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Transformation matrix from D-H Parameters
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Transformation matrix from D-H Parameters

This tool helps in calculating Transformation matrices often required when working on Serial Robots for kinematics, control, and dynamics. It uses the most common method of representing joints and links — DH parameters. Follow the steps below to use it for your application.

Step 1: Define Z Axis

Choose z_i along the axis of motion of the (i+1)th link.

Step 1: Define Z Axis Step 1: Define Z Axis

Go along all the joints in the robot and define the Z axis for each joint as shown above.

Step 2: Define X Axis

Choose x_i such that it is the shortest vector between z_(i-1) and z_i.

Step 2: Define X Axis

Step 3: Get D-H Parameters

Step 3: Get D-H Parameters Step 3: Get D-H Parameters

Now enter the 4 DH parameters for each joint:

  • a_i — the distance between z_(i-1) and x_i along the direction of x_i
  • alpha_i — the angle between z_(i-1) and z_i along x_i (in degrees)
  • d_i — the distance between z_(i-1) and x_i along the direction of z_(i-1)
  • theta_i — the angle between x_(i-1) and x_i along z_(i-1) (in degrees)

Note: units of a and d must be the same.

Step 4: Calculate

Enter your robot’s DH parameters below. Click Load ABB IRB120 demo to see a worked example with the ABB IRB120 6-DOF arm.

D-H Parameter Calculator

#aα (°)dθ (°)
1

Individual matrices

T1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1

Combined — T = T₁ · T₂ · … · Tn

T_total
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1

Demo: ABB IRB120

The calculator includes a built-in example using the ABB IRB120 6-DOF industrial arm. The images below show the robot, its DH frame assignments, and the parameter table used in the demo.

ABB IRB120 robot arm

ABB IRB120 with DH frame assignments

IRB120 DH parameter table IRB120 DH parameters — robot images are courtesy of abb.com and used here as reference only.