# Gear Box

Gear box in mechanical systems

Mechanisms

## Description

The Gear Box block represents an ideal, nonplanetary, fixed gear ratio gear box. The gear ratio is determined as the ratio of the input shaft angular velocity to that of the output shaft.

The gear box is described with the following equations:

`${\omega }_{1}=N·{\omega }_{2}$`
`${T}_{2}=N·{T}_{1}$`
`${P}_{1}={\omega }_{1}·{T}_{1}$`
`${P}_{2}=-{\omega }_{2}·{T}_{2}$`

where

 ω1 Input shaft angular velocity ω2 Output shaft angular velocity `N` Gear ratio `T1` Torque on the input shaft `T2` Torque on the output shaft `P1` Power on the input shaft `P2` Power on the output shaft. Notice the minus sign in computing `P2`. One of the network rules is that the power flowing through a conserving port is positive if it is removed (dissipated) from the circuit, and is negative if the component generates power into the system.

Connections S and O are mechanical rotational conserving ports associated with the box input and output shaft, respectively. The block positive directions are from S to the reference point and from the reference point to O.

## Dialog Box and Parameters

### Parameters Tab

Gear ratio

The ratio of the input shaft angular velocity to that of the output shaft. You can specify both positive and negative values. The default value is `5`.

### Variables Tab

Use the Variables tab in the block dialog box (or the Variables section in the block Property Inspector) to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.

## Ports

The block has the following ports:

`S`

Mechanical rotational conserving port associated with input shaft.

`O`

Mechanical rotational conserving port associated with the output shaft.