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Inverse Kinematics — Palletizing Robot (160 kg)

2-link planar IK for a palletizing robot (160 kg): both elbow solutions for a target XY, with reachability check.

0
θ₁ (elbow-up) (°)
0
θ₂ (elbow-up) (°)
0
θ₁ (elbow-down) (°)
0
θ₂ (elbow-down) (°)

Pallet patterns repeat thousands of times, so palletizing IK is solved offline once per layer. The useful trick this solver shows: the top far corner of the stack is the IK stress case — if θ₂ goes near-straight there, lower the conveyor, not the pallet.

Formula

cosθ₂ = (x²+y²−L₁²−L₂²)/(2L₁L₂) · θ₁ = atan2(y,x) − atan2(L₂sinθ₂, L₁+L₂cosθ₂)
References: Craig, J., Introduction to Robotics: Mechanics and Control, 4th ed.; Siciliano & Khatib (eds.), Springer Handbook of Robotics, 2nd ed.

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 palletizing robot (160 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 — Palletizing Robot (160 kg)

Inverse Kinematics — Palletizing Robot (160 kg) computes the governing relationship cosθ₂ = (x²+y²−L₁²−L₂²)/(2L₁L₂) · θ₁ = atan2(y,x) − atan2(L₂sinθ₂, L₁+L₂cosθ₂) live as you type. Pallet patterns repeat thousands of times, so palletizing IK is solved offline once per layer. The useful trick this solver shows: the top far corner of the stack is the IK stress case — if θ₂ goes near-straight there, lower the conveyor, not the pallet. 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 — Palletizing Robot (160 kg)

  1. 1Enter your values — Link 1 length L₁, Link 2 length L₂, Target X, Target Y (sensible defaults are pre-filled).
  2. 2Read the live results: θ₁ (elbow-up), θ₂ (elbow-up), θ₁ (elbow-down), θ₂ (elbow-down).
  3. 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.
  4. 4Adjust inputs until the scenario matches yours, then copy or share the result.

Why use Inverse Kinematics — Palletizing Robot (160 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.)
  • Pallet patterns repeat thousands of times, so palletizing IK is solved offline once per layer.
  • 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 — palletizing robot (160 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?+

Pallet patterns repeat thousands of times, so palletizing IK is solved offline once per layer. 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 palletizing robot (160 kg): both elbow solutions for a target XY, with reachability check. A free industrial robot kinematics & cell design tool. The useful trick this solver shows: the top far corner of the stack is the IK stress case — if θ₂ goes near-straight there, lower the conveyor, not the pallet. 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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