185 lines
9.0 KiB
Python
185 lines
9.0 KiB
Python
# Code for handling the kinematics of deltesian robots
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#
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# Copyright (C) 2022 Fabrice Gallet <tircown@gmail.com>
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#
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# This file may be distributed under the terms of the GNU GPLv3 license.
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import math, logging
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import stepper
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# Slow moves once the ratio of tower to XY movement exceeds SLOW_RATIO
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SLOW_RATIO = 3.
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# Minimum angle with the horizontal for the arm to not exceed - in degrees
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MIN_ANGLE = 5.
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class DeltesianKinematics:
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def __init__(self, toolhead, config):
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self.rails = [None] * 3
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stepper_configs = [config.getsection('stepper_' + s)
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for s in ['left', 'right', 'y']]
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self.rails[0] = stepper.PrinterRail(
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stepper_configs[0], need_position_minmax = False)
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def_pos_es = self.rails[0].get_homing_info().position_endstop
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self.rails[1] = stepper.PrinterRail(
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stepper_configs[1], need_position_minmax = False,
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default_position_endstop = def_pos_es)
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self.rails[2] = stepper.LookupMultiRail(stepper_configs[2])
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arm_x = self.arm_x = [None] * 2
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arm_x[0] = stepper_configs[0].getfloat('arm_x_length', above=0.)
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arm_x[1] = stepper_configs[1].getfloat('arm_x_length', arm_x[0],
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above=0.)
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arm = [None] * 2
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arm[0] = stepper_configs[0].getfloat('arm_length', above=arm_x[0])
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arm[1] = stepper_configs[1].getfloat('arm_length', arm[0],
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above=arm_x[1])
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arm2 = self.arm2 = [a**2 for a in arm]
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self.rails[0].setup_itersolve(
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'deltesian_stepper_alloc', arm2[0], -arm_x[0])
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self.rails[1].setup_itersolve(
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'deltesian_stepper_alloc', arm2[1], arm_x[1])
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self.rails[2].setup_itersolve('cartesian_stepper_alloc', b'y')
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for s in self.get_steppers():
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s.set_trapq(toolhead.get_trapq())
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toolhead.register_step_generator(s.generate_steps)
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config.get_printer().register_event_handler(
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"stepper_enable:motor_off", self._motor_off)
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self.limits = [(1.0, -1.0)] * 3
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# X axis limits
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min_angle = config.getfloat('min_angle', MIN_ANGLE,
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minval=0., maxval=90.)
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cos_angle = math.cos(math.radians(min_angle))
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x_kin_min = math.ceil( -min(arm_x[0], cos_angle * arm[1] - arm_x[1]))
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x_kin_max = math.floor( min(arm_x[1], cos_angle * arm[0] - arm_x[0]))
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x_kin_range = min(x_kin_max - x_kin_min, x_kin_max * 2, -x_kin_min * 2)
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print_width = config.getfloat('print_width', None, minval=0.,
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maxval=x_kin_range)
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if print_width:
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self.limits[0] = (-print_width * 0.5, print_width * 0.5)
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else:
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self.limits[0] = (x_kin_min, x_kin_max)
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# Y axis limits
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self.limits[1] = self.rails[2].get_range()
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# Z axis limits
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pmax = [r.get_homing_info().position_endstop for r in self.rails[:2]]
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self._abs_endstop = [p + math.sqrt(a2 - ax**2) for p, a2, ax
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in zip( pmax, arm2, arm_x )]
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self.home_z = self._actuator_to_cartesian(self._abs_endstop)[1]
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z_max = min([self._pillars_z_max(x) for x in self.limits[0]])
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z_min = config.getfloat('minimum_z_position', 0, maxval=z_max)
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self.limits[2] = (z_min, z_max)
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# Limit the speed/accel if is is at the extreme values of the x axis
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slow_ratio = config.getfloat('slow_ratio', SLOW_RATIO, minval=0.)
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self.slow_x2 = self.very_slow_x2 = None
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if slow_ratio > 0.:
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sr2 = slow_ratio ** 2
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self.slow_x2 = min([math.sqrt((sr2 * a2) / (sr2 + 1))
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- axl for a2, axl in zip(arm2, arm_x)]) ** 2
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self.very_slow_x2 = min([math.sqrt((2 * sr2 * a2) / (2 * sr2 + 1))
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- axl for a2, axl in zip(arm2, arm_x)]) ** 2
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logging.info("Deltesian kinematics: moves slowed past %.2fmm"
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" and %.2fmm"
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% (math.sqrt(self.slow_x2),
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math.sqrt(self.very_slow_x2)))
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# Setup boundary checks
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max_velocity, max_accel = toolhead.get_max_velocity()
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self.max_z_velocity = config.getfloat('max_z_velocity', max_velocity,
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above=0., maxval=max_velocity)
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self.max_z_accel = config.getfloat('max_z_accel', max_accel,
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above=0., maxval=max_accel)
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self.axes_min = toolhead.Coord(*[l[0] for l in self.limits], e=0.)
