1️⃣ Using the Built-In Feedback Device (Most Accurate Method)

Most industrial servo motors (like the ones you handle in repair environments) use:

• Incremental encoders
• Absolute encoders
• Resolvers

A) Incremental Encoder

An incremental encoder provides pulses per revolution (PPR).

Formula:

θ=NNtotal×360∘\theta = \frac{N}{N_{total}} \times 360^\circθ=Ntotal​N​×360∘

Where:

• NNN = counted pulses
• NtotalN_{total}Ntotal​ = pulses per revolution (PPR × 4 if quadrature)
• θ\thetaθ = mechanical angle

Example:

Encoder = 2500 PPR

Quadrature decoding → 2500 × 4 = 10,000 counts/rev

If counted pulses = 2500

θ=250010000×360=90∘\theta = \frac{2500}{10000} \times 360 = 90^\circθ=100002500​×360=90∘

B) Absolute Encoder

Absolute encoders directly provide position value.

For n-bit encoder:

Resolution=360∘2n\text{Resolution} = \frac{360^\circ}{2^n}Resolution=2n360∘​

Example:

17-bit encoder:

360131072=0.00275∘ per count\frac{360}{131072} = 0.00275^\circ \text{ per count}131072360​=0.00275∘ per count

Angle:

θ=Encoder Value×Resolution\theta = \text{Encoder Value} \times \text{Resolution}θ=Encoder Value×Resolution

C) Resolver (Common in Industrial Servo Motors)

Resolver outputs sin/cos signals:

θ=tan⁡−1(VsinVcos)\theta = \tan^{-1} \left( \frac{V_{sin}}{V_{cos}} \right)θ=tan−1(Vcos​Vsin​​)

This gives electrical angle. Drive converts to mechanical angle.