# Code for handling the kinematics of linear delta robots
#
# Copyright (C) 2016,2017 Kevin O'Connor <kevin@koconnor.net>
#
# This file may be distributed under the terms of the GNU GPLv3 license.
import math, logging
import stepper, homing
StepList = (0, 1, 2)
# Slow moves once the ratio of tower to XY movement exceeds SLOW_RATIO
SLOW_RATIO = 3.
class DeltaKinematics:
def __init__(self, toolhead, printer, config):
stepper_configs = [config.getsection('stepper_' + n)
for n in ['a', 'b', 'c']]
stepper_a = stepper.PrinterHomingStepper(printer, stepper_configs[0])
stepper_b = stepper.PrinterHomingStepper(
printer, stepper_configs[1],
default_position=stepper_a.position_endstop)
stepper_c = stepper.PrinterHomingStepper(
printer, stepper_configs[2],
default_position=stepper_a.position_endstop)
self.steppers = [stepper_a, stepper_b, stepper_c]
self.need_motor_enable = self.need_home = True
radius = config.getfloat('delta_radius', above=0.)
arm_length_a = stepper_configs[0].getfloat('arm_length', above=radius)
arm_lengths = [sconfig.getfloat('arm_length', arm_length_a, above=radius)
for sconfig in stepper_configs]
self.arm2 = [arm**2 for arm in arm_lengths]
self.endstops = [s.position_endstop + math.sqrt(arm2 - radius**2)
for s, arm2 in zip(self.steppers, self.arm2)]
self.limit_xy2 = -1.
self.max_z = min([s.position_endstop for s in self.steppers])
self.limit_z = min([ep - arm
for ep, arm in zip(self.endstops, arm_lengths)])
logging.info(
"Delta max build height %.2fmm (radius tapered above %.2fmm)" % (
self.max_z, self.limit_z))
# Setup stepper max halt velocity
self.max_velocity, self.max_accel = toolhead.get_max_velocity()
self.max_z_velocity = config.getfloat(
'max_z_velocity', self.max_velocity,
above=0., maxval=self.max_velocity)
max_halt_velocity = toolhead.get_max_axis_halt()
for s in self.steppers:
s.set_max_jerk(max_halt_velocity, self.max_accel)
# Determine tower locations in cartesian space
angles = [sconfig.getfloat('angle', angle)
for sconfig, angle in zip(stepper_configs, [210., 330., 90.])]
self.towers = [(math.cos(math.radians(angle)) * radius,
math.sin(math.radians(angle)) * radius)
for angle in angles]
# Find the point where an XY move could result in excessive
# tower movement
half_min_step_dist = min([s.step_dist for s in self.steppers]) * .5
min_arm_length = min(arm_lengths)
def ratio_to_dist(ratio):
return (ratio * math.sqrt(min_arm_length**2 / (ratio**2 + 1.)
- half_min_step_dist**2)
+ half_min_step_dist)
self.slow_xy2 = (ratio_to_dist(SLOW_RATIO) - radius)**2
self.very_slow_xy2 = (ratio_to_dist(2. * SLOW_RATIO) - radius)**2
self.max_xy2 = min(radius, min_arm_length - radius,
ratio_to_dist(4. * SLOW_RATIO) - radius)**2
logging.info(
"Delta max build radius %.2fmm (moves slowed past %.2fmm and %.2fmm)"
% (math.sqrt(self.max_xy2), math.sqrt(self.slow_xy2),
math.sqrt(self.very_slow_xy2)))
self.set_position([0., 0., 0.])
def get_steppers(self):
return list(self.steppers)
def _cartesian_to_actuator(self, coord):
return [math.sqrt(self.arm2[i] - (self.towers[i][0] - coord[0])**2
- (self.towers[i][1] - coord[1])**2) + coord[2]
for i in StepList]
def _actuator_to_cartesian(self, pos):
# Find nozzle position using trilateration (see wikipedia)
carriage1 = list(self.towers[0]) + [pos[0]]
carriage2 = list(self.towers[1]) + [pos[1]]
carriage3 = list(self.towers[2]) + [pos[2]]
s21 = matrix_sub(carriage2, carriage1)
s31 = matrix_sub(carriage3, carriage1)
d = math.sqrt(matrix_magsq(s21))
ex = matrix_mul(s21, 1. / d)
i = matrix_dot(ex, s31)
vect_ey = matrix_sub(s31, matrix_mul(ex, i))
ey = matrix_mul(vect_ey, 1. / math.sqrt(matrix_magsq(vect_ey)))
ez = matrix_cross(ex, ey)
j = matrix_dot(ey, s31)
x = (self.arm2[0] - self.arm2[1] + d**2) / (2. * d)
y = (self.arm2[0] - self.arm2[2] - x**2 + (x-i)**2 + j**2) / (2. * j)
z = -math.sqrt(self.arm2[0] - x**2 - y**2)
ex_x = matrix_mul(ex, x)
ey_y = matrix_mul(ey, y)
ez_z = matrix_mul(ez, z)
return matrix_add(carriage1, matrix_add(ex_x, matrix_add(ey_y, ez_z)))
def set_position(self, newpos):
pos = self._cartesian_to_actuator(newpos)
for i in StepList:
self.steppers[i].set_position(pos[i])
self.limit_xy2 = -1.
