Inverse Kinematics — Arc-Welding 6-Axis (8 kg)
2-link planar IK for a arc-welding 6-axis (8 kg): both elbow solutions for a target XY, with reachability check.
Weld paths constrain orientation hard (work and travel angles), which eats IK freedom: a seam reachable in position can be unreachable in pose. Solving the planar reach first — this tool — filters fixture positions before full 6-DOF reachability gets expensive.
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 arc-welding 6-axis (8 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 — Arc-Welding 6-Axis (8 kg)
Inverse Kinematics — Arc-Welding 6-Axis (8 kg) computes the governing relationship cosθ₂ = (x²+y²−L₁²−L₂²)/(2L₁L₂) · θ₁ = atan2(y,x) − atan2(L₂sinθ₂, L₁+L₂cosθ₂) live as you type. Weld paths constrain orientation hard (work and travel angles), which eats IK freedom: a seam reachable in position can be unreachable in pose. Solving the planar reach first — this tool — filters fixture positions before full 6-DOF reachability gets expensive. 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 — Arc-Welding 6-Axis (8 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 — Arc-Welding 6-Axis (8 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.)
- ✓Weld paths constrain orientation hard (work and travel angles), which eats IK freedom: a seam reachable in position can be unreachable in pose.
- ✓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 — arc-welding 6-axis (8 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?+
Weld paths constrain orientation hard (work and travel angles), which eats IK freedom: a seam reachable in position can be unreachable in pose. 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 arc-welding 6-axis (8 kg): both elbow solutions for a target XY, with reachability check. A free industrial robot kinematics & cell design tool. Solving the planar reach first — this tool — filters fixture positions before full 6-DOF reachability gets expensive. 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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