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.
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
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)
- 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 — 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.
Related tools
- Inverse Kinematics — Heavy 6-Axis (210 kg)
- Inverse Kinematics — Delta Picker (1 kg)
- Inverse Kinematics — Arc-Welding 6-Axis (8 kg)
- Inverse Kinematics — Cartesian Gantry (50 kg)
- Payload Torque Check — SCARA (400 mm class)
- Payload Torque Check — 6-Axis Benchtop (5 kg)
- Payload Torque Check — Collaborative Robot (5 kg)
- Strength Gain Curve — 50% GGBS Blend
- Capacity Check — Crawler Crane
Related Manufacturing tools
Spindle Speed Calculator — Aluminum 6061
Carbide starting RPM for milling Aluminum 6061: n = 1000·Vc/(π·D) with a handbook cutting speed preset.
● LiveSpindle Speed Calculator — Mild Steel 1018
Carbide starting RPM for milling Mild Steel 1018: n = 1000·Vc/(π·D) with a handbook cutting speed preset.
● LiveSpindle Speed Calculator — Stainless 304
Carbide starting RPM for milling Stainless 304: n = 1000·Vc/(π·D) with a handbook cutting speed preset.
● Live