Robot Arm Kinematics Calculator — Forward & Inverse Kinematics, 2-6 DOF, 3D Visualizer
Robot Arm Forward & Inverse Kinematics Calculator — FK, IK, DH & Jacobian Online
This free robot kinematics calculator runs forward kinematics (FK) and inverse kinematics (IK) for serial manipulators from 2 to 6 DOF in your browser. It uses Denavit–Hartenberg (DH) parameters, supports both revolute and prismatic joints, and includes preset models for planar arms, articulated arms, SCARA, and a fully editable custom DH chain. A live 3D robot arm visualization shows joint labels, links, base coordinate axes, end-effector pose, and tool-frame directions, with Free orbit plus locked XY / YZ / ZX views for teaching, debugging homework, and comparing against your own MATLAB, ROS, or simulation code.
Search-friendly topics covered here: online FK calculator, inverse kinematics solver, Jacobian damped least squares, DH parameter table, end-effector position and RPY, robot singularity, manipulability, SCARA kinematics, 6 DOF articulated arm, and custom robot DH editor. All solver and graphics code executes locally—no robot data is uploaded.
Forward Kinematics vs Inverse Kinematics (Robot Arm)
Use forward kinematics when you already know every joint value and want the unique end-effector pose (position and orientation) obtained by multiplying the DH transformation chain. Use inverse kinematics when you have a desired tool position in space (and optionally orientation on 6-DOF-class arms) and want one set of joint angles that reaches it. IK may have multiple mathematical solutions; this tool picks a numerically stable iterate and exposes elbow-style options where the model allows.
Forward Kinematics (FK): joint variables → homogeneous transform chain → end-effector frame. Always well-defined for a consistent DH model.
Inverse Kinematics (IK): desired EE pose → iterative Jacobian DLS (spatial presets) or closed-form geometry (planar presets). Updates automatically when targets or DH data change.
Global units: one length unit (mm, m, in) and one angle unit (degrees or radians) apply to every input, slider, and printed result for fewer conversion mistakes.
Denavit–Hartenberg — 6-DOF Articulated
Each link uses standard DH data: link length a, link twist α, joint angle θ (with offset for revolute joints), and link offset d. The tool uses a Craig-style homogeneous transform per row. The table below reflects the currently selected robot type and your link-length fields (or Custom DH edits).
Kinematics convention: for revolute joints, applied θ = (your joint input converted to radians) + θ offset; for prismatic joints, link offset d is taken from the joint value stored in millimeters (displayed in your chosen length unit).
- 6 revolute joints in a common industrial layout: base height, upper arm, forearm, then three wrist rotations (α alternates 90°, −90°, 90°, final row α=0).
- Optional full 6D pose IK: enable Orientation in IK mode and enter target roll, pitch, yaw (when available).
- Jacobian DLS with singularity / manipulability feedback—avoid poses where the wrist or elbow lines up badly.
Current DH table
Read-only mirror of the preset DH built from your link lengths. Change lengths in the calculator to refresh these values.
| Joint | Type | a (mm) | d (mm) | α (°) | θ (°) |
|---|---|---|---|---|---|
| J1 | Rev | 0.0000 | 150.0000 | 90.0000 | 0.0000 |
| J2 | Rev | 250.0000 | 0.0000 | 0.0000 | 0.0000 |
| J3 | Rev | 0.0000 | 0.0000 | 90.0000 | 0.0000 |
| J4 | Rev | 0.0000 | 200.0000 | -90.0000 | 0.0000 |
| J5 | Rev | 0.0000 | 0.0000 | 90.0000 | 0.0000 |
| J6 | Rev | 0.0000 | 60.0000 | 0.0000 | 0.0000 |
Lengths and angles use the same global units as the calculator (mm/m/in and ° or rad).
Calculator Features — Jacobian, Singularity, 3D View
- Real-time FK with joint sliders and numeric fields synced to DH geometry.
- Numerical IK with damped least squares Jacobian updates for spatial chains.
- End-effector readout: X Y Z in your length unit; roll, pitch, yaw in your angle unit.
- IK target panel with live position error; optional orientation block on supported arms.
- Singularity awareness via Jacobian-derived manipulability and user-visible warnings near rank-deficient poses.
- 3D scene: color-coded joints, EE marker, tool axes X' Y' Z', IK target glyph, absolute-scale ground grid.
- Copy All Results for pasting into lab reports, ROS YAML, or spreadsheets.
Interactive 3D Robot Arm Visualization
The canvas renders the manipulator against a fixed millimeter grid so shorter links appear genuinely shorter. Free mode uses drag-to-orbit and scroll or pinch zoom. XY, YZ, ZX modes fix the camera to orthographic-style projections and let you spin about one world axis—useful for comparing textbook figures and CAD screenshots. Reset restores the default orbit and returns to Free view. Base frame axes use arrowheads; the tool frame at the EE shows compact labeled directions.
How to Use This Online Robot Kinematics Tool
Follow these steps to reproduce the structured data (HowTo) search engines read from this page:
- Choose robot model and units. Select planar, articulated, SCARA, or custom DH; set global length and angle units.
- Forward kinematics. In FK mode, adjust joints and link lengths; read EE pose and watch the 3D arm update.
- Inverse kinematics. Switch to IK, enter target X Y Z; enable orientation and fill RPY if your arm supports 6D IK.
- Check IK quality. Read position error, watch for singularity warnings, and try elbow up/down if the solution is awkward.
- Export and document. Click Copy All Results; capture the 3D view from Free or plane modes for reports.
Frequently Asked Questions — Robot FK / IK Calculator
What is the difference between forward kinematics and inverse kinematics for a robot arm?
Forward kinematics maps joint variables to a single end-effector pose using the DH chain. Inverse kinematics finds joint variables for a desired pose; solutions may be absent or non-unique, and numerical methods are used for general spatial arms.
Which Denavit–Hartenberg convention does this robot kinematics calculator use?
Standard DH parameters per row (a, α, θ with offset, d) in a Craig-consistent layout. Presets encode typical geometries; Custom mode lets you type any consistent table.
How is inverse kinematics solved for non-planar robots?
Planar presets use geometric closed-form IK where applicable. Spatial arms use a Jacobian-based iterative solver with damped least squares for stable steps toward the target.
What does singularity or low manipulability mean?
Near a singularity the Jacobian drops rank: IK becomes sensitive and joint speeds can explode for tiny Cartesian moves. The tool warns you and shows a manipulability-style scalar so you can move the arm to a better-conditioned pose.
Can I define a custom robot with my own DH table?
Yes. Use Custom (DH), set DOF, edit each link’s DH numbers and joint type (revolute or prismatic). FK updates immediately; IK uses the same Jacobian framework as other spatial models.
Does IK support full 6D pose with orientation?
For the 6-DOF articulated preset (and compatible custom setups), enable orientation IK and enter target roll, pitch, yaw. Other presets focus on position-first IK.
How do Free, XY, YZ, and ZX views work?
Free is full orbit plus zoom. XY/YZ/ZX lock to side-style views and drag-spins about world Z, X, or Y. Reset restores default camera and Free tab. The grid is absolute in millimeters so scale matches real link lengths.
Is my data sent to a server?
No. FK, Jacobian, IK, and canvas drawing all run locally in the browser.
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