Forward Kinematics — SCARA (400 mm class)
2-link planar FK for a scara (400 mm class): TCP position and reach from joint angles and link lengths.
SCARA arms solve kinematics in a plane, which is exactly why they own small-parts assembly: two revolute joints place XY, a ball screw drops Z. With a 225/175 mm link pair the dexterous annulus is a ring — parts at dead center are as unreachable as parts beyond full stretch.
Formula
Note: Planning-level engineering estimate — final robot selection, guarding layout and risk assessment must follow the integrator's calculations and a documented ISO 12100/10218 risk assessment.
2-link planar FK for a scara (400 mm class): TCP position and reach from joint angles and link lengths. A free industrial robot kinematics & cell design tool — no sign-up, no upload, instant results in your browser.
About Forward Kinematics — SCARA (400 mm class)
Forward Kinematics — SCARA (400 mm class) computes the governing relationship x = L₁cosθ₁ + L₂cos(θ₁+θ₂) · y = L₁sinθ₁ + L₂sin(θ₁+θ₂) live as you type. SCARA arms solve kinematics in a plane, which is exactly why they own small-parts assembly: two revolute joints place XY, a ball screw drops Z. With a 225/175 mm link pair the dexterous annulus is a ring — parts at dead center are as unreachable as parts beyond full stretch. Defaults are pre-filled with realistic values for this exact scenario, and the worked example substitutes your numbers step by step so the math is never a black box.
How to use Forward Kinematics — SCARA (400 mm class)
- 1Enter your values — Link 1 length L₁, Link 2 length L₂, Joint 1 angle θ₁, Joint 2 angle θ₂ (sensible defaults are pre-filled).
- 2Read the live results: TCP X, TCP Y, Radial distance, Max reach.
- 3Check the "with your numbers" line to see x = L₁cosθ₁ + L₂cos(θ₁+θ₂) · y = L₁sinθ₁ + L₂sin(θ₁+θ₂) substituted step by step.
- 4Adjust inputs until the scenario matches yours, then copy or share the result.
Why use Forward Kinematics — SCARA (400 mm class)?
- ✓Instant, free and private — every calculation runs client-side in your browser; nothing is uploaded
- ✓Built on the stated formula x = L₁cosθ₁ + L₂cos(θ₁+θ₂) · y = L₁sinθ₁ + L₂sin(θ₁+θ₂) with authoritative sources cited on the page (Craig, J., Introduction to Robotics: Mechanics and Control, 4th ed.; Siciliano & Khatib (eds.), Springer Handbook of Robotics, 2nd ed.)
- ✓SCARA arms solve kinematics in a plane, which is exactly why they own small-parts assembly: two revolute joints place XY, a ball screw drops Z.
- ✓SI ⇄ Imperial toggle converts your inputs in place, so you can work in the units your drawings use
Frequently asked questions
What formula does the forward kinematics — scara (400 mm class) use?+
It evaluates x = L₁cosθ₁ + L₂cos(θ₁+θ₂) · y = L₁sinθ₁ + L₂sin(θ₁+θ₂), exactly as published. Sources: Craig, J., Introduction to Robotics: Mechanics and Control, 4th ed.; Siciliano & Khatib (eds.), Springer Handbook of Robotics, 2nd ed.. The substituted worked example on the page lets you verify every step against the textbook.
How should I read the result — and how far can I trust it?+
SCARA arms solve kinematics in a plane, which is exactly why they own small-parts assembly: two revolute joints place XY, a ball screw drops Z. Planning-level engineering estimate — final robot selection, guarding layout and risk assessment must follow the integrator's calculations and a documented ISO 12100/10218 risk assessment.
When is this calculator the right tool for the job?+
2-link planar FK for a scara (400 mm class): TCP position and reach from joint angles and link lengths. A free industrial robot kinematics & cell design tool. With a 225/175 mm link pair the dexterous annulus is a ring — parts at dead center are as unreachable as parts beyond full stretch. For neighbouring scenarios, the related tools below cover the same engine with different presets.
Does it support both metric and imperial units?+
Yes — the SI ⇄ Imperial toggle converts the values already in the fields, preserving the physical quantity, so you can flip mid-calculation without re-entering anything.
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