Is the Planar 2-DOF Robot Arm Inverse Kinematics Calculator?
Inverse kinematics computes the joint angles needed to place a robot manipulator end-effector at a specific point.
How Does the Planar 2-DOF Robot Arm Inverse Kinematics Calculator Work?
Applies the Law of Cosines to solve for the elbow angle θ₂, followed by atan2 projection for the base angle θ₁.
Planar 2-DOF Robot Arm Inverse Kinematics Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
cos( heta_2) = rac{x^2 + y^2 - L_1^2 - L_2^2}{2 L_1 L_2}, quad heta_1 = operatorname{atan2}(y, x) - operatorname{atan2}(L_2 sin heta_2, L_1 + L_2 cos heta_2)
Law of cosines and trigonometric decomposition for 2-link inverse kinematics.
How to Use the Planar 2-DOF Robot Arm Inverse Kinematics Calculator
- Input the lengths of link 1 and link 2, and the desired Cartesian coordinates (x, y) of the target.
Step-by-Step Example Calculation
SCARA Pick-and-Place Positioning
Input Values:
link1LengthM:0.5
link2LengthM:0.4
targetXM:0.5
targetYM:0.4
Worked Steps: Yields elbow-down angles θ₁ = 12.3°, θ₂ = 62.7° with total reach distance 0.640 m.
Understanding Your Result
Gives both elbow-down and elbow-up configurations; checks whether the point is within the reachable workspace.
Factors That Affect the Result
- Physical joint limit constraints and singularities when the arm is fully extended or folded.
When Should You Use This Calculator?
- Robotic motion planning, CNC arm path generation, and educational robotics design.
Assumptions & Limitations
- Applies to 2D planar arms; ignores joint limits, cable tension, and structural deflection.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact analytical solution for 2-link planar mechanisms.