251 lines
11 KiB
Python
251 lines
11 KiB
Python
# Code for handling the kinematics of linear delta robots
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#
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# Copyright (C) 2016,2017 Kevin O'Connor <kevin@koconnor.net>
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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, homing, chelper
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StepList = (0, 1, 2)
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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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class DeltaKinematics:
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def __init__(self, toolhead, printer, config):
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stepper_configs = [config.getsection('stepper_' + n)
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for n in ['a', 'b', 'c']]
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stepper_a = stepper.PrinterHomingStepper(
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printer, stepper_configs[0], need_position_minmax = False)
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stepper_b = stepper.PrinterHomingStepper(
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printer, stepper_configs[1], need_position_minmax = False,
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default_position_endstop=stepper_a.position_endstop)
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stepper_c = stepper.PrinterHomingStepper(
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printer, stepper_configs[2], need_position_minmax = False,
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default_position_endstop=stepper_a.position_endstop)
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self.steppers = [stepper_a, stepper_b, stepper_c]
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self.need_motor_enable = self.need_home = True
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self.radius = radius = config.getfloat('delta_radius', above=0.)
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arm_length_a = stepper_configs[0].getfloat('arm_length', above=radius)
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self.arm_lengths = arm_lengths = [
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sconfig.getfloat('arm_length', arm_length_a, above=radius)
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for sconfig in stepper_configs]
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self.arm2 = [arm**2 for arm in arm_lengths]
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self.endstops = [s.position_endstop + math.sqrt(arm2 - radius**2)
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for s, arm2 in zip(self.steppers, self.arm2)]
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self.limit_xy2 = -1.
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self.max_z = min([s.position_endstop for s in self.steppers])
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self.min_z = config.getfloat('minimum_z_position', 0, maxval=self.max_z)
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self.limit_z = min([ep - arm
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for ep, arm in zip(self.endstops, arm_lengths)])
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logging.info(
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"Delta max build height %.2fmm (radius tapered above %.2fmm)" % (
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self.max_z, self.limit_z))
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# Setup stepper max halt velocity
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self.max_velocity, self.max_accel = toolhead.get_max_velocity()
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self.max_z_velocity = config.getfloat(
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'max_z_velocity', self.max_velocity,
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above=0., maxval=self.max_velocity)
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max_halt_velocity = toolhead.get_max_axis_halt()
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for s in self.steppers:
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s.set_max_jerk(max_halt_velocity, self.max_accel)
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# Determine tower locations in cartesian space
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self.angles = [sconfig.getfloat('angle', angle)
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for sconfig, angle in zip(stepper_configs,
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[210., 330., 90.])]
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self.towers = [(math.cos(math.radians(angle)) * radius,
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math.sin(math.radians(angle)) * radius)
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for angle in self.angles]
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# Setup iterative solver
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ffi_main, ffi_lib = chelper.get_ffi()
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self.cmove = ffi_main.gc(ffi_lib.move_alloc(), ffi_lib.free)
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self.move_fill = ffi_lib.move_fill
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for s, a, t in zip(self.steppers, self.arm2, self.towers):
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sk = ffi_main.gc(ffi_lib.delta_stepper_alloc(a, t[0], t[1]),
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ffi_lib.free)
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s.setup_itersolve(sk)
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# Find the point where an XY move could result in excessive
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# tower movement
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half_min_step_dist = min([s.step_dist for s in self.steppers]) * .5
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min_arm_length = min(arm_lengths)
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def ratio_to_dist(ratio):
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return (ratio * math.sqrt(min_arm_length**2 / (ratio**2 + 1.)
