## Electronic gear ratio (on-line) calculator – Belt mechanism

This article provides an online calculator for the Belt or Roller Mechanism to quickly find the servo’s electronic gear ratio and provide additional simulation information to evaluate whether the system parameters meet the requirements. The steps are as follows:

1. Define  eg, How many PUUs correspond to 1 mm
2. Enter the mechanical Reduction ratio (1:1 without deceleration)
3. Enter the diameter(D) or circumference of the pully, including the belt.
4. Enter Encoder Resolution(PLS), PLS number per turn of the Encoder,ie,when the electronic gear ratio is 1:1, how many PUUs the drive has to receive in order to rotate 1 turn.
5. Press the “Calculate” button to get the numerator and denominator of the E-Gear Ratio
6. Select “Significant digit number“: to specify the numeric width of the numerator,  suggest 6 or above [Note 1].
7. Enter the Line Speed(​​V) of the machine to check if the simulation results meet the requirements ?

## Electronic Gear Ratio Formula Derivation – Ball Screw

In this article, the formula for the electronic gear ratio of the servo drive for the screw mechanism is derived. The principle of deciding the gear ratio is to first determine the position unit PUU (Pos of User Unit), must be easily observed, usually PUU = 1 or 10 μm, and then calculate the corresponding Gear ratio. Instead of deciding on the gear ratio and then calculating the length of a PUU, otherwise it is asking for trouble (refer to the PUU concept). First, the symbol is defined as follows :

• PUU corresponding to 1 mm (P): How many PUUs respect to 1 mm
• Mechanical reduction ratio (N1 : N2): N1 <= N2 for Deceleration
• Turns of screw rotates (REV): uppercase
• Turns of motor rotates(rev): lowercase, rev = REV ×(N2/N1)
• Pitch of the screw(Pitch): the mechanical movement corresponds to 1 turn of the screw(mm/REV)
• Encoder resolution (R): PLS number per turn of encoder(PLS/rev )
• Electronic Gear Ratio (Num/Den): Scaling factor from PUU to PLS

## What is the PLS position unit?

The PLS unit is based on the resolution of the encoder. Take Delta A2 servo as an example. Although the resolution of the encoder is 17 bits/rev or 20 bits/rev, the PLS units are all set to 1280000 PLS/rev, which cannot be changed by the user. That is, when the electronic gear ratio is set to 1:1, the driver must receive 1280000 pulses then the motor will make one revolution.Due to the high resolution, the PLS unit is suitable for inner motor control of servo drives. However, in the motion control system, an absolute coordinate system must be established. If PLS is used as the position unit, neither the command nor the feedback is suitable, the reason is as follows :

## PUU position unit explanation

In the motion control system, there are a number of position counters to record the current position, commands and errors of the machine. It is not appropriate to use PLS as a unit (for reasons see Link). Therefore, a new  position unit must be introduced, called the Position of User Unit (PUU), which is similar to the Pulse Equivalent Unit in the traditional system that uses pulses as the position command , indicates the moving distance of a pulse. Because the current control system can send commands through communication, there is no physical pulse, the user can be more freely choose the desired position unit, ie PUU. The relationship between PUU and PLS is the electronic gear ratio (N/M) defined as follows:

PUU (counts) * N/M (electronic gear ratio numerator/denominator) = PLS (counts)