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self.axes_max = toolhead.Coord(*[l[1] for l in self.limits], e=0.)
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self.homed_axis = [False] * 3
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self.set_position([0., 0., 0.], ())
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def get_steppers(self):
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return [s for rail in self.rails for s in rail.get_steppers()]
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def _actuator_to_cartesian(self, sp):
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arm_x, arm2 = self.arm_x, self.arm2
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dx, dz = sum(arm_x), sp[1] - sp[0]
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pivots = math.sqrt(dx**2 + dz**2)
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# Trilateration w/ reference frame along left to right pivots
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xt = (pivots**2 + arm2[0] - arm2[1]) / (2 * pivots)
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zt = math.sqrt(arm2[0] - xt**2)
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# Rotation and translation of the reference frame
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x = xt * dx / pivots + zt * dz / pivots - arm_x[0]
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z = xt * dz / pivots - zt * dx / pivots + sp[0]
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return [x, z]
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def _pillars_z_max(self, x):
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arm_x, arm2 = self.arm_x, self.arm2
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dz = (math.sqrt(arm2[0] - (arm_x[0] + x)**2),
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math.sqrt(arm2[1] - (arm_x[1] - x)**2))
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return min([o - z for o, z in zip(self._abs_endstop, dz)])
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def calc_position(self, stepper_positions):
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sp = [stepper_positions[rail.get_name()] for rail in self.rails]
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x, z = self._actuator_to_cartesian(sp[:2])
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return [x, sp[2], z]
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def set_position(self, newpos, homing_axes):
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for rail in self.rails:
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rail.set_position(newpos)
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for n in homing_axes:
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self.homed_axis[n] = True
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def home(self, homing_state):
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homing_axes = homing_state.get_axes()
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home_xz = 0 in homing_axes or 2 in homing_axes
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home_y = 1 in homing_axes
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forceaxes = ([0, 1, 2] if (home_xz and home_y) else
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[0, 2] if home_xz else [1] if home_y else [])
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homing_state.set_axes(forceaxes)
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homepos = [None] * 4
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if home_xz:
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homing_state.set_axes([0, 1, 2] if home_y else [0, 2])
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homepos[0], homepos[2] = 0., self.home_z
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forcepos = list(homepos)
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dz2 = [(a2 - ax ** 2) for a2, ax in zip(self.arm2, self.arm_x)]
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forcepos[2] = -1.5 * math.sqrt(max(dz2))
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homing_state.home_rails(self.rails[:2], forcepos, homepos)
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if home_y:
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position_min, position_max = self.rails[2].get_range()
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hi = self.rails[2].get_homing_info()
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homepos[1] = hi.position_endstop
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forcepos = list(homepos)
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if hi.positive_dir:
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forcepos[1] -= 1.5 * (hi.position_endstop - position_min)
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else:
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forcepos[1] += 1.5 * (position_max - hi.position_endstop)
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homing_state.home_rails([self.rails[2]], forcepos, homepos)
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def _motor_off(self, print_time):
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self.homed_axis = [False] * 3
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def check_move(self, move):
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limits = list(map(list, self.limits))
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spos, epos = move.start_pos, move.end_pos
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homing_move = False
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if epos[0] == 0. and epos[2] == self.home_z and not move.axes_d[1]:
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# Identify a homing move
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homing_move = True
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elif epos[2] > limits[2][1]:
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# Moves at the very top - adapt limits depending on the X position
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limits[2][1] = self._pillars_z_max(epos[0])
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for i in (i for i, v in enumerate(move.axes_d[:3]) if v):
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if not self.homed_axis[i]:
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raise move.move_error("Must home axis first")
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# Move out of range - verify not a homing move
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if epos[i] < limits[i][0] or epos[i] > limits[i][1]:
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if not homing_move:
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raise move.move_error()
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if move.axes_d[2]:
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z_ratio = move.move_d / abs(move.axes_d[2])
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move.limit_speed(
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self.max_z_velocity * z_ratio, self.max_z_accel * z_ratio)
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# Limit the speed/accel if is is at the extreme values of the x axis
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if move.axes_d[0] and self.slow_x2 and self.very_slow_x2:
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move_x2 = max(spos[0] ** 2, epos[0] ** 2)
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if move_x2 > self.very_slow_x2:
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move.limit_speed(self.max_velocity *0.25, self.max_accel *0.25)
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elif move_x2 > self.slow_x2:
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move.limit_speed(self.max_velocity *0.50, self.max_accel *0.50)
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def get_status(self, eventtime):
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axes = [a for a, b in zip("xyz", self.homed_axis) if b]
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return {
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'homed_axes': "".join(axes),
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'axis_minimum': self.axes_min,
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'axis_maximum': self.axes_max,
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}
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def load_kinematics(toolhead, config):
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return DeltesianKinematics(toolhead, config)
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