D-H Table Explain

In the AR4 D-H table, the θ offset simply corrects for the difference between the robot’s mechanical zero (where each joint is physically aligned to its home mark) and the mathematical zero required by the D-H convention.

Mathematically:

[

\thetai = \theta{measured} + \text{offset}_i

]

That offset ensures the robot’s forward kinematics produce the correct pose when all joints are at their home position.

For example, if your J2 link points horizontally when the D-H convention expects it to start vertically, the offset rotates it into alignment.

Why α₃ = +90° instead of 90°

The α (alpha) parameter defines the twist angle between two consecutive joint axes - the rotation about the x₃ axis from z₂ to z₃.

Using the right-hand rule, a positive rotation about x₃ moves z₂ toward z₃.

In the AR4’s geometry:

• z₂ points along the J2 joint axis (vertical in the home position).

• z₃ points forward along the J3 joint axis (horizontal).

To rotate z₂ (+Z up) into z₃ (+Z forward) following the right-hand rule about the x₃ axis, you rotate +90°, not −90°.

If you reversed one of the coordinate frame directions (for example, flipped an x or z axis), then α₃ would indeed be −90°, but that would also break consistency with the right-hand rule used throughout the AR4’s DH frame assignments.

In short

• The θ offset aligns mechanical zero with the D-H reference zero.

• α₃ = +90° because, per the right-hand rule, rotating +90° about x₃ correctly brings z₂ into z₃ for the AR4’s joint orientation.

Both values are consistent with the AR4’s 3D model, joint motion direction, and the Modified D-H convention used in the official kinematics code.