# Adding 90 degrees to DH parameter

I am trying to learn DH parameters for this anthropomorphic arm is.

What I understand is robot's/or serial arms can have different initial position.

But here, how is theta 3 = theta 3 + pi/2?

I am struggling to intuitively understand why the pi/2 is added

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## 2 Answers

A joint angle $$\theta_n$$ is defined as the angle between $$X_{n-1}$$ and $$X_n$$ measured about $$Z_{n-1}$$. In the case of $$\theta_3$$, please notice that there is an initial angle of $$+\pi/2$$ (anti-clockwise direction) between $$X_2$$ and $$X_3$$, when measured about $$Z_2$$. Hence, that additional $$+\pi/2$$ comes in the picture.

There are two kinds of (rotary or linear) position encoders: relative and absolute. A relative encoder only "knows" what the position is relative to what position it was in when the encoder was powered on.

The DH parameters define the arm's joint arrangement. It looks like your upper/first image would be the DH parameters with the joints all at an absolute zero value.

If the encoders were relative, you could turn power off to the arm, reposition it manually, and then power it back on. The relative encoder has no knowledge of what happened while it was powered off and so they always default to zero on startup.

The joint configuration didn't change, but your value for $$\theta_3$$ changed because it's now offset - this is the information that was lost when the joint was reconfigured.

The $$\pi/2$$ value is the "joint angle correction" to account for the fact that you are treating the joint angle $$\theta_3$$ as "zero" when the arm is straight.