Inverse Kinematics — 6-Axis Benchtop (5 kg)
2-link planar IK for a 6-axis benchtop (5 kg): both elbow solutions for a target XY, with reachability check.
On small 6-axis arms the elbow singularity sits embarrassingly close to common work heights. If your target needs θ₂ near zero (arm straight), expect the controller to slow down and joint speeds to spike — re-rooting the part 50 mm closer usually cures it.
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 IK for a 6-axis benchtop (5 kg): both elbow solutions for a target XY, with reachability check. A free industrial robot kinematics & cell design tool — no sign-up, no upload, instant results in your browser.
About Inverse Kinematics — 6-Axis Benchtop (5 kg)
Inverse Kinematics — 6-Axis Benchtop (5 kg) computes the governing relationship cosθ₂ = (x²+y²−L₁²−L₂²)/(2L₁L₂) · θ₁ = atan2(y,x) − atan2(L₂sinθ₂, L₁+L₂cosθ₂) live as you type. On small 6-axis arms the elbow singularity sits embarrassingly close to common work heights. If your target needs θ₂ near zero (arm straight), expect the controller to slow down and joint speeds to spike — re-rooting the part 50 mm closer usually cures it. 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 Inverse Kinematics — 6-Axis Benchtop (5 kg)
- 1Enter your values — Link 1 length L₁, Link 2 length L₂, Target X, Target Y (sensible defaults are pre-filled).
- 2Read the live results: θ₁ (elbow-up), θ₂ (elbow-up), θ₁ (elbow-down), θ₂ (elbow-down).
- 3Check the "with your numbers" line to see cosθ₂ = (x²+y²−L₁²−L₂²)/(2L₁L₂) · θ₁ = atan2(y,x) − atan2(L₂sinθ₂, L₁+L₂cosθ₂) substituted step by step.
- 4Adjust inputs until the scenario matches yours, then copy or share the result.
Why use Inverse Kinematics — 6-Axis Benchtop (5 kg)?
- ✓Instant, free and private — every calculation runs client-side in your browser; nothing is uploaded
- ✓Built on the stated formula cosθ₂ = (x²+y²−L₁²−L₂²)/(2L₁L₂) · θ₁ = atan2(y,x) − atan2(L₂sinθ₂, L₁+L₂cosθ₂) 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.)
- ✓On small 6-axis arms the elbow singularity sits embarrassingly close to common work heights.
- ✓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 inverse kinematics — 6-axis benchtop (5 kg) use?+
It evaluates cosθ₂ = (x²+y²−L₁²−L₂²)/(2L₁L₂) · θ₁ = atan2(y,x) − atan2(L₂sinθ₂, L₁+L₂cosθ₂), 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?+
On small 6-axis arms the elbow singularity sits embarrassingly close to common work heights. 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 IK for a 6-axis benchtop (5 kg): both elbow solutions for a target XY, with reachability check. A free industrial robot kinematics & cell design tool. If your target needs θ₂ near zero (arm straight), expect the controller to slow down and joint speeds to spike — re-rooting the part 50 mm closer usually cures it. 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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