DH Transformation Calculator

STANDARD DH RotZθ TransZd TransXa RotXα, not modified DH, coordinate interpretation independently established. Caller independently establishes units, regime, calibration and applicability; this does not establish design-code compliance, authenticity, operational safety, treatment efficacy or a validated forecast.

Description

A Denavit-Hartenberg transformation maps coordinates between linked reference frames.

A Denavit-Hartenberg transformation maps coordinates between linked reference frames.^[1]

Standard and modified conventions differ, so the adopted frame definition must match the matrix. Use DH Transformation Calculator to evaluate the supplied inputs under the specific model below.

When to use DH Transformation Calculator

Use DH Transformation Calculator to evaluate the supplied inputs under the specific model below. Establish the units, measurement scope and applicable model or recipe assumptions before entering values.

How to use DH Transformation Calculator and understand its results

Establish the units, measurement scope and applicable model or recipe assumptions before entering values.
Enter Dh link length m, Dh link twist rad, Dh link offset m, Dh joint angle rad using the field table and validation rules below, then run the tool.
Read Standard dh transform and interpret units, signs, ordering and placeholders as explained below.
If the tool reports an input error, correct that field and rerun. A successful false result, empty match list or unknown-evidence placeholder has the specific meaning described here; check the limitations before applying the result.

Input field	Meaning	Value type	Requirement
dhLinkLengthM	Dh link length m	number	Required; constraints below
dhLinkTwistRad	Dh link twist rad	number	Required; constraints below
dhLinkOffsetM	Dh link offset m	number	Required; constraints below
dhJointAngleRad	Dh joint angle rad	number	Required; constraints below

Enter finite standard DH a and d translations in m with absolute values at most 1000000, and α and θ angles in radians. The tool constructs the standard 4×4 homogeneous transform Rz(θ)Tz(d)Tx(a)Rx(α), with the final row [0,0,0,1]. Signed translations are allowed. Apply the result only to the corresponding standard DH frame convention.

T = Rz(θ)×Tz(d)×Tx(a)×Rx(α)

Field order, units and branch conditions follow the implementation explanation above.

Output field	Meaning	Value type
standardDhTransform	Standard dh transform	array of array

json

{
  "input": {
    "dhLinkLengthM": 2,
    "dhLinkTwistRad": 0,
    "dhLinkOffsetM": 3,
    "dhJointAngleRad": 0
  },
  "output": {
    "standardDhTransform": [
      [
        1,
        0,
        0,
        2
      ],
      [
        0,
        1,
        0,
        0
      ],
      [
        0,
        0,
        1,
        3
      ],
      [
        0,
        0,
        0,
        1
      ]
    ]
  }
}

Limitations and assumptions

Standard and modified conventions differ, so the adopted frame definition must match the matrix. Apply the exact scope and assumptions described above.

All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse arrays fail validation. Domain-specific bounds, alignments and supported tokens are stated above; extremely large inputs or outputs can also be rejected. These errors differ from successful results such as false, no matches or unknown evidence.

Alternative or Complementary methods

Use Epicyclic Gear Train Ratio Calculator for a related task: A simple planetary gear relation links sun, ring and carrier speeds.

Use Rotate Origin Offset Effect Note for a related task: Rotation about an offset origin first expresses the point relative to that origin.

References

DH Transformation Calculator — tool.io

Similar or alternative tools

Epicyclic Gear Train Ratio Calculator
A simple planetary gear relation links sun, ring and carrier speeds.
Rotate Origin Offset Effect Note
Rotation about an offset origin first expresses the point relative to that origin.