klipper-dgus/klippy/kinematics/delta.py

# Code for handling the kinematics of linear delta robots
#
# Copyright (C) 2016-2018  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, mathutil

# Slow moves once the ratio of tower to XY movement exceeds SLOW_RATIO
SLOW_RATIO = 3.

class DeltaKinematics:
    def __init__(self, toolhead, config):
        # Setup tower rails
        stepper_configs = [config.getsection('stepper_' + n)
                           for n in ['a', 'b', 'c']]
        rail_a = stepper.PrinterRail(
            stepper_configs[0], need_position_minmax = False)
        a_endstop = rail_a.get_homing_info().position_endstop
        rail_b = stepper.PrinterRail(
            stepper_configs[1], need_position_minmax = False,
            default_position_endstop=a_endstop)
        rail_c = stepper.PrinterRail(
            stepper_configs[2], need_position_minmax = False,
            default_position_endstop=a_endstop)
        self.rails = [rail_a, rail_b, rail_c]
        # Read radius and arm lengths
        self.radius = radius = config.getfloat('delta_radius', above=0.)
        arm_length_a = stepper_configs[0].getfloat('arm_length', above=radius)
        self.arm_lengths = 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 = [(rail.get_homing_info().position_endstop
                          + math.sqrt(arm2 - radius**2))
                         for rail, arm2 in zip(self.rails, self.arm2)]
        # Setup boundary checks
        self.need_motor_enable = self.need_home = True
        self.limit_xy2 = -1.
        self.max_z = min([rail.get_homing_info().position_endstop
                          for rail in self.rails])
        self.min_z = config.getfloat('minimum_z_position', 0, maxval=self.max_z)
        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 rail in self.rails:
            rail.set_max_jerk(max_halt_velocity, self.max_accel)
        # Determine tower locations in cartesian space
        self.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 self.angles]
        for r, a, t in zip(self.rails, self.arm2, self.towers):
            r.setup_itersolve('delta_stepper_alloc', a, t[0], t[1])
        # Find the point where an XY move could result in excessive
        # tower movement
        half_min_step_dist = min([r.get_steppers()[0].get_step_dist()
                                  for r in self.rails]) * .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_rails(self, flags=""):
        return list(self.rails)
    def _actuator_to_cartesian(self, spos):
        sphere_coords = [(t[0], t[1], sp) for t, sp in zip(self.towers, spos)]
        return mathutil.trilateration(sphere_coords, self.arm2)
    def calc_position(self):
        spos = [rail.get_commanded_position() for rail in self.rails]
        return self._actuator_to_cartesian(spos)
    def set_position(self, newpos, homing_axes):
        for rail in self.rails:
            rail.set_position(newpos)
        self.limit_xy2 = -1.
        if tuple(homing_axes) == (0, 1, 2):
            self.need_home = False
    def home(self, homing_state):
        # All axes are homed simultaneously
        homing_state.set_axes([0, 1, 2])
        endstops = [es for rail in self.rails for es in rail.get_endstops()]
        # Initial homing - assume homing speed same for all steppers
        hi = self.rails[0].get_homing_info()
        homing_speed = min(hi.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] - hi.retract_dist
        homing_state.retract(coord, homing_speed)
        # Home again
        coord[2] -= hi.retract_dist
        homing_state.home(coord, homepos, endstops,
                          homing_speed/2.0, second_home=True)
        # Set final homed position
        spos = [ep + rail.get_homed_offset()
                for ep, rail in zip(self.endstops, self.rails)]
        homing_state.set_homed_position(self._actuator_to_cartesian(spos))
    def motor_off(self, print_time):
        self.limit_xy2 = -1.
        for rail in self.rails:
            rail.motor_enable(print_time, 0)
        self.need_motor_enable = self.need_home = True
    def _check_motor_enable(self, print_time):
        for rail in self.rails:
            rail.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] < self.min_z 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)
        for rail in self.rails:
            rail.step_itersolve(move.cmove)
    # Helper functions for DELTA_CALIBRATE script
    def get_stable_position(self):
        steppers = [rail.get_steppers()[0] for rail in self.rails]
        return [int((ep - s.get_commanded_position()) / s.get_step_dist() + .5)
                for ep, s in zip(self.endstops, steppers)]
    def get_calibrate_params(self):
        out = { 'radius': self.radius }
        for i, axis in enumerate('abc'):
            rail = self.rails[i]
            out['endstop_'+axis] = rail.get_homing_info().position_endstop
            out['stepdist_'+axis] = rail.get_steppers()[0].get_step_dist()
            out['angle_'+axis] = self.angles[i]
            out['arm_'+axis] = self.arm_lengths[i]
        return out
    def get_positions_from_stable(self, stable_positions, params):
        angle_names = ['angle_a', 'angle_b', 'angle_c']
        angles = [math.radians(params[an]) for an in angle_names]
        radius = params['radius']
        radius2 = radius**2
        towers = [(math.cos(a) * radius, math.sin(a) * radius) for a in angles]
        arm2 = [params[an]**2 for an in ['arm_a', 'arm_b', 'arm_c']]
        stepdist_names = ['stepdist_a', 'stepdist_b', 'stepdist_c']
        stepdists = [params[sn] for sn in stepdist_names]
        endstop_names = ['endstop_a', 'endstop_b', 'endstop_c']
        endstops = [params[en] + math.sqrt(a2 - radius2)
                    for en, a2 in zip(endstop_names, arm2)]
        out = []
        for spos in stable_positions:
            sphere_coords = [
                (t[0], t[1], es - sp * sd)
                for t, es, sd, sp in zip(towers, endstops, stepdists, spos) ]
            out.append(mathutil.trilateration(sphere_coords, arm2))
        return out

def load_kinematics(toolhead, config):
    return DeltaKinematics(toolhead, config)