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560 lines
24 KiB
Python
560 lines
24 KiB
Python
from __future__ import division
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import math
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import logging
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from cnc.config import *
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from cnc.enums import *
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from cnc.coordinates import Coordinates
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SECONDS_IN_MINUTE = 60.0
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class PulseGenerator(object):
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""" Stepper motors pulses generator.
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It generates time for each pulses for specified path as accelerated
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movement for specified velocity, then moves linearly and then braking
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with the same acceleration.
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Internally this class treat movement as uniform movement and then
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translate timings to accelerated movements. To do so, it base on
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formulas for distance of uniform movement and accelerated move.
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S = V * Ta = a * Tu^2 / 2
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where Ta - time for accelerated and Tu for uniform movement.
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Velocity will never be more then Vmax - maximum velocity of all axises.
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At the point of maximum velocity we change accelerated movement to
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uniform, so we can translate time for accelerated movement with this
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formula:
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Ta(Tu) = a * Tu^2 / Vmax / 2
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Now we need just to calculate how much time will accelerate and
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brake will take and recalculate time for them. Linear part will be as
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is. Since maximum velocity and acceleration is always the same, there
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is the ACCELERATION_FACTOR_PER_SEC variable.
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In the same way round or other interpolation can be implemented based on
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this class.
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Note: round interpolation would require direction change during movement.
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It's not implemented yet.
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"""
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def __init__(self, delta):
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""" Create object. Do not create directly this object, inherit this class
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and implement interpolation function and related methods.
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All child have to call this method ( super().__init__() ).
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:param delta: overall movement delta in mm, uses for debug purpose.
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"""
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self._iteration_x = 0
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self._iteration_y = 0
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self._iteration_z = 0
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self._iteration_e = 0
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self._iteration_direction = None
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self._acceleration_time_s = 0.0
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self._linear_time_s = 0.0
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self._2Vmax_per_a = 0.0
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self._delta = delta
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def _get_movement_parameters(self):
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""" Get parameters for interpolation. This method have to be
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reimplemented in parent classes and should calculate 3 parameters.
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:return: Tuple of three values:
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acceleration_time_s: time for accelerating and breaking motors
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during movement
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linear_time_s: time for uniform movement, it is total movement
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time minus acceleration and braking time
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max_axis_velocity_mm_per_sec: maximum axis velocity of all
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axises during movement. Even if
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whole movement is accelerated,
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this value should be calculated
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as top velocity.
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"""
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raise NotImplemented
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def _interpolation_function(self, ix, iy, iz, ie):
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""" Get function for interpolation path. This function should returned
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values as it is uniform movement. There is only one trick, function
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must be expressed in terms of position, i.e. t = S / V for linear,
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where S - distance would be increment on motor minimum step.
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:param ix: number of pulse for X axis.
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:param iy: number of pulse for Y axis.
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:param iz: number of pulse for Z axis.
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:param ie: number of pulse for E axis.
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:return: Two tuples. First is tuple is directions for each axis,
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positive means forward, negative means reverse. Second is
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tuple of times for each axis in us or None if movement for
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axis is finished.
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"""
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raise NotImplemented
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def __iter__(self):
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""" Get iterator.
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:return: iterable object.
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"""
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self._acceleration_time_s, self._linear_time_s, \
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max_axis_velocity_mm_per_sec = self._get_movement_parameters()
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# helper variable
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self._2Vmax_per_a = 2.0 * max_axis_velocity_mm_per_sec \
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/ STEPPER_MAX_ACCELERATION_MM_PER_S2
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self._iteration_x = 0
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self._iteration_y = 0
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self._iteration_z = 0
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self._iteration_e = 0
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self._iteration_direction = None
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logging.debug(', '.join("%s: %s" % i for i in vars(self).items()))
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return self
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def _to_accelerated_time(self, pt_s):
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""" Internal function to translate uniform movement time to time for
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accelerated movement.
