Inverse Kinematics — Collaborative Robot (5 kg)
2-link planar IK for a collaborative robot (5 kg): both elbow solutions for a target XY, with reachability check.
Cobots ship with IK that quietly respects speed/force limits, so an awkward elbow-near-singular solution costs you doubly: worse dexterity AND a forced collaborative slowdown. Solve for targets that keep θ₂ between roughly 30° and 150°.
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.
Disclaimer: This tool is for general informational and estimation purposes only and is not professional financial, tax, accounting or legal advice. All figures are estimates — verify with a qualified professional before making decisions. Read the full disclaimer.
2-link planar IK for a collaborative robot (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 — Collaborative Robot (5 kg)
Inverse Kinematics — Collaborative Robot (5 kg) computes the governing relationship cosθ₂ = (x²+y²−L₁²−L₂²)/(2L₁L₂) · θ₁ = atan2(y,x) − atan2(L₂sinθ₂, L₁+L₂cosθ₂) live as you type. Cobots ship with IK that quietly respects speed/force limits, so an awkward elbow-near-singular solution costs you doubly: worse dexterity AND a forced collaborative slowdown. Solve for targets that keep θ₂ between roughly 30° and 150°. 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 — Collaborative Robot (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 — Collaborative Robot (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.)
- ✓Cobots ship with IK that quietly respects speed/force limits, so an awkward elbow-near-singular solution costs you doubly: worse dexterity AND a forced collaborative slowdown.
- ✓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 — collaborative robot (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?+
Cobots ship with IK that quietly respects speed/force limits, so an awkward elbow-near-singular solution costs you doubly: worse dexterity AND a forced collaborative slowdown. 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 collaborative robot (5 kg): both elbow solutions for a target XY, with reachability check. A free industrial robot kinematics & cell design tool. Solve for targets that keep θ₂ between roughly 30° and 150°. 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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