# Denavit-Hartenberg conventions

### From Tekkotsu Wiki

- d = height of reference frame n's origin above the x
_{n-1}-y_{n-1}plane - θ = x
_{n}'s angular offset (about the z_{n-1}axis) from the x_{n-1}axis - r = distance to travel from z
_{n-1}along the x_{n}axis to reach the origin of reference frame n - α = z
_{n}'s angular offset (about the x_{n}axis) from z_{n-1}

When z_{n} is parallel to z_{n-1}, the value of d is arbitrary, and α is 0.

## Another Illustration

This version uses a slightly different order of operations: θ, d, r (called a), and α. Switching the d and θ steps has no effect on the final result.

Step 1: Rotate around z _{0} by θ | |

Step 2: Displace along z _{0} by d | |

Step 3: Displace along x _{1} by a (or r) | |

Step 4: Rotate around x _{1} by α | |

All in one |