--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/motion_control.cpp Sat Nov 07 13:23:07 2015 +0100
@@ -0,0 +1,147 @@
+/*
+ motion_control.c - high level interface for issuing motion commands
+ Part of Grbl
+
+ Copyright (c) 2009-2011 Simen Svale Skogsrud
+ Copyright (c) 2011 Sungeun K. Jeon
+
+ Grbl 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.
+
+ Grbl 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 Grbl. If not, see <http://www.gnu.org/licenses/>.
+*/
+
+#include "Marlin.h"
+#include "stepper.h"
+#include "planner.h"
+
+// The arc is approximated by generating a huge number of tiny, linear segments. The length of each
+// segment is configured in settings.mm_per_arc_segment.
+void mc_arc(float *position, float *target, float *offset, uint8_t axis_0, uint8_t axis_1,
+ uint8_t axis_linear, float feed_rate, float radius, uint8_t isclockwise, uint8_t extruder)
+{
+ // int acceleration_manager_was_enabled = plan_is_acceleration_manager_enabled();
+ // plan_set_acceleration_manager_enabled(false); // disable acceleration management for the duration of the arc
+ float center_axis0 = position[axis_0] + offset[axis_0];
+ float center_axis1 = position[axis_1] + offset[axis_1];
+ float linear_travel = target[axis_linear] - position[axis_linear];
+ float extruder_travel = target[E_AXIS] - position[E_AXIS];
+ float r_axis0 = -offset[axis_0]; // Radius vector from center to current location
+ float r_axis1 = -offset[axis_1];
+ float rt_axis0 = target[axis_0] - center_axis0;
+ float rt_axis1 = target[axis_1] - center_axis1;
+
+ // CCW angle between position and target from circle center. Only one atan2() trig computation required.
+ float angular_travel = atan2(r_axis0*rt_axis1-r_axis1*rt_axis0, r_axis0*rt_axis0+r_axis1*rt_axis1);
+ if (angular_travel < 0) { angular_travel += 2*M_PI; }
+ if (isclockwise) { angular_travel -= 2*M_PI; }
+
+ float millimeters_of_travel = hypot(angular_travel*radius, fabs(linear_travel));
+ if (millimeters_of_travel < 0.001) { return; }
+ uint16_t segments = floor(millimeters_of_travel/MM_PER_ARC_SEGMENT);
+ if(segments == 0) segments = 1;
+
+ /*
+ // Multiply inverse feed_rate to compensate for the fact that this movement is approximated
+ // by a number of discrete segments. The inverse feed_rate should be correct for the sum of
+ // all segments.
+ if (invert_feed_rate) { feed_rate *= segments; }
+ */
+ float theta_per_segment = angular_travel/segments;
+ float linear_per_segment = linear_travel/segments;
+ float extruder_per_segment = extruder_travel/segments;
+
+ /* Vector rotation by transformation matrix: r is the original vector, r_T is the rotated vector,
+ and phi is the angle of rotation. Based on the solution approach by Jens Geisler.
+ r_T = [cos(phi) -sin(phi);
+ sin(phi) cos(phi] * r ;
+
+ For arc generation, the center of the circle is the axis of rotation and the radius vector is
+ defined from the circle center to the initial position. Each line segment is formed by successive
+ vector rotations. This requires only two cos() and sin() computations to form the rotation
+ matrix for the duration of the entire arc. Error may accumulate from numerical round-off, since
+ all double numbers are single precision on the Arduino. (True double precision will not have
+ round off issues for CNC applications.) Single precision error can accumulate to be greater than
+ tool precision in some cases. Therefore, arc path correction is implemented.
+
+ Small angle approximation may be used to reduce computation overhead further. This approximation
+ holds for everything, but very small circles and large mm_per_arc_segment values. In other words,
+ theta_per_segment would need to be greater than 0.1 rad and N_ARC_CORRECTION would need to be large
+ to cause an appreciable drift error. N_ARC_CORRECTION~=25 is more than small enough to correct for
+ numerical drift error. N_ARC_CORRECTION may be on the order a hundred(s) before error becomes an
+ issue for CNC machines with the single precision Arduino calculations.
+
+ This approximation also allows mc_arc to immediately insert a line segment into the planner
+ without the initial overhead of computing cos() or sin(). By the time the arc needs to be applied
+ a correction, the planner should have caught up to the lag caused by the initial mc_arc overhead.
+ This is important when there are successive arc motions.
+ */
+ // Vector rotation matrix values
+ float cos_T = 1-0.5*theta_per_segment*theta_per_segment; // Small angle approximation
+ float sin_T = theta_per_segment;
+
+ float arc_target[4];
+ float sin_Ti;
+ float cos_Ti;
+ float r_axisi;
+ uint16_t i;
+ int8_t count = 0;
+
+ // Initialize the linear axis
+ arc_target[axis_linear] = position[axis_linear];
+
+ // Initialize the extruder axis
+ arc_target[E_AXIS] = position[E_AXIS];
+
+ for (i = 1; i<segments; i++) { // Increment (segments-1)
+
+ if (count < N_ARC_CORRECTION) {
+ // Apply vector rotation matrix
+ r_axisi = r_axis0*sin_T + r_axis1*cos_T;
+ r_axis0 = r_axis0*cos_T - r_axis1*sin_T;
+ r_axis1 = r_axisi;
+ count++;
+ } else {
+ // Arc correction to radius vector. Computed only every N_ARC_CORRECTION increments.
+ // Compute exact location by applying transformation matrix from initial radius vector(=-offset).
+ cos_Ti = cos(i*theta_per_segment);
+ sin_Ti = sin(i*theta_per_segment);
+ r_axis0 = -offset[axis_0]*cos_Ti + offset[axis_1]*sin_Ti;
+ r_axis1 = -offset[axis_0]*sin_Ti - offset[axis_1]*cos_Ti;
+ count = 0;
+ }
+
+ // Update arc_target location
+ arc_target[axis_0] = center_axis0 + r_axis0;
+ arc_target[axis_1] = center_axis1 + r_axis1;
+ arc_target[axis_linear] += linear_per_segment;
+ arc_target[E_AXIS] += extruder_per_segment;
+
+ if (min_software_endstops) {
+ if (arc_target[X_AXIS] < X_HOME_POS) arc_target[X_AXIS] = X_HOME_POS;
+ if (arc_target[Y_AXIS] < Y_HOME_POS) arc_target[Y_AXIS] = Y_HOME_POS;
+ if (arc_target[Z_AXIS] < Z_HOME_POS) arc_target[Z_AXIS] = Z_HOME_POS;
+ }
+
+ if (max_software_endstops) {
+ if (arc_target[X_AXIS] > max_length[X_AXIS]) arc_target[X_AXIS] = max_length[X_AXIS];
+ if (arc_target[Y_AXIS] > max_length[Y_AXIS]) arc_target[Y_AXIS] = max_length[Y_AXIS];
+ if (arc_target[Z_AXIS] > max_length[Z_AXIS]) arc_target[Z_AXIS] = max_length[Z_AXIS];
+ }
+ plan_buffer_line(arc_target[X_AXIS], arc_target[Y_AXIS], arc_target[Z_AXIS], arc_target[E_AXIS], feed_rate, extruder);
+
+ }
+ // Ensure last segment arrives at target location.
+ plan_buffer_line(target[X_AXIS], target[Y_AXIS], target[Z_AXIS], target[E_AXIS], feed_rate, extruder);
+
+ // plan_set_acceleration_manager_enabled(acceleration_manager_was_enabled);
+}
+