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:param pt_s: pseudo time of uniform movement.
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:return: time for each axis or None if movement for axis is finished.
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"""
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# acceleration
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# S = Tpseudo * Vmax = a * t^2 / 2
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t = math.sqrt(pt_s * self._2Vmax_per_a)
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if t <= self._acceleration_time_s:
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return t
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# linear
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# pseudo acceleration time Tpseudo = t^2 / ACCELERATION_FACTOR_PER_SEC
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t = self._acceleration_time_s + pt_s - (self._acceleration_time_s ** 2
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/ self._2Vmax_per_a)
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# pseudo breaking time
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bt = t - self._acceleration_time_s - self._linear_time_s
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if bt <= 0:
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return t
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# braking
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# Vmax * Tpseudo = Vlinear * t - a * t^2 / 2
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# V on start braking is Vlinear = Taccel * a = Tbreaking * a
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# Vmax * Tpseudo = Tbreaking * a * t - a * t^2 / 2
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d = self._acceleration_time_s ** 2 - self._2Vmax_per_a * bt
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if d > 0:
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d = math.sqrt(d)
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else:
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d = 0
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return 2.0 * self._acceleration_time_s + self._linear_time_s - d
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def __next__(self):
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# for python3
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return self.next()
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def next(self):
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""" Iterate pulses.
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:return: Tuple of five values:
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- first is boolean value, if it is True, motors direction
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should be changed and next pulse should performed in
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this direction.
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- values for all machine axises. For direction update,
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positive values means forward movement, negative value
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means reverse movement. For normal pulse, values are
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represent time for the next pulse in microseconds.
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This iteration strictly guarantees that next pulses time will
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not be earlier in time then current. If there is no pulses
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left StopIteration will be raised.
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"""
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dir, (tx, ty, tz, te) = self._interpolation_function(self._iteration_x,
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self._iteration_y,
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self._iteration_z,
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self._iteration_e)
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# check if direction update:
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if dir != self._iteration_direction:
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self._iteration_direction = dir
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return (True,) + dir
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# check condition to stop
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if tx is None and ty is None and tz is None and te is None:
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raise StopIteration
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# convert to real time
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m = min(x for x in (tx, ty, tz, te) if x is not None)
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am = self._to_accelerated_time(m)
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# sort pulses in time
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if tx is not None:
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if tx > m:
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tx = None
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else:
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tx = am
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self._iteration_x += 1
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if ty is not None:
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if ty > m:
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ty = None
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else:
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ty = am
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self._iteration_y += 1
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if tz is not None:
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if tz > m:
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tz = None
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else:
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tz = am
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self._iteration_z += 1
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if te is not None:
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if te > m:
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te = None
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else:
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te = am
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self._iteration_e += 1
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return False, tx, ty, tz, te
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def total_time_s(self):
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""" Get total time for movement.
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:return: time in seconds.
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"""
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acceleration_time_s, linear_time_s, _ = self._get_movement_parameters()
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return acceleration_time_s * 2.0 + linear_time_s
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def delta(self):
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""" Get overall movement distance.
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:return: Movement distance for each axis in millimeters.
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"""
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return self._delta
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class PulseGeneratorLinear(PulseGenerator):
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def __init__(self, delta_mm, velocity_mm_per_min):
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""" Create pulse generator for linear interpolation.
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:param delta_mm: movement distance of each axis.
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:param velocity_mm_per_min: desired velocity.