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- half_min_step_dist**2)
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+ half_min_step_dist)
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self.slow_xy2 = (ratio_to_dist(SLOW_RATIO) - radius)**2
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self.very_slow_xy2 = (ratio_to_dist(2. * SLOW_RATIO) - radius)**2
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self.max_xy2 = min(radius, min_arm_length - radius,
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ratio_to_dist(4. * SLOW_RATIO) - radius)**2
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logging.info(
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"Delta max build radius %.2fmm (moves slowed past %.2fmm and %.2fmm)"
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% (math.sqrt(self.max_xy2), math.sqrt(self.slow_xy2),
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math.sqrt(self.very_slow_xy2)))
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self.set_position([0., 0., 0.], ())
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def get_steppers(self, flags=""):
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return list(self.steppers)
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def _cartesian_to_actuator(self, coord):
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return [math.sqrt(self.arm2[i] - (self.towers[i][0] - coord[0])**2
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- (self.towers[i][1] - coord[1])**2) + coord[2]
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for i in StepList]
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def _actuator_to_cartesian(self, pos):
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return actuator_to_cartesian(self.towers, self.arm2, pos)
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def get_position(self):
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spos = [s.mcu_stepper.get_commanded_position() for s in self.steppers]
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return self._actuator_to_cartesian(spos)
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def set_position(self, newpos, homing_axes):
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pos = self._cartesian_to_actuator(newpos)
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for i in StepList:
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self.steppers[i].set_position(pos[i])
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self.limit_xy2 = -1.
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if tuple(homing_axes) == StepList:
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self.need_home = False
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def home(self, homing_state):
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# All axes are homed simultaneously
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homing_state.set_axes([0, 1, 2])
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endstops = [es for s in self.steppers for es in s.get_endstops()]
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s = self.steppers[0] # Assume homing speed same for all steppers
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# Initial homing
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homing_speed = min(s.homing_speed, self.max_z_velocity)
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homepos = [0., 0., self.max_z, None]
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coord = list(homepos)
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coord[2] = -1.5 * math.sqrt(max(self.arm2)-self.max_xy2)
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homing_state.home(coord, homepos, endstops, homing_speed)
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# Retract
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coord[2] = homepos[2] - s.homing_retract_dist
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homing_state.retract(coord, homing_speed)
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# Home again
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coord[2] -= s.homing_retract_dist
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homing_state.home(coord, homepos, endstops,
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homing_speed/2.0, second_home=True)
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# Set final homed position
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spos = [ep + s.get_homed_offset()
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for ep, s in zip(self.endstops, self.steppers)]
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homing_state.set_homed_position(self._actuator_to_cartesian(spos))
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def motor_off(self, print_time):
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self.limit_xy2 = -1.
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for stepper in self.steppers:
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stepper.motor_enable(print_time, 0)
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self.need_motor_enable = self.need_home = True
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def _check_motor_enable(self, print_time):
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for i in StepList:
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self.steppers[i].motor_enable(print_time, 1)
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self.need_motor_enable = False
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def check_move(self, move):
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end_pos = move.end_pos
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xy2 = end_pos[0]**2 + end_pos[1]**2
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if xy2 <= self.limit_xy2 and not move.axes_d[2]:
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# Normal XY move
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return
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if self.need_home:
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raise homing.EndstopMoveError(end_pos, "Must home first")
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limit_xy2 = self.max_xy2
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if end_pos[2] > self.limit_z:
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limit_xy2 = min(limit_xy2, (self.max_z - end_pos[2])**2)
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if xy2 > limit_xy2 or end_pos[2] < self.min_z or end_pos[2] > self.max_z:
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raise homing.EndstopMoveError(end_pos)
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if move.axes_d[2]:
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move.limit_speed(self.max_z_velocity, move.accel)
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limit_xy2 = -1.
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# Limit the speed/accel of this move if is is at the extreme
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# end of the build envelope
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extreme_xy2 = max(xy2, move.start_pos[0]**2 + move.start_pos[1]**2)
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if extreme_xy2 > self.slow_xy2:
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r = 0.5
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if extreme_xy2 > self.very_slow_xy2:
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r = 0.25
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max_velocity = self.max_velocity
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if move.axes_d[2]:
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max_velocity = self.max_z_velocity
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move.limit_speed(max_velocity * r, self.max_accel * r)
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limit_xy2 = -1.
