Forward Kinematics — Cartesian Gantry (50 kg)
2-link planar FK for a cartesian gantry (50 kg): TCP position and reach from joint angles and link lengths.
A gantry's 'kinematics' are gloriously boring — X is X, Y is Y — and that is the engineering argument: no singularities, no configuration flips, stiffness everywhere. This planar model (treat L1/L2 as axis strokes) maps the rectangular envelope serial arms can't match per dollar.
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 FK for a cartesian gantry (50 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 — Cartesian Gantry (50 kg)
Forward Kinematics — Cartesian Gantry (50 kg) computes the governing relationship x = L₁cosθ₁ + L₂cos(θ₁+θ₂) · y = L₁sinθ₁ + L₂sin(θ₁+θ₂) live as you type. A gantry's 'kinematics' are gloriously boring — X is X, Y is Y — and that is the engineering argument: no singularities, no configuration flips, stiffness everywhere. This planar model (treat L1/L2 as axis strokes) maps the rectangular envelope serial arms can't match per dollar. 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 — Cartesian Gantry (50 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 — Cartesian Gantry (50 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.)
- ✓A gantry's 'kinematics' are gloriously boring — X is X, Y is Y — and that is the engineering argument: no singularities, no configuration flips, stiffness everywhere.
- ✓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 — cartesian gantry (50 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?+
A gantry's 'kinematics' are gloriously boring — X is X, Y is Y — and that is the engineering argument: no singularities, no configuration flips, stiffness everywhere. 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 cartesian gantry (50 kg): TCP position and reach from joint angles and link lengths. A free industrial robot kinematics & cell design tool. This planar model (treat L1/L2 as axis strokes) maps the rectangular envelope serial arms can't match per dollar. 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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