MotorLab sizing suite
Rack and pinion motor sizing
Model linear motion driven by a pinion. Simple mode estimates torque and speed; advanced mode adds friction, external forces, and duty cycle.
Inputs
Direction
Horizontal (H)
Pinion diameter
mm
Linear speed
mm/s
Load mass
kg
Time to reach speed
s
Friction coefficient
Effective friction coefficient for guides and rack support.
Gear ratio (pinion : motor)
Transmission ratio from pinion torque to motor torque.
Drive efficiency
Overall drivetrain efficiency from 0 to 1.
Results
Key resultsRequired motor performance
Required continuous torque
0.178Nm
Required peak torque
0.178Nm
Required speed
763.9RPM
Use these results to find motors
All results
Radius
0.025
mLinear speed
0.5
m/sAcceleration
0.5
m/s^2Normal force
196.2
NFriction force
15.696
NForce (no friction)
10
NTotal linear force
25.696
NPinion torque
0.642
NmPinion speed
191
RPMMotor torque
0.178
NmMotor speed
763.9
RPMRack & pinion motor sizing - Mode 1
Inputs
| Item | Value | Unit |
|---|---|---|
| Direction | H | |
| Pinion diameter | 50 | mm |
| Linear speed | 500 | mm/s |
| Load mass | 20 | kg |
| Time to reach speed | 1 | s |
| Friction coefficient | 0.08 | |
| Gear ratio (pinion : motor) | 4 | |
| Drive efficiency | 0.9 |
Key results
| Item | Value | Unit |
|---|---|---|
| Required continuous torque | 0.178 | Nm |
| Required peak torque | 0.178 | Nm |
| Required speed | 763.9 | RPM |
Outputs
| Item | Value | Unit |
|---|---|---|
| Radius | 0.025 | m |
| Linear speed | 0.5 | m/s |
| Acceleration | 0.5 | m/s^2 |
| Normal force | 196.2 | N |
| Friction force | 15.696 | N |
| Force (no friction) | 10 | N |
| Total linear force | 25.696 | N |
| Pinion torque | 0.642 | Nm |
| Pinion speed | 191 | RPM |
| Motor torque | 0.178 | Nm |
| Motor speed | 763.9 | RPM |