SCARA Robot Inverse Kinematics Calculator

Industrial robotics & high-speed assembly: Compute closed-form inverse kinematics joint angles ($ heta_1, heta_2, d_3, heta_4$), reachability radius, and elbow configurations for 4-DOF SCARA manipulators.

Target Pose & Arm Geometry

Target X (mm): End-effector X coordinate

Target Y (mm): End-effector Y coordinate

Target Z (mm): Vertical height displacement

End-Effector Yaw ψ (°): Gripper tool orientation angle

Inner Link Length L₁ (mm): Shoulder-to-elbow distance

Outer Link Length L₂ (mm): Elbow-to-wrist distance

Elbow Configuration: Kinematic branch solution

Z-Axis Base Offset d_base (mm): Base mounting datum

Calculated Joint Variables

Joint 1 Angle (θ₁ - Shoulder)

Joint 2 Angle (θ₂ - Elbow)

Joint 3 Stroke (d₃ - Quill Z)

Prismatic vertical travel

Joint 4 Angle (θ₄ - Wrist Roll)

θ₄ = ψ - θ₁ - θ₂

Horizontal Radial Distance (R)

√(X² + Y²)

Arm Reach Envelope

R_max = L₁ + L₂

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Frequently Asked Questions

Why is a SCARA robot compliant horizontally but rigid vertically?

The two revolute joints have vertical axes of rotation, allowing flexible horizontal motion with minimal effort. The solid vertical quill provides immense axial rigidity, enabling precise vertical component insertion without bending.

What is a SCARA kinematic singularity?

A singularity occurs when θ2 = 0° (arm fully extended straight) or θ2 = 180° (arm completely folded onto itself). In these configurations, the Jacobian loses rank, and the end-effector cannot move along the radial direction.

Why are there two solutions (Elbow-Up vs Elbow-Down)?

For any point in the horizontal workspace (except at the outer boundary), two distinct arm poses reach the same (X, Y) coordinate. Programmers select the elbow configuration that avoids factory obstacles and minimizes cycle time.