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rackpiniongear

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rackpiniongear

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Library

Iconic Diagrams\Mechanical\Rotation\Gears

Iconic Diagrams\Mechanical\Translation\Transmission

Implementations

FixedPinion

FixedRack

Use

Domains: Continuous. Size: 1-D. Kind: Iconic Diagrams (Rotation/Translation).

Description - FixedPionion

This models represents a rack and pinion gear. The connection to the pinion gear is through the rotation port p_rot. The connection to the rack is through the translation port p_trans. The model is ideal, i.e. there is no compliance nor inertia nor backlash.

 

RackPinion

 

In this model the pinion bearing is connected to the fixed world and the rack is free to move. This in contrary to the model FixedRackPinionGear where the pinion bearing is free to move and the rack is connected to the fixed world.

 

The causality of this model is always mixed: torque out & velocity out or angular velocity out & force out:

 

p_rot.T = radius * p_trans.F

p_trans.v = radius * p_rot.omega

 

or:

 

p_trans.F = 1/radius * p_rot.T

p_rot.omega = 1/radius * p_trans.v

 

The rack position is determined by the internal variable x. For x = 0, the pinion gear is at the middle of the rack. When the pinion crosses the end of the rack, i.e.

 

abs(x) > rack_length/2

 

a warning is given, "WARNING: rack length has been exceeded at the rack and pinion gear!", and the simulation is stopped.

Interface - FixedPionion

Ports

Description

p_rot

p_trans

Rotation port.

Translation port.

Causality

 

p_rot notequal p_trans

 

Parameters

 

radius

rack_length

pinion gear pitch radius [m]

rack length [m]

Variables

 

x

Internal variable which denotes the rack position, abs(x) < rack_length/2 else simulation halted.

Initial values

 

x_initial

Initial rack position, abs(x_initial) < rack_length/2

Description - FixedRack

This models represents a fixed rack and pinion gear. The connection to the pinion gear is through the rotation port p_rot. The connection to the rack is through the translation port p_trans. The model is ideal, i.e. there is no compliance nor inertia nor backlash.

 

FixedRackPinion

 

In this model the pinion bearing is free to move and the rack is connected to the fixed world. This in contrary to the model RackPinionGear where the pinion bearing is connected to the fixed world and the rack is free to move.

 

The causality of this model is always mixed: torque out & velocity out or angular velocity out & force out:

 

p_rot.T = radius * p_trans.F

p_trans.v = radius * p_rot.omega

 

or:

 

p_trans.F = 1/radius * p_rot.T

p_rot.omega = 1/radius * p_trans.v

 

The rack position is determined by the internal variable x. For x = 0 the pinion gear is at the middle of the rack. When the pinion crosses the end of the rack, i.e.

 

abs(x) > rack_length/2

 

a warning is given, "WARNING: rack length has been exceeded at the rack and pinion gear!", and the simulation is stopped.

Interface - FixedRack

Ports

Description

p_rot

p_trans

Rotation port.

Translation port.

Causality

 

p_rot notequal p_trans

 

Parameters

 

radius

rack_length

pinion gear pitch radius [m]

rack length [m]

Variables

 

x

Internal variable which denotes the rack position, abs(x) < rack_length/2 else simulation halted.

Initial values

 

x_initial

Initial rack position, abs(x_initial) < rack_length/2