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The image represents a robotic arm with multiple joints and links. We are asked to calculate the position of the final point of the tool (in frame Z) relative to the base (frame zero). To do this, we need to analyze the kinematics of the system, taking into account the given angles and link lengths.

The arm consists of:
1. A base link of 20 cm.
2. A middle link of 30 cm, which is inclined by 20°.
3. A final link of 25 cm, inclined by 65°.

We can break down this robotic arm using Denavit-Hartenberg parameters or through forward kinematics, applying basic trigonometry to find the position of the final point. The arm is articulated and moves in a plane, so we can project each segment's motion based on the given angles.

### Step-by-step Plan:
1. Start at the origin point (0,0,40 cm) in the \(Z_0\) axis.
2. The first link is horizontal (20 cm), along the \(X_0\) axis.
3. The second link (30 cm) is inclined at 20°, so we calculate its components using sine and cosine functions.
4. The third link (25 cm) is inclined at 65°, so we apply the same trigonometric principles to this final link.

Would you like me to go ahead and perform these calculations for the final \(Z\)-coordinate?

Considerando la trama cero que se encuentra en la base del diagrama y la trama final mostrada en el herramental, calcular la posición en z del punto final [3,0,2] respecto a la trama base (trama cero).

This problem involves calculating the Z-position of the final point of a robotic arm, considering joint angles of 20° and 65°, and link lengths of 20 cm, 30 cm, and 25 cm. The problem covers trigonometry and forward kinematics, suitable for university-level engineering students.

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