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"""
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super(PulseGeneratorLinear, self).__init__(delta_mm)
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# this class doesn't care about direction
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self._distance_mm = abs(delta_mm)
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# velocity of each axis
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distance_total_mm = self._distance_mm.length()
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self.max_velocity_mm_per_sec = self._distance_mm * (
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velocity_mm_per_min / SECONDS_IN_MINUTE / distance_total_mm)
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# acceleration time
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self.acceleration_time_s = self.max_velocity_mm_per_sec.find_max() \
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/ STEPPER_MAX_ACCELERATION_MM_PER_S2
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# check if there is enough space to accelerate and brake, adjust time
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# S = a * t^2 / 2
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if STEPPER_MAX_ACCELERATION_MM_PER_S2 * self.acceleration_time_s ** 2 \
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> distance_total_mm:
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self.acceleration_time_s = math.sqrt(distance_total_mm /
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STEPPER_MAX_ACCELERATION_MM_PER_S2)
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self.linear_time_s = 0.0
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# V = a * t -> V = 2 * S / t, take half of total distance for
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# acceleration and braking
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self.max_velocity_mm_per_sec = self._distance_mm \
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/ self.acceleration_time_s
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else:
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# calculate linear time
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linear_distance_mm = distance_total_mm \
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- self.acceleration_time_s ** 2 \
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* STEPPER_MAX_ACCELERATION_MM_PER_S2
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self.linear_time_s = linear_distance_mm \
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/ self.max_velocity_mm_per_sec.length()
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self._direction = math.copysign(1, delta_mm.x), \
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math.copysign(1, delta_mm.y), \
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math.copysign(1, delta_mm.z), \
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math.copysign(1, delta_mm.e)
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def _get_movement_parameters(self):
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""" Return movement parameters, see super class for details.
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"""
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return self.acceleration_time_s, \
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self.linear_time_s, \
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self.max_velocity_mm_per_sec.find_max()
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def __linear(self, position_mm, distance_mm, velocity_mm_per_sec):
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""" Helper function for linear movement.
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"""
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# check if need to calculate for this axis
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if distance_mm == 0.0 or position_mm >= distance_mm:
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return None
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# Linear movement, S = V * t -> t = S / V
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return position_mm / velocity_mm_per_sec
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def _interpolation_function(self, ix, iy, iz, ie):
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""" Calculate interpolation values for linear movement, see super class
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for details.
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"""
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t_x = self.__linear(ix / STEPPER_PULSES_PER_MM_X, self._distance_mm.x,
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self.max_velocity_mm_per_sec.x)
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t_y = self.__linear(iy / STEPPER_PULSES_PER_MM_Y, self._distance_mm.y,
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self.max_velocity_mm_per_sec.y)
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t_z = self.__linear(iz / STEPPER_PULSES_PER_MM_Z, self._distance_mm.z,
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self.max_velocity_mm_per_sec.z)
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t_e = self.__linear(ie / STEPPER_PULSES_PER_MM_E, self._distance_mm.e,
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self.max_velocity_mm_per_sec.e)
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return self._direction, (t_x, t_y, t_z, t_e)
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class PulseGeneratorCircular(PulseGenerator):
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def __init__(self, delta, radius, plane, direction, velocity):
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""" Create pulse generator for circular interpolation.
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Position calculates based on formulas:
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R^2 = x^2 + y^2
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x = R * sin(phi)
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y = R * cos(phi)
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phi = omega * t, 2 * pi / omega = 2 * pi * R / V
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phi = V * t / R
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omega is angular_velocity.
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so t = V / R * phi
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phi can be calculated based on steps position.
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Each axis can calculate circle phi base on iteration number, the
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only one difference, that there is four quarters of circle and
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signs for movement and solving expressions are different. So
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we use additional variables to control it.
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:param delta: finish position delta from the beginning, must be on
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circle on specified plane. Zero means full circle.
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:param radius: vector to center of circle.
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:param plane: plane to interpolate.
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:param direction: clockwise or counterclockwise.
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:param velocity: velocity in mm per min.
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"""
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super(PulseGeneratorCircular, self).__init__(delta)
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self._plane = plane
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self._direction = direction
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velocity = velocity / SECONDS_IN_MINUTE
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# Get circle start point and end point.
