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Signed-off-by: Damien Martin <damlobster@gmail.com>

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docs/Kinematics.md
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@ -1,11 +1,12 @@
# Kinematics
This document provides an overview of how Klipper implements robot
motion (its [kinematics](https://en.wikipedia.org/wiki/Kinematics)).
The contents may be of interest to both developers interested in
working on the Klipper software as well as users interested in better
understanding the mechanics of their machines.
Acceleration
============
## Acceleration
Klipper implements a constant acceleration scheme whenever the print
head changes velocity - the velocity is gradually changed to the new
@ -31,8 +32,7 @@ acceleration is:
velocity(time) = start_velocity + accel*time
```
Trapezoid generator
===================
## Trapezoid generator
Klipper uses a traditional "trapezoid generator" to model the motion
of each move - each move has a start speed, it accelerates to a
@ -54,8 +54,7 @@ of zero duration (if the end speed is equal to the cruising speed).
![trapezoids](img/trapezoids.svg.png)
Look-ahead
==========
## Look-ahead
The "look-ahead" system is used to determine cornering speeds between
moves.
@ -97,8 +96,7 @@ Key formula for look-ahead:
end_velocity^2 = start_velocity^2 + 2*accel*move_distance
```
Smoothed look-ahead
-------------------
### Smoothed look-ahead
Klipper also implements a mechanism for smoothing out the motions of
short "zigzag" moves. Consider the following moves:
@ -127,8 +125,7 @@ however, this limit reduces the top speed. Note that it does not
change the actual acceleration within the move - the move continues to
use the normal acceleration scheme up to its adjusted top-speed.
Generating steps
================
## Generating steps
Once the look-ahead process completes, the print head movement for the
given move is fully known (time, start position, end position,
@ -167,8 +164,7 @@ cartesian_y_position = start_y + move_distance * total_y_movement / total_moveme
cartesian_z_position = start_z + move_distance * total_z_movement / total_movement
```
Cartesian Robots
----------------
### Cartesian Robots
Generating steps for cartesian printers is the simplest case. The
movement on each axis is directly related to the movement in cartesian
@ -181,8 +177,7 @@ stepper_y_position = cartesian_y_position
stepper_z_position = cartesian_z_position
```
CoreXY Robots
----------------
### CoreXY Robots
Generating steps on a CoreXY machine is only a little more complex
than basic cartesian robots. The key formulas are:
@ -192,8 +187,7 @@ stepper_b_position = cartesian_x_position - cartesian_y_position
stepper_z_position = cartesian_z_position
```
Delta Robots
------------
### Delta Robots
Step generation on a delta robot is based on Pythagoras's theorem:
```
@ -224,8 +218,7 @@ this limit, moves at the extreme edge of the build envelope (where a
stepper arm may be nearly horizontal) will have a lower maximum
acceleration and velocity.
Extruder kinematics
-------------------
### Extruder kinematics ###
Klipper implements extruder motion in its own kinematic class. Since
the timing and speed of each print head movement is fully known for