Input Parameters
Use the responsive grid below. It shows three columns on large screens, two on medium screens, and one on mobile.
Example Data Table
This sample represents a simple three-link serial robot using standard D-H values and degree-based angles.
| Link | Joint Type | a | α | d | θ |
|---|---|---|---|---|---|
| 1 | Revolute | 0.00 | 90 | 0.40 | 30 |
| 2 | Revolute | 0.60 | 0 | 0.00 | 45 |
| 3 | Revolute | 0.40 | 0 | 0.00 | 20 |
Formula Used
1) Standard Denavit Hartenberg Matrix
Ai = Rotz(θi) × Transz(di) × Transx(ai) × Rotx(αi)
Ai = [ cosθ, -sinθcosα, sinθsinα, a cosθ; sinθ, cosθcosα, -cosθsinα, a sinθ; 0, sinα, cosα, d; 0, 0, 0, 1 ]
2) Modified Denavit Hartenberg Matrix
Ai = Rotx(αi) × Transx(ai) × Rotz(θi) × Transz(di)
Ai = [ cosθ, -sinθ, 0, a; sinθcosα, cosθcosα, -sinα, -d sinα; sinθsinα, cosθsinα, cosα, d cosα; 0, 0, 0, 1 ]
3) Cumulative Transformation
T0n = A1 × A2 × ... × An
4) End Effector Position
The Cartesian position is read directly from the final matrix translation column: (x, y, z) = (T[0][3], T[1][3], T[2][3]).
5) Orientation Extraction
This calculator extracts roll, pitch, and yaw from the final rotation matrix using a ZYX Euler angle convention.
How to Use This Calculator
- Select the number of robot links you want to model.
- Choose standard or modified D-H convention.
- Pick angle and length units that match your design data.
- Enter a, α, d, and θ values for each visible link.
- Use a descriptive label for every link to improve traceability.
- Press Calculate Kinematics to place the result above the form.
- Review the final matrix, frame coordinates, and roll-pitch-yaw values.
- Inspect the 3D Plotly graph to verify manipulator geometry.
- Download CSV for tabular data or PDF for reporting.
FAQs
1) What does this calculator compute?
It computes link transformation matrices, cumulative forward kinematics, joint coordinates, end effector position, reach, path length, and roll-pitch-yaw orientation.
2) What is the difference between standard and modified D-H?
Both describe robot geometry, but the order of elementary transformations differs. The chosen convention must match the frame assignment used in your robot model.
3) Can I use revolute and prismatic joints together?
Yes. The calculator lets you label each row as revolute or prismatic. You still provide full numeric values, so mixed chains are supported easily.
4) Which parameters are measured in angles?
The link twist α and joint angle θ use the selected angle unit. Link length a and offset d use the selected length unit.
5) Why is the final matrix important?
It contains the full pose of the end effector relative to the base frame. The last column gives position, while the upper-left block gives orientation.
6) What does the Plotly graph show?
It plots the base, every computed frame origin, and the connecting manipulator chain in 3D so you can visually check link geometry and pose.
7) Is this suitable for robot design studies?
Yes. It is useful for education, mechanism planning, forward kinematics verification, workspace discussions, and quick design documentation with exports.
8) Can I use more than six links?
This file is configured for up to six links for clarity. You can expand the repeated input blocks and loop limit if needed.