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27 files changed, 2324 insertions, 3 deletions
diff --git a/docs/Code_Overview.md b/docs/Code_Overview.md index 011de21a..07df5599 100644 --- a/docs/Code_Overview.md +++ b/docs/Code_Overview.md @@ -113,7 +113,8 @@ Code flow of a move command A typical printer movement starts when a "G1" command is sent to the Klippy host and it completes when the corresponding step pulses are produced on the micro-controller. This section outlines the code flow -of a typical move command. +of a typical move command. The [kinematics](Kinematics.md) document +provides further information on the mechanics of moves. * Processing for a move command starts in gcode.py. The goal of gcode.py is to translate G-code into internal calls. Changes in diff --git a/docs/Kinematics.md b/docs/Kinematics.md new file mode 100644 index 00000000..924d1291 --- /dev/null +++ b/docs/Kinematics.md @@ -0,0 +1,266 @@ +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 +============ + +Klipper implements a constant acceleration scheme whenever the print +head changes velocity - the velocity is gradually changed to the new +speed instead of suddenly jerking to it. Klipper always enforces +acceleration between the tool head and the print. The filament +leaving the extruder can be quite fragile - rapid jerks and/or +extruder flow changes lead to poor quality and poor bed adhesion. Even +when not extruding, if the print head is at the same level as the +print then rapid jerking of the head can cause disruption of recently +deposited filament. Limiting speed changes of the print head (relative +to the print) reduces risks of disrupting the print. + +It is also important to enforce a maximum acceleration of the stepper +motors to ensure they do not skip or put excessive stress on the +machine. Klipper limits the acceleration of each stepper by virtue of +limiting the acceleration of the print head. Enforcing acceleration at +the print head naturally also enforces acceleration at the steppers +that control that print head (the inverse is not always true). + +Klipper implements constant acceleration. The key formula for +constant acceleration is: +``` +velocity(time) = start_velocity + accel*time +``` + +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 +cruising speed at constant acceleration, it cruises at a constant +speed, and then decelerates to the end speed using constant +acceleration. + + + +It's called a "trapezoid generator" because a velocity diagram of the +move looks like a trapezoid. + +The cruising speed is always greater than or equal to both the start +speed and the end speed. The acceleration phase may be of zero +duration (if the start speed is equal to the cruising speed), the +cruising phase may be of zero duration (if the move immediately starts +decelerating after acceleration), and/or the deceleration phase may be +of zero duration (if the end speed is equal to the cruising speed). + + + +Lookahead +========= + +The "lookahead" system is used to determine cornering speeds between +moves. + +Consider the following two moves contained on an XY plane: + + + +In the above situation it is possible to fully decelerate after the +first move and then fully accelerate at the start of the next move, +but that is not ideal as all that acceleration and deceleration would +greatly increase the print time and the frequent changes in extruder +flow would result in poor print quality. + +To solve this, the "lookahead" 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 junction speeds are determined using "approximated centripetal +acceleration". Best +[described](https://onehossshay.wordpress.com/2011/09/24/improving_grbl_cornering_algorithm/) +by the author. + +Klipper implements lookahead between moves contained in the XY plane +that have similar extruder flow rates. Other moves are rare and +implementing lookahead between them is unnecessary. + +Key formula for lookahead: +``` +end_velocity^2 = start_velocity^2 + 2*accel*move_distance +``` + +Smoothed lookahead +------------------ + +Klipper also implements a mechanism for smoothing out the motions of +short "zig-zag" moves. Consider the following moves: + + + +In the above, the frequent changes from acceleration to deceleration +can cause the machine to vibrate which causes stress on the machine +and increases the noise. To reduce this, Klipper tracks both regular +move acceleration as well as a virtual "acceleration to deceleration" +rate. Using this system, the top speed of these short "zig zag" moves +are limited to smooth out the printer motion: + + + +In the above, note the dashed gray lines - this is a graphical +representation of the "pseudo acceleration". Where the two dashed +lines meet enforces a limit on the move's top speed. For most moves +the limit will be at or above the move's existing limits and no change +in behavior is induced. However, for short "zig-zag" moves the limit +comes into play and it reduces the top speed. Note that the grey lines +represent a pseudo-acceleration to limit top speed only - the move +continues to use it's normal acceleration scheme up to its adjusted +top-speed. + +Generating steps +================ + +Once the lookahead process completes, the print head movement for the +given move is fully known (time, start position, end position, +velocity at each point) and it is possible