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+/**
+ * Marlin 3D Printer Firmware
+ * Copyright (c) 2020 MarlinFirmware [https://github.com/MarlinFirmware/Marlin]
+ *
+ * Based on Sprinter and grbl.
+ * Copyright (c) 2011 Camiel Gubbels / Erik van der Zalm
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program. If not, see <https://www.gnu.org/licenses/>.
+ *
+ */
+
+/**
+ * delta.cpp
+ */
+
+#include "../inc/MarlinConfig.h"
+
+#if ENABLED(DELTA)
+
+#include "delta.h"
+#include "motion.h"
+
+// For homing:
+#include "planner.h"
+#include "endstops.h"
+#include "../lcd/marlinui.h"
+#include "../MarlinCore.h"
+
+#if HAS_BED_PROBE
+ #include "probe.h"
+#endif
+
+#if ENABLED(SENSORLESS_HOMING)
+ #include "../feature/tmc_util.h"
+ #include "stepper/indirection.h"
+#endif
+
+#define DEBUG_OUT ENABLED(DEBUG_LEVELING_FEATURE)
+#include "../core/debug_out.h"
+
+// Initialized by settings.load()
+float delta_height;
+abc_float_t delta_endstop_adj{0};
+float delta_radius,
+ delta_diagonal_rod,
+ delta_segments_per_second;
+abc_float_t delta_tower_angle_trim;
+xy_float_t delta_tower[ABC];
+abc_float_t delta_diagonal_rod_2_tower;
+float delta_clip_start_height = Z_MAX_POS;
+abc_float_t delta_diagonal_rod_trim;
+
+float delta_safe_distance_from_top();
+
+/**
+ * Recalculate factors used for delta kinematics whenever
+ * settings have been changed (e.g., by M665).
+ */
+void recalc_delta_settings() {
+ constexpr abc_float_t trt = DELTA_RADIUS_TRIM_TOWER;
+ delta_tower[A_AXIS].set(cos(RADIANS(210 + delta_tower_angle_trim.a)) * (delta_radius + trt.a), // front left tower
+ sin(RADIANS(210 + delta_tower_angle_trim.a)) * (delta_radius + trt.a));
+ delta_tower[B_AXIS].set(cos(RADIANS(330 + delta_tower_angle_trim.b)) * (delta_radius + trt.b), // front right tower
+ sin(RADIANS(330 + delta_tower_angle_trim.b)) * (delta_radius + trt.b));
+ delta_tower[C_AXIS].set(cos(RADIANS( 90 + delta_tower_angle_trim.c)) * (delta_radius + trt.c), // back middle tower
+ sin(RADIANS( 90 + delta_tower_angle_trim.c)) * (delta_radius + trt.c));
+ delta_diagonal_rod_2_tower.set(sq(delta_diagonal_rod + delta_diagonal_rod_trim.a),
+ sq(delta_diagonal_rod + delta_diagonal_rod_trim.b),
+ sq(delta_diagonal_rod + delta_diagonal_rod_trim.c));
+ update_software_endstops(Z_AXIS);
+ set_all_unhomed();
+}
+
+/**
+ * Get a safe radius for calibration
+ */
+
+#if EITHER(DELTA_AUTO_CALIBRATION, DELTA_CALIBRATION_MENU)
+
+ #if ENABLED(DELTA_AUTO_CALIBRATION)
+ float calibration_radius_factor = 1;
+ #endif
+
+ float delta_calibration_radius() {
+ return calibration_radius_factor * (
+ #if HAS_BED_PROBE
+ FLOOR((DELTA_PRINTABLE_RADIUS) - _MAX(HYPOT(probe.offset_xy.x, probe.offset_xy.y), PROBING_MARGIN))
+ #else
+ DELTA_PRINTABLE_RADIUS
+ #endif
+ );
+ }
+
+#endif
+
+/**
+ * Delta Inverse Kinematics
+ *
+ * Calculate the tower positions for a given machine
+ * position, storing the result in the delta[] array.
+ *
+ * This is an expensive calculation, requiring 3 square
+ * roots per segmented linear move, and strains the limits
+ * of a Mega2560 with a Graphical Display.
+ *
+ * Suggested optimizations include:
+ *
+ * - Disable the home_offset (M206) and/or position_shift (G92)
+ * features to remove up to 12 float additions.