def home(self, homing_state):
# All axes are homed simultaneously
homing_state.set_axes([0, 1, 2])
endstops = [es for s in self.steppers for es in s.get_endstops()]
s = self.steppers[0] # Assume homing speed same for all steppers
self.need_home = False
# Initial homing
homing_speed = min(s.homing_speed, self.max_z_velocity)
homepos = [0., 0., self.max_z, None]
coord = list(homepos)
coord[2] = -1.5 * math.sqrt(max(self.arm2)-self.max_xy2)
homing_state.home(coord, homepos, endstops, homing_speed)
# Retract
coord[2] = homepos[2] - s.homing_retract_dist
homing_state.retract(coord, homing_speed)
# Home again
coord[2] -= s.homing_retract_dist
homing_state.home(coord, homepos, endstops,
homing_speed/2.0, second_home=True)
# Set final homed position
spos = [ep + s.get_homed_offset()
for ep, s in zip(self.endstops, self.steppers)]
homing_state.set_homed_position(self._actuator_to_cartesian(spos))
def motor_off(self, print_time):
self.limit_xy2 = -1.
for stepper in self.steppers:
stepper.motor_enable(print_time, 0)
self.need_motor_enable = self.need_home = True
def _check_motor_enable(self, print_time):
for i in StepList:
self.steppers[i].motor_enable(print_time, 1)
self.need_motor_enable = False
def check_move(self, move):
end_pos = move.end_pos
xy2 = end_pos[0]**2 + end_pos[1]**2
if xy2 <= self.limit_xy2 and not move.axes_d[2]:
# Normal XY move
return
if self.need_home:
raise homing.EndstopMoveError(end_pos, "Must home first")
limit_xy2 = self.max_xy2
if end_pos[2] > self.limit_z:
limit_xy2 = min(limit_xy2, (self.max_z - end_pos[2])**2)
if xy2 > limit_xy2 or end_pos[2] < 0. or end_pos[2] > self.max_z:
raise homing.EndstopMoveError(end_pos)
if move.axes_d[2]:
move.limit_speed(self.max_z_velocity, move.accel)
limit_xy2 = -1.
# Limit the speed/accel of this move if is is at the extreme
# end of the build envelope
extreme_xy2 = max(xy2, move.start_pos[0]**2 + move.start_pos[1]**2)
if extreme_xy2 > self.slow_xy2:
r = 0.5
if extreme_xy2 > self.very_slow_xy2:
r = 0.25
max_velocity = self.max_velocity
if move.axes_d[2]:
max_velocity = self.max_z_velocity
move.limit_speed(max_velocity * r, self.max_accel * r)
limit_xy2 = -1.
self.limit_xy2 = min(limit_xy2, self.slow_xy2)
def move(self, print_time, move):
if self.need_motor_enable:
self._check_motor_enable(print_time)
axes_d = move.axes_d
move_d = move.move_d
movexy_r = 1.
movez_r = 0.
inv_movexy_d = 1. / move_d
if not axes_d[0] and not axes_d[1]:
# Z only move
movez_r = axes_d[2] * inv_movexy_d
movexy_r = inv_movexy_d = 0.
elif axes_d[2]:
# XY+Z move
movexy_d = math.sqrt(axes_d[0]**2 + axes_d[1]**2)
movexy_r = movexy_d * inv_movexy_d
movez_r = axes_d[2] * inv_movexy_d
inv_movexy_d = 1. / movexy_d
origx, origy, origz = move.start_pos[:3]
accel = move.accel
cruise_v = move.cruise_v
accel_d = move.accel_r * move_d
cruise_d = move.cruise_r * move_d
decel_d = move.decel_r * move_d
for i in StepList:
# Calculate a virtual tower along the line of movement at
# the point closest to this stepper's tower.
towerx_d = self.towers[i][0] - origx
towery_d = self.towers[i][1] - origy
vt_startxy_d = (towerx_d*axes_d[0] + towery_d*axes_d[1])*inv_movexy_d
tangentxy_d2 = towerx_d**2 + towery_d**2 - vt_startxy_d**2
vt_arm_d = math.sqrt(self.arm2[i] - tangentxy_d2)
vt_startz = origz
# Generate steps
step_delta = self.steppers[i].step_delta
move_time = print_time
if accel_d:
step_delta(move_time, accel_d, move.start_v, accel,
vt_startz, vt_startxy_d, vt_arm_d, movez_r)
vt_startz += accel_d * movez_r
vt_startxy_d -= accel_d * movexy_r
move_time += move.accel_t
if cruise_d:
step_delta(move_time, cruise_d, cruise_v, 0.,
vt_startz, vt_startxy_d, vt_arm_d, movez_r)
vt_startz += cruise_d * movez_r
vt_startxy_d -= cruise_d * movexy_r
move_time += move.cruise_t
if decel_d:
step_delta(move_time, decel_d, cruise_v, -accel,
vt_startz, vt_startxy_d, vt_arm_d, movez_r)
######################################################################
# Matrix helper functions for 3x1 matrices
######################################################################
def matrix_cross(m1, m2):
return [m1[1] * m2[2] - m1[2] * m2[1],
m1[2] * m2[0] - m1[0] * m2[2],
m1[0] * m2[1] - m1[1] * m2[0]]
def matrix_dot(m1, m2):
return m1[0] * m2[0] + m1[1] * m2[1] + m1[2] * m2[2]
def matrix_magsq(m1):
return m1[0]**2 + m1[1]**2 + m1[2]**2
def matrix_add(m1, m2):
return [m1[0] + m2[0], m1[1] + m2[1], m1[2] + m2[2]]
def matrix_sub(m1, m2):
return [m1[0] - m2[0], m1[1] - m2[1], m1[2] - m2[2]]
def matrix_mul(m1, s):
return [m1[0]*s, m1[1]*s, m1[2]*s]