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if self._plane == PLANE_XY:
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sa = -radius.x
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sb = -radius.y
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ea = sa + delta.x
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eb = sb + delta.y
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apm = STEPPER_PULSES_PER_MM_X
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bpm = STEPPER_PULSES_PER_MM_Y
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elif self._plane == PLANE_YZ:
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sa = -radius.y
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sb = -radius.z
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ea = sa + delta.y
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eb = sb + delta.z
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apm = STEPPER_PULSES_PER_MM_Y
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bpm = STEPPER_PULSES_PER_MM_Z
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elif self._plane == PLANE_ZX:
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sa = -radius.z
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sb = -radius.x
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ea = sa + delta.z
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eb = sb + delta.x
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apm = STEPPER_PULSES_PER_MM_Z
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bpm = STEPPER_PULSES_PER_MM_X
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# adjust radius to fit into axises step.
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self._radius = round(math.sqrt(sa * sa + sb * sb) * min(apm, bpm)) \
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/ min(apm, bpm)
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self._radius2 = self._radius * self._radius
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self._start_a = sa
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self._start_b = sb
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assert round(math.sqrt(ea * ea + eb * eb) * min(apm, bpm)) \
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/ min(apm, bpm) == self._radius, "Wrong end point"
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# Calculate angles and directions.
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start_angle = self.__angle(sa, sb)
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end_angle = self.__angle(ea, eb)
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delta_angle = end_angle - start_angle
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if delta_angle < 0 or (delta_angle == 0 and direction == CW):
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delta_angle += 2 * math.pi
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if direction == CCW:
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delta_angle -= 2 * math.pi
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if direction == CW:
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if start_angle >= math.pi:
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self._dir_b = 1
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else:
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self._dir_b = -1
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if math.pi / 2 <= start_angle < 3 * math.pi / 2:
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self._dir_a = -1
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else:
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self._dir_a = 1
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elif direction == CCW:
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if 0 < start_angle <= math.pi:
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self._dir_b = 1
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else:
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self._dir_b = -1
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if start_angle <= math.pi / 2 or start_angle > 3 * math.pi / 2:
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self._dir_a = -1
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else:
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self._dir_a = 1
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self._side_a = self._start_b < 0 or (self._start_b == 0 and self._dir_b < 0)
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self._side_b = self._start_a < 0 or (self._start_a == 0 and self._dir_a < 0)
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self._start_angle = start_angle
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logging.debug("start angle {}, end angle {}, delta {}".format(
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start_angle * 180.0 / math.pi,
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end_angle * 180.0 / math.pi,
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delta_angle * 180.0 / math.pi))
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delta_angle = abs(delta_angle)
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self._delta_angle = delta_angle
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# calculate values for interpolation.
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# calculate travel distance for axis in circular move.
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self._iterations_a = 0
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self._iterations_b = 0
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end_angle_m = end_angle
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if start_angle >= end_angle:
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end_angle_m += 2 * math.pi
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rstart = int(start_angle / (math.pi / 2.0))
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rend = int(end_angle_m / (math.pi / 2.0))
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if rend - rstart >= 4:
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self._iterations_a = 4 * int(self._radius * apm)
