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Diffstat (limited to 'docs/Kinematics.md')
| -rw-r--r-- | docs/Kinematics.md | 41 |
1 files changed, 22 insertions, 19 deletions
diff --git a/docs/Kinematics.md b/docs/Kinematics.md index 92de88ad..401554f8 100644 --- a/docs/Kinematics.md +++ b/docs/Kinematics.md @@ -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).  +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. + + + 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. +  -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.  -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: ``` |