h3n3/klipper
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

docs: Kinematics document image updates

Browse Source 
Signed-off-by: Kevin O'Connor <kevin@koconnor.net>
This commit is contained in:
Kevin O'Connor
2017-04-27 11:19:30 -04:00
parent 917c6aa94a
commit a97e074022
12 changed files with 304 additions and 48 deletions
Download Patch File Download Diff File Expand all files Collapse all files

41
docs/Kinematics.md
View File

@@ -73,21 +73,24 @@ flow would result in poor print quality.
To solve this, the "look-ahead" mechanism queues multiple incoming
moves and analyzes the angles between moves to determine a reasonable
speed that can be obtained during the "junction" between two moves. If
the next move forms an acute angle (the head is going to travel in
nearly a reverse direction on the next move) then only a small
junction speed is permitted. If the next move is nearly in the same
direction then the head need only slow down a little (if at all).
the next move is nearly in the same direction then the head need only
slow down a little (if at all).
![lookahead](img/lookahead.svg.png)
If the next move forms an acute angle (the head is going to travel in
nearly a reverse direction on the next move) then only a small
junction speed is permitted.
![lookahead](img/lookahead-slow.svg.png)
The junction speeds are determined using "approximated centripetal
acceleration". Best
[described](https://onehossshay.wordpress.com/2011/09/24/improving_grbl_cornering_algorithm/)
by the author.
[described by the author](https://onehossshay.wordpress.com/2011/09/24/improving_grbl_cornering_algorithm/).
Klipper implements look-ahead between moves contained in the XY plane
that have similar extruder flow rates. Other moves are rare and
implementing look-ahead between them is unnecessary.
that have similar extruder flow rates. Other moves are relatively rare
and implementing look-ahead between them is unnecessary.
Key formula for look-ahead:
```
@@ -158,20 +161,20 @@ To generate step times on Delta printers it is necessary to correlate
the movement in cartesian space with the movement on each stepper
tower.
To simplify the math, for each stepper tower, the code calculates the
location of a "virtual tower" that is along the line of movement.
This virtual tower is chosen at the point where the line of movement
(extended infinitely in both directions) would be closest to the
actual tower.
![delta-tower](img/delta-tower.svg.png)
To simplify the math, for each move contained in an XY plane, the code
calculates the location of a "virtual tower" that is along the line of
movement. This virtual tower is chosen at the point where the line of
movement (extended infinitely in both directions) would be closest to
the actual tower.
It is then possible to calculate where the head will be along the line
of movement after each step is taken on the virtual tower.
![virtual-tower](img/virtual-tower.svg.png)
It is then possible to calculate where the head will be along the line
of movement after each step is taken on the virtual tower. The key
formula is Pythagoras's theorem:
The key formula is Pythagoras's theorem:
```
distance_to_tower^2 = arm_length^2 - tower_height^2
```
@@ -196,7 +199,7 @@ must also be used in the calculations.
Should the move contain only Z movement (ie, no XY movement at all)
then the same math is used - just in this case the tower is parallel
to the line of movement (its slope is 1.0).
to the line of movement.
### Stepper motor acceleration limits ###
@@ -248,7 +251,7 @@ pressure. Pressure increases when filament is pushed into the extruder
(as in [Hooke's law](https://en.wikipedia.org/wiki/Hooke%27s_law)) and
the pressure necessary to extrude is dominated by the flow rate
through the nozzle orifice (as in
[Poiseuille law](https://en.wikipedia.org/wiki/Poiseuille_law)). The
[Poiseuille's law](https://en.wikipedia.org/wiki/Poiseuille_law)). The
key idea is that the relationship between filament, pressure, and flow
rate can be modeled using a linear coefficient:
```