+ */
+
+#define DELTA_DEBUG(VAR) do { \
+ SERIAL_ECHOLNPAIR_P(PSTR("Cartesian X"), VAR.x, SP_Y_STR, VAR.y, SP_Z_STR, VAR.z); \
+ SERIAL_ECHOLNPAIR_P(PSTR("Delta A"), delta.a, SP_B_STR, delta.b, SP_C_STR, delta.c); \
+ }while(0)
+
+void inverse_kinematics(const xyz_pos_t &raw) {
+ #if HAS_HOTEND_OFFSET
+ // Delta hotend offsets must be applied in Cartesian space with no "spoofing"
+ xyz_pos_t pos = { raw.x - hotend_offset[active_extruder].x,
+ raw.y - hotend_offset[active_extruder].y,
+ raw.z };
+ DELTA_IK(pos);
+ //DELTA_DEBUG(pos);
+ #else
+ DELTA_IK(raw);
+ //DELTA_DEBUG(raw);
+ #endif
+}
+
+/**
+ * Calculate the highest Z position where the
+ * effector has the full range of XY motion.
+ */
+float delta_safe_distance_from_top() {
+ xyz_pos_t cartesian{0};
+ inverse_kinematics(cartesian);
+ const float centered_extent = delta.a;
+ cartesian.y = DELTA_PRINTABLE_RADIUS;
+ inverse_kinematics(cartesian);
+ return ABS(centered_extent - delta.a);
+}
+
+/**
+ * Delta Forward Kinematics
+ *
+ * See the Wikipedia article "Trilateration"
+ * https://en.wikipedia.org/wiki/Trilateration
+ *
+ * Establish a new coordinate system in the plane of the
+ * three carriage points. This system has its origin at
+ * tower1, with tower2 on the X axis. Tower3 is in the X-Y
+ * plane with a Z component of zero.
+ * We will define unit vectors in this coordinate system
+ * in our original coordinate system. Then when we calculate
+ * the Xnew, Ynew and Znew values, we can translate back into
+ * the original system by moving along those unit vectors
+ * by the corresponding values.
+ *
+ * Variable names matched to Marlin, c-version, and avoid the
+ * use of any vector library.
+ *
+ * by Andreas Hardtung 2016-06-07
+ * based on a Java function from "Delta Robot Kinematics V3"
+ * by Steve Graves
+ *
+ * The result is stored in the cartes[] array.
+ */
+void forward_kinematics_DELTA(const float &z1, const float &z2, const float &z3) {
+ // Create a vector in old coordinates along x axis of new coordinate
+ const float p12[3] = { delta_tower[B_AXIS].x - delta_tower[A_AXIS].x, delta_tower[B_AXIS].y - delta_tower[A_AXIS].y, z2 - z1 },
+
+ // Get the reciprocal of Magnitude of vector.
+ d2 = sq(p12[0]) + sq(p12[1]) + sq(p12[2]), inv_d = RSQRT(d2),
+
+ // Create unit vector by multiplying by the inverse of the magnitude.
+ ex[3] = { p12[0] * inv_d, p12[1] * inv_d, p12[2] * inv_d },
+
+ // Get the vector from the origin of the new system to the third point.
+ p13[3] = { delta_tower[C_AXIS].x - delta_tower[A_AXIS].x, delta_tower[C_AXIS].y - delta_tower[A_AXIS].y, z3 - z1 },
+
+ // Use the dot product to find the component of this vector on the X axis.
+ i = ex[0] * p13[0] + ex[1] * p13[1] + ex[2] * p13[2],
+
+ // Create a vector along the x axis that represents the x component of p13.
+ iex[3] = { ex[0] * i, ex[1] * i, ex[2] * i };
+
+ // Subtract the X component from the original vector leaving only Y. We use the
+ // variable that will be the unit vector after we scale it.
+ float ey[3] = { p13[0] - iex[0], p13[1] - iex[1], p13[2] - iex[2] };
+
+ // The magnitude and the inverse of the magnitude of Y component
+ const float j2 = sq(ey[0]) + sq(ey[1]) + sq(ey[2]), inv_j = RSQRT(j2);
+
+ // Convert to a unit vector
+ ey[0] *= inv_j; ey[1] *= inv_j; ey[2] *= inv_j;
+
+ // The cross product of the unit x and y is the unit z
+ // float[] ez = vectorCrossProd(ex, ey);
+ const float ez[3] = {
+ ex[1] * ey[2] - ex[2] * ey[1],
+ ex[2] * ey[0] - ex[0] * ey[2],
+ ex[0] * ey[1] - ex[1] * ey[0]
+ },
+
+ // We now have the d, i and j values defined in Wikipedia.