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self._iterations_b = 4 * int(self._radius * apm)
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else:
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if rstart == rend:
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self._iterations_a = int(abs(sa - ea) * apm)
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self._iterations_b = int(abs(sb - eb) * bpm)
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else:
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for r in range(rstart, rend + 1):
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i = r
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if i >= 4:
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i -= 4
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if r == rstart:
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if i == 0 or i == 2:
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self._iterations_a += int(self._radius * apm) - int(abs(sa) * apm)
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else:
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self._iterations_a += int(abs(sa) * apm)
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if i == 1 or i == 3:
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self._iterations_b += int(self._radius * bpm) - int(abs(sb) * bpm)
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else:
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self._iterations_b += int(abs(sb) * bpm)
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elif r == rend:
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if i == 0 or i == 2:
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self._iterations_a += int(abs(ea) * apm)
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else:
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self._iterations_a += int(self._radius * apm) - int(abs(ea) * apm)
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if i == 1 or i == 3:
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self._iterations_b += int(abs(eb) * bpm)
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else:
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self._iterations_b += int(self._radius * bpm) - int(abs(eb) * bpm)
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else:
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self._iterations_a += int(self._radius * apm)
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self._iterations_b += int(self._radius * bpm)
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if direction == CCW:
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self._iterations_a = 4 * int(self._radius * apm) - self._iterations_a
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self._iterations_b = 4 * int(self._radius * bpm) - self._iterations_b
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arc = delta_angle * self._radius
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e2 = delta.e * delta.e
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if self._plane == PLANE_XY:
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self._iterations_3rd = abs(delta.z) * STEPPER_PULSES_PER_MM_Z
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l = math.sqrt(arc * arc + delta.z * delta.z + e2)
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self._velocity_3rd = abs(delta.z) / l * velocity
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self._third_dir = math.copysign(1, delta.z)
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elif self._plane == PLANE_YZ:
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self._iterations_3rd = abs(delta.x) * STEPPER_PULSES_PER_MM_X
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l = math.sqrt(arc * arc + delta.x * delta.x + e2)
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self._velocity_3rd = abs(delta.x) / l * velocity
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self._third_dir = math.copysign(1, delta.x)
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elif self._plane == PLANE_ZX:
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self._iterations_3rd = abs(delta.y) * STEPPER_PULSES_PER_MM_Y
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l = math.sqrt(arc * arc + delta.y * delta.y + e2)
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self._velocity_3rd = abs(delta.y) / l * velocity
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self._third_dir = math.copysign(1, delta.y)
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self._iterations_e = abs(delta.e) * STEPPER_PULSES_PER_MM_E
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# Velocity splits with corresponding distance.
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cV = arc / l * velocity
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self._RdivV = self._radius / cV
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self._e_velocity = abs(delta.e) / l * velocity
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self._e_dir = math.copysign(1, delta.e)
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self.max_velocity_mm_per_sec = max(cV, self._velocity_3rd,
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self._e_velocity)
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self.acceleration_time_s = self.max_velocity_mm_per_sec \
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/ STEPPER_MAX_ACCELERATION_MM_PER_S2
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if STEPPER_MAX_ACCELERATION_MM_PER_S2 * self.acceleration_time_s ** 2 \
|
|
> l:
|
|
self.acceleration_time_s = math.sqrt(l /
|
|
STEPPER_MAX_ACCELERATION_MM_PER_S2)
|
|
self.linear_time_s = 0.0
|
|
self.max_velocity_mm_per_sec = l / self.acceleration_time_s
|
|
else:
|
|
linear_distance_mm = l - self.acceleration_time_s ** 2 \
|
|
* STEPPER_MAX_ACCELERATION_MM_PER_S2
|
|
self.linear_time_s = linear_distance_mm / velocity
|
|
|
|
def __angle(self, a, b):
|
|
# Calculate angle of entry point (a, b) of circle with center in (0,0)
|
|
angle = math.acos(b / math.sqrt(a * a + b * b))
|
|
if a < 0:
|
|
return 2 * math.pi - angle
|
|
return angle
|
|
|
|
def _get_movement_parameters(self):
|
|
""" Return movement parameters, see super class for details.