to generate the step times +for the move. This process is done within "kinematic classes" in the +Klipper code. Outside of these kinematic classes, everything is +tracked in millimeters, seconds, and in cartesian coordinate space. +It's the task of the kinematic classes to convert from this generic +coordinate system to the hardware specifics of the particular printer. + +In general, the code determines each step time by first calculating +where along the line of movement the head would be if a step is +taken. It then calculates what time the head should be at that +position. Determining the time along the line of movement can be done +using the formulas for constant acceleration and constant velocity: + +``` +time = sqrt(2*distance/accel + (start_velocity/accel)^2) - start_velocity/accel +time = distance/cruise_velocity +``` + +Cartesian Robots +---------------- + +Generating steps for cartesian printers is the simplest case. The +movement on each axis is directly related to the movement in cartesian +space. + +Delta Robots +------------ + +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 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. The key +formula is Pythagorean's formula: + +``` +distance_to_tower^2 = arm_length^2 - tower_height^2 +``` + +One complexity is that if the print head passes the virtual tower +location then the stepper direction must be reversed. In this case +forward steps will be taken at the start of the move and reverse steps +will be taken at the end of the move. + +### Delta movements beyond simple XY plane ### + +Movement calculation is a little more complicated if the move is not +fully contained within a simple XY plane. A virtual tower along the +line of movement is still calculated, but in this case the tower is +not at a 90 degree angle relative to the line of movement: + + + +The code continues to calculate step times using the same general +scheme as delta moves within an XY plane, but the slope of the tower +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). + +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 +each move, it's possible to calculate the step times for the extruder +independently from the step time calculations of the print head +movement. + +Basic extruder movement is simple to calculate. The step time +generation uses the same constant acceleration and constant velocity +formulas that cartesian robots use. + +### Pressure advance ### + +Experimentation has shown that it's possible to improve the modeling +of the extruder beyond the basic extruder formula. In the ideal case, +as an extrusion move progresses, the same volume of filament should be +deposited at each point along the move and there should be no volume +extruded after the move. Unfortunately, it's common to find that the +basic extrusion formulas cause too little filament to exit the +extruder at the start of extrusion moves and for excess filament to +extrude after extrusion ends. This is often referred to as "ooze". + + + +The "pressure advance" system attempts to account for this by using a +different model for the extruder. Instead of naively believing that +each mm^3 of filament fed into the extruder will result in that amount +of mm^3 immediately exiting the extruder, it uses a model based on +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 +details of the above physics are not important - only that the +relationship between pressure and flow rate is linear. It is expected +that an appropriate "pressure advance" value for a particular filament +and extruder will be determined experimentally. + +Once configured, Klipper will push in an additional amount of filament +during acceleration and retract that additional filament during +deceleration. The higher the desired filament flow rate, the more +filament must be pushed in during acceleration to account for +pressure. Any additional filament pushed in during head acceleration +is retracted during head deceleration (the extruder will have a +negative velocity). + + + +One may notice that the pressure advance algorithm can cause the +extruder motor to make sudden velocity changes. This is tolerated +based on the idea that the majority of the inertia in the system is in +changing the extruder pressure. As long as the extruder pressure does +not change rapidly it is okay to make some sudden changes in extruder +motor velocity. + +One area where sudden velocity changes become problematic is during +small changes in head speed due to cornering. + + + +To prevent this, the Klipper pressure advance code utilizes the move +lookahead queue to detect intermittent speed changes. In these cases +the amount of pressure increased and decreased will be reduced or +eliminated. diff --git a/docs/Overview.md b/docs/Overview.md index 8b221763..14fb5bd3 100644 --- a/docs/Overview.md +++ b/docs/Overview.md @@ -1,7 +1,9 @@ See [installation](Installation.md) for information on compiling, installing, and running Klipper. Read [features](Features.md) for a -high-level description of useful capabilities. The history of releases -is available at [releases](Releases.md). +high-level description of useful capabilities. The +[kinematics](Kinematics.md) document provides information on how +movement is implemented. The history of releases is available at +[releases](Releases.md). 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