# Kinematic Equations

Equations relating linear speeds to motor speeds

The equations on this page are affected by the following specs of your FarmBot hardware:

Motor Resolution |
200 steps/revolution |

Pulley Size |
20 teeth/revolution |

Belt Pitch |
2mm/tooth |

Leadscrew Lead |
8mm/revolution |

# Convert motor speed into linear speed

## Belt-driven axes (X and Y)

**Linear Speed** = **Motor Speed** / **Motor Resolution** x **Pulley Size** x **Belt Pitch**

For an example Motor Speed of 500 steps/second on the stock belt-driven (X and Y) axes, the equation works out to:

**Linear Speed (mm/second)** = 500 / 200 x 20 x 2 = **100 mm/s**

## Leadscrew-driven axes (Z)

**Linear Speed** = **Motor Speed** / **Motor Resolution** x **Leadscrew Lead**

For an example Motor Speed of 500 steps/second on the stock leadscrew-driven (Z) axis, the equation works out to:

**Linear Speed (mm/second)** = 500 / 200 x 8 = **20 mm/s**

# Calculate steps per mm

## Belt-driven axes (X and Y)

**Steps per mm** = **Motor Resolution** / **Pulley Size** / **Belt Pitch**

For the stock belt-driven (X and Y) axes, the equation works out to:

**Steps per mm** = 200 / 20 / 2 = **5 steps/mm**

## Leadscrew-driven axes (Z)

**Linear Distance** = **Motor Resolution** / **Leadscrew Lead**

For the stock leadscrew-driven (Z) axis, the equations works out to:

**Steps per mm** = 200 / 8 = **25 steps/mm**