|
|
"""
|
|
return self.acceleration_time_s, \
|
|
self.linear_time_s, \
|
|
self.max_velocity_mm_per_sec
|
|
|
|
def __circularHelper(self, start, i, pulses_per_mm, side, dir):
|
|
np = start + dir * i / pulses_per_mm
|
|
np = round(np, 10)
|
|
if np > self._radius:
|
|
np -= 2 * (np - self._radius)
|
|
np = round(np, 10)
|
|
dir = -dir
|
|
side = not side
|
|
if np < -self._radius:
|
|
np -= 2 * (np + self._radius)
|
|
np = round(np, 10)
|
|
dir = -dir
|
|
side = not side
|
|
if np > self._radius:
|
|
np -= 2 * (np - self._radius)
|
|
np = round(np, 10)
|
|
dir = -dir
|
|
side = not side
|
|
return np, dir, side
|
|
|
|
def __circularFindTime(self, a, b):
|
|
angle = self.__angle(a, b)
|
|
if self._direction == CW:
|
|
delta_angle = angle - self._start_angle
|
|
else:
|
|
delta_angle = self._start_angle - angle
|
|
if delta_angle <= 0:
|
|
delta_angle += 2 * math.pi
|
|
return self._RdivV * delta_angle
|
|
|
|
def __circularA(self, i, pulses_per_mm):
|
|
if i >= self._iterations_a:
|
|
return self._dir_a, None
|
|
a, dir, side = self.__circularHelper(self._start_a, i + 1,
|
|
pulses_per_mm, self._side_a,
|
|
self._dir_a)
|
|
# last item can be slightly more then end angle due to float precision
|
|
if i + 1 == self._iterations_a:
|
|
return dir, self._RdivV * self._delta_angle
|
|
b = math.sqrt(self._radius2 - a * a)
|
|
if side:
|
|
b = -b
|
|
return dir, self.__circularFindTime(a, b)
|
|
|
|
def __circularB(self, i, pulses_per_mm):
|
|
if i >= self._iterations_b:
|
|
return self._dir_b, None
|
|
b, dir, side = self.__circularHelper(self._start_b, i + 1,
|
|
pulses_per_mm, self._side_b,
|
|
self._dir_b)
|
|
# last item can be slightly more then end angle due to float precision
|
|
if i + 1 == self._iterations_b:
|
|
return dir, self._RdivV * self._delta_angle
|
|
a = math.sqrt(self._radius2 - b * b)
|
|
if side:
|
|
a = -a
|
|
return dir, self.__circularFindTime(a, b)
|
|
|
|
def __linear(self, i, total_i, pulses_per_mm, velocity):
|
|
if i >= total_i:
|
|
return None
|
|
return i / pulses_per_mm / velocity
|
|
|
|
def _interpolation_function(self, ix, iy, iz, ie):
|
|
""" Calculate interpolation values for linear movement, see super class
|
|
for details.
|
|
"""
|
|
if self._plane == PLANE_XY:
|
|
dx, tx = self.__circularA(ix, STEPPER_PULSES_PER_MM_X)
|
|
dy, ty = self.__circularB(iy, STEPPER_PULSES_PER_MM_Y)
|
|
tz = self.__linear(iz, self._iterations_3rd, STEPPER_PULSES_PER_MM_Z,
|
|
self._velocity_3rd)
|
|
dz = self._third_dir
|
|
elif self._plane == PLANE_YZ:
|
|
dy, ty = self.__circularA(iy, STEPPER_PULSES_PER_MM_Y)
|
|
dz, tz = self.__circularB(iz, STEPPER_PULSES_PER_MM_Z)
|
|
tx = self.__linear(ix, self._iterations_3rd, STEPPER_PULSES_PER_MM_X,
|
|
self._velocity_3rd)
|
|
dx = self._third_dir
|
|
elif self._plane == PLANE_ZX:
|
|
dz, tz = self.__circularA(iz, STEPPER_PULSES_PER_MM_Z)
|
|
dx, tx = self.__circularB(ix, STEPPER_PULSES_PER_MM_X)
|
|
ty = self.__linear(iy, self._iterations_3rd, STEPPER_PULSES_PER_MM_Y,
|
|
self._velocity_3rd)
|
|
dy = self._third_dir
|
|
te = self.__linear(ie, self._iterations_e, STEPPER_PULSES_PER_MM_E,
|
|
self._e_velocity)
|
|
return (dx, dy, dz, self._e_dir), (tx, ty, tz, te)
|