Forward Kinematics Calculator

Calculator

Enter Denavit–Hartenberg parameters per joint, then calculate the end-effector pose.

Limits: 1–6 joints.

Number of joints

Changing this updates the table.

Length units for a and d

Angles remain in degrees.

Quick fill

Example uses a 3-link planar arm.

DH parameter table

Joint	Type	a (m)	α (deg)	d (m)	θ (deg)
1
2
3

For prismatic joints, enter the current extension in d. For revolute joints, enter the current angle in θ.

Example data

This example produces a valid pose and is useful for testing exports.

Joint	Type	a	d	θ (deg)
1	Revolute	0.30	0.15	30
2	Revolute	0.25	0.00	45
3	Revolute	0.10	0.00	-20

Formula used

For each joint i, the Denavit–Hartenberg transform is:

A_i = [ cosθ -sinθ cosα sinθ sinα a cosθ ]
      [ sinθ cosθ cosα -cosθ sinα a sinθ ]
      [ 0 sinα cosα d ]
      [ 0 0 0 1 ]

The end-effector transform is the product: T = A1 · A2 · ... · An. Position is p = [T14, T24, T34].

How to use this calculator

Choose the number of joints for your mechanism.
Select your length units for a and d.
Enter DH parameters for every joint row.
Press Submit to compute the pose.
Use the download buttons to export results.

FAQs

1) What does forward kinematics compute?

It computes the end-effector pose from joint values and geometry. The output is position and orientation, usually as a 4×4 homogeneous transform.

2) Which DH convention is used here?

This uses the standard Denavit–Hartenberg matrix with parameters a, α, d, θ. Angles are in degrees and lengths are in your selected units.

3) How do I treat revolute vs prismatic joints?

For revolute joints, θ changes and d is typically constant. For prismatic joints, d changes and θ is typically constant. Enter the current value in the corresponding field.

4) Why can my result look incorrect?

Common issues include wrong frame assignment, swapped α sign, mixing degrees and radians, or using modified DH parameters. Re-check your link frames and parameter definitions.

5) What are the Euler angles shown?

They are ZYX yaw-pitch-roll angles extracted from the rotation matrix. Near pitch ±90°, yaw/roll can become coupled due to a kinematic singularity.

6) Can I export intermediate joint transforms?

This page exports the final pose plus the input table. If you need per-joint transforms, compute each A_i and cumulative product in your workflow.

7) What joint count is supported?

Up to six joints are supported to fit many common robot arms. If you need more, extend the joint rows and multiply additional DH matrices.