+ // Plug them into the equations defined in Wikipedia for Xnew, Ynew and Znew
+ Xnew = (delta_diagonal_rod_2_tower.a - delta_diagonal_rod_2_tower.b + d2) * inv_d * 0.5,
+ Ynew = ((delta_diagonal_rod_2_tower.a - delta_diagonal_rod_2_tower.c + sq(i) + j2) * 0.5 - i * Xnew) * inv_j,
+ Znew = SQRT(delta_diagonal_rod_2_tower.a - HYPOT2(Xnew, Ynew));
+
+ // Start from the origin of the old coordinates and add vectors in the
+ // old coords that represent the Xnew, Ynew and Znew to find the point
+ // in the old system.
+ cartes.set(delta_tower[A_AXIS].x + ex[0] * Xnew + ey[0] * Ynew - ez[0] * Znew,
+ delta_tower[A_AXIS].y + ex[1] * Xnew + ey[1] * Ynew - ez[1] * Znew,
+ z1 + ex[2] * Xnew + ey[2] * Ynew - ez[2] * Znew);
+}
+
+/**
+ * A delta can only safely home all axes at the same time
+ * This is like quick_home_xy() but for 3 towers.
+ */
+void home_delta() {
+ DEBUG_SECTION(log_home_delta, "home_delta", DEBUGGING(LEVELING));
+
+ // Init the current position of all carriages to 0,0,0
+ current_position.reset();
+ destination.reset();
+ sync_plan_position();
+
+ // Disable stealthChop if used. Enable diag1 pin on driver.
+ #if ENABLED(SENSORLESS_HOMING)
+ TERN_(X_SENSORLESS, sensorless_t stealth_states_x = start_sensorless_homing_per_axis(X_AXIS));
+ TERN_(Y_SENSORLESS, sensorless_t stealth_states_y = start_sensorless_homing_per_axis(Y_AXIS));
+ TERN_(Z_SENSORLESS, sensorless_t stealth_states_z = start_sensorless_homing_per_axis(Z_AXIS));
+ #endif
+
+ // Move all carriages together linearly until an endstop is hit.
+ current_position.z = (delta_height + 10 - TERN0(HAS_BED_PROBE, probe.offset.z));
+ line_to_current_position(homing_feedrate(Z_AXIS));
+ planner.synchronize();
+
+ // Re-enable stealthChop if used. Disable diag1 pin on driver.
+ #if ENABLED(SENSORLESS_HOMING)
+ TERN_(X_SENSORLESS, end_sensorless_homing_per_axis(X_AXIS, stealth_states_x));
+ TERN_(Y_SENSORLESS, end_sensorless_homing_per_axis(Y_AXIS, stealth_states_y));
+ TERN_(Z_SENSORLESS, end_sensorless_homing_per_axis(Z_AXIS, stealth_states_z));
+ #endif
+
+ endstops.validate_homing_move();
+
+ // At least one carriage has reached the top.
+ // Now re-home each carriage separately.
+ homeaxis(A_AXIS);
+ homeaxis(B_AXIS);
+ homeaxis(C_AXIS);
+
+ // Set all carriages to their home positions
+ // Do this here all at once for Delta, because
+ // XYZ isn't ABC. Applying this per-tower would
+ // give the impression that they are the same.
+ LOOP_XYZ(i) set_axis_is_at_home((AxisEnum)i);
+
+ sync_plan_position();
+
+ #if DISABLED(DELTA_HOME_TO_SAFE_ZONE) && defined(HOMING_BACKOFF_POST_MM)
+ constexpr xyz_float_t endstop_backoff = HOMING_BACKOFF_POST_MM;
+ if (endstop_backoff.z) {
+ current_position.z -= ABS(endstop_backoff.z) * Z_HOME_DIR;
+ line_to_current_position(homing_feedrate(Z_AXIS));
+ }
+ #endif
+}
+
+#endif // DELTA