Forward Kinematics — Collaborative Robot (5 kg)
2-link planar FK for a collaborative robot (5 kg): TCP position and reach from joint angles and link lengths.
The 850 mm reach of a 5 kg cobot is tuned to a human workstation — it covers what a seated worker covers. FK here tells you whether the arm can keep its elbow tucked over the bench while the TCP works the far corner, the difference between a calm cell and a flailing one.
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 FK for a collaborative robot (5 kg): TCP position and reach from joint angles and link lengths. A free industrial robot kinematics & cell design tool — no sign-up, no upload, instant results in your browser.
About Forward Kinematics — Collaborative Robot (5 kg)
Forward Kinematics — Collaborative Robot (5 kg) computes the governing relationship x = L₁cosθ₁ + L₂cos(θ₁+θ₂) · y = L₁sinθ₁ + L₂sin(θ₁+θ₂) live as you type. The 850 mm reach of a 5 kg cobot is tuned to a human workstation — it covers what a seated worker covers. FK here tells you whether the arm can keep its elbow tucked over the bench while the TCP works the far corner, the difference between a calm cell and a flailing one. 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 Forward Kinematics — Collaborative Robot (5 kg)
- 1Enter your values — Link 1 length L₁, Link 2 length L₂, Joint 1 angle θ₁, Joint 2 angle θ₂ (sensible defaults are pre-filled).
- 2Read the live results: TCP X, TCP Y, Radial distance, Max reach.
- 3Check the "with your numbers" line to see x = L₁cosθ₁ + L₂cos(θ₁+θ₂) · y = L₁sinθ₁ + L₂sin(θ₁+θ₂) substituted step by step.
- 4Adjust inputs until the scenario matches yours, then copy or share the result.
Why use Forward 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 x = L₁cosθ₁ + L₂cos(θ₁+θ₂) · y = L₁sinθ₁ + L₂sin(θ₁+θ₂) 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.)
- ✓The 850 mm reach of a 5 kg cobot is tuned to a human workstation — it covers what a seated worker covers.
- ✓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 forward kinematics — collaborative robot (5 kg) use?+
It evaluates x = L₁cosθ₁ + L₂cos(θ₁+θ₂) · y = L₁sinθ₁ + L₂sin(θ₁+θ₂), 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?+
The 850 mm reach of a 5 kg cobot is tuned to a human workstation — it covers what a seated worker covers. 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 FK for a collaborative robot (5 kg): TCP position and reach from joint angles and link lengths. A free industrial robot kinematics & cell design tool. FK here tells you whether the arm can keep its elbow tucked over the bench while the TCP works the far corner, the difference between a calm cell and a flailing one. 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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