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self.limit_xy2 = min(limit_xy2, self.slow_xy2)
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def move(self, print_time, move):
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if self.need_motor_enable:
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self._check_motor_enable(print_time)
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self.move_fill(
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self.cmove, print_time,
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move.accel_t, move.cruise_t, move.decel_t,
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move.start_pos[0], move.start_pos[1], move.start_pos[2],
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move.axes_d[0], move.axes_d[1], move.axes_d[2],
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move.start_v, move.cruise_v, move.accel)
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for stepper in self.steppers:
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stepper.step_itersolve(self.cmove)
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# Helper functions for DELTA_CALIBRATE script
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def get_stable_position(self):
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return [int((ep - s.mcu_stepper.get_commanded_position())
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/ s.mcu_stepper.get_step_dist() + .5)
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* s.mcu_stepper.get_step_dist()
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for ep, s in zip(self.endstops, self.steppers)]
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def get_calibrate_params(self):
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return {
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'endstop_a': self.steppers[0].position_endstop,
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'endstop_b': self.steppers[1].position_endstop,
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'endstop_c': self.steppers[2].position_endstop,
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'angle_a': self.angles[0], 'angle_b': self.angles[1],
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'angle_c': self.angles[2], 'radius': self.radius,
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'arm_a': self.arm_lengths[0], 'arm_b': self.arm_lengths[1],
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'arm_c': self.arm_lengths[2] }
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######################################################################
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# Matrix helper functions for 3x1 matrices
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######################################################################
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def matrix_cross(m1, m2):
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return [m1[1] * m2[2] - m1[2] * m2[1],
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m1[2] * m2[0] - m1[0] * m2[2],
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m1[0] * m2[1] - m1[1] * m2[0]]
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def matrix_dot(m1, m2):
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return m1[0] * m2[0] + m1[1] * m2[1] + m1[2] * m2[2]
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def matrix_magsq(m1):
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return m1[0]**2 + m1[1]**2 + m1[2]**2
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def matrix_add(m1, m2):
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return [m1[0] + m2[0], m1[1] + m2[1], m1[2] + m2[2]]
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def matrix_sub(m1, m2):
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return [m1[0] - m2[0], m1[1] - m2[1], m1[2] - m2[2]]
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def matrix_mul(m1, s):
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return [m1[0]*s, m1[1]*s, m1[2]*s]
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def actuator_to_cartesian(towers, arm2, pos):
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# Find nozzle position using trilateration (see wikipedia)
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carriage1 = list(towers[0]) + [pos[0]]
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carriage2 = list(towers[1]) + [pos[1]]
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carriage3 = list(towers[2]) + [pos[2]]
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s21 = matrix_sub(carriage2, carriage1)
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s31 = matrix_sub(carriage3, carriage1)
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d = math.sqrt(matrix_magsq(s21))
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ex = matrix_mul(s21, 1. / d)
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i = matrix_dot(ex, s31)
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vect_ey = matrix_sub(s31, matrix_mul(ex, i))
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ey = matrix_mul(vect_ey, 1. / math.sqrt(matrix_magsq(vect_ey)))
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ez = matrix_cross(ex, ey)
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j = matrix_dot(ey, s31)
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x = (arm2[0] - arm2[1] + d**2) / (2. * d)
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y = (arm2[0] - arm2[2] - x**2 + (x-i)**2 + j**2) / (2. * j)
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z = -math.sqrt(arm2[0] - x**2 - y**2)
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ex_x = matrix_mul(ex, x)
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ey_y = matrix_mul(ey, y)
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ez_z = matrix_mul(ez, z)
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return matrix_add(carriage1, matrix_add(ex_x, matrix_add(ey_y, ez_z)))
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def get_position_from_stable(spos, params):
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angles = [params['angle_a'], params['angle_b'], params['angle_c']]
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radius = params['radius']
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radius2 = radius**2
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towers = [(math.cos(angle) * radius, math.sin(angle) * radius)
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for angle in map(math.radians, angles)]
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arm2 = [a**2 for a in [params['arm_a'], params['arm_b'], params['arm_c']]]
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endstops = [params['endstop_a'], params['endstop_b'], params['endstop_c']]
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pos = [es + math.sqrt(a2 - radius2) - p
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for es, a2, p in zip(endstops, arm2, spos)]
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return actuator_to_cartesian(towers, arm2, pos)
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