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docs: Use only single space at start of new sentence

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Signed-off-by: Kevin O'Connor <kevin@koconnor.net>
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Kevin O'Connor 2017-05-01 11:36:07 -04:00
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docs/Kinematics.md
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@ -9,14 +9,14 @@ 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.
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
@ -25,8 +25,8 @@ 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:
Klipper implements constant acceleration. The key formula for constant
acceleration is:
```
velocity(time) = start_velocity + accel*time
```
@ -101,15 +101,15 @@ Smoothed look-ahead
-------------------
Klipper also implements a mechanism for smoothing out the motions of
short "zigzag" moves. Consider the following moves:
short "zigzag" moves. Consider the following moves:
![zigzag](img/zigzag.svg.png)
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
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 "zigzag" moves
rate. Using this system, the top speed of these short "zigzag" moves
are limited to smooth out the printer motion:
![smoothed](img/smoothed.svg.png)
@ -133,8 +133,8 @@ Generating steps
Once the look-ahead 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
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.
@ -223,7 +223,7 @@ acceleration and velocity.
Extruder kinematics
-------------------
Klipper implements extruder motion in its own kinematic class. Since
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