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138 lines
6.4 KiB
138 lines
6.4 KiB
/*
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motion_control.c - high level interface for issuing motion commands
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Part of Grbl
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Copyright (c) 2009-2011 Simen Svale Skogsrud
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Copyright (c) 2011 Sungeun K. Jeon
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Grbl is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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Grbl is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with Grbl. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "Marlin.h"
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#include "stepper.h"
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#include "planner.h"
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// The arc is approximated by generating a huge number of tiny, linear segments. The length of each
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// segment is configured in settings.mm_per_arc_segment.
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void mc_arc(float *position, float *target, float *offset, uint8_t axis_0, uint8_t axis_1,
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uint8_t axis_linear, float feed_rate, float radius, uint8_t isclockwise, uint8_t extruder)
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{
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// int acceleration_manager_was_enabled = plan_is_acceleration_manager_enabled();
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// plan_set_acceleration_manager_enabled(false); // disable acceleration management for the duration of the arc
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float center_axis0 = position[axis_0] + offset[axis_0];
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float center_axis1 = position[axis_1] + offset[axis_1];
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float linear_travel = target[axis_linear] - position[axis_linear];
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float extruder_travel = target[E_AXIS] - position[E_AXIS];
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float r_axis0 = -offset[axis_0]; // Radius vector from center to current location
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float r_axis1 = -offset[axis_1];
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float rt_axis0 = target[axis_0] - center_axis0;
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float rt_axis1 = target[axis_1] - center_axis1;
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// CCW angle between position and target from circle center. Only one atan2() trig computation required.
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float angular_travel = atan2(r_axis0*rt_axis1-r_axis1*rt_axis0, r_axis0*rt_axis0+r_axis1*rt_axis1);
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if (angular_travel < 0) { angular_travel += 2*M_PI; }
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if (isclockwise) { angular_travel -= 2*M_PI; }
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float millimeters_of_travel = hypot(angular_travel*radius, fabs(linear_travel));
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if (millimeters_of_travel < 0.001) { return; }
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uint16_t segments = floor(millimeters_of_travel/MM_PER_ARC_SEGMENT);
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if(segments == 0) segments = 1;
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/*
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// Multiply inverse feed_rate to compensate for the fact that this movement is approximated
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// by a number of discrete segments. The inverse feed_rate should be correct for the sum of
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// all segments.
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if (invert_feed_rate) { feed_rate *= segments; }
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*/
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float theta_per_segment = angular_travel/segments;
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float linear_per_segment = linear_travel/segments;
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float extruder_per_segment = extruder_travel/segments;
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/* Vector rotation by transformation matrix: r is the original vector, r_T is the rotated vector,
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and phi is the angle of rotation. Based on the solution approach by Jens Geisler.
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r_T = [cos(phi) -sin(phi);
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sin(phi) cos(phi] * r ;
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For arc generation, the center of the circle is the axis of rotation and the radius vector is
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defined from the circle center to the initial position. Each line segment is formed by successive
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vector rotations. This requires only two cos() and sin() computations to form the rotation
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matrix for the duration of the entire arc. Error may accumulate from numerical round-off, since
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all double numbers are single precision on the Arduino. (True double precision will not have
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round off issues for CNC applications.) Single precision error can accumulate to be greater than
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tool precision in some cases. Therefore, arc path correction is implemented.
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Small angle approximation may be used to reduce computation overhead further. This approximation
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holds for everything, but very small circles and large mm_per_arc_segment values. In other words,
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theta_per_segment would need to be greater than 0.1 rad and N_ARC_CORRECTION would need to be large
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to cause an appreciable drift error. N_ARC_CORRECTION~=25 is more than small enough to correct for
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numerical drift error. N_ARC_CORRECTION may be on the order a hundred(s) before error becomes an
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issue for CNC machines with the single precision Arduino calculations.
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This approximation also allows mc_arc to immediately insert a line segment into the planner
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without the initial overhead of computing cos() or sin(). By the time the arc needs to be applied
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a correction, the planner should have caught up to the lag caused by the initial mc_arc overhead.
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This is important when there are successive arc motions.
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*/
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// Vector rotation matrix values
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float cos_T = 1-0.5*theta_per_segment*theta_per_segment; // Small angle approximation
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float sin_T = theta_per_segment;
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float arc_target[4];
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float sin_Ti;
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float cos_Ti;
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float r_axisi;
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uint16_t i;
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int8_t count = 0;
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// Initialize the linear axis
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arc_target[axis_linear] = position[axis_linear];
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// Initialize the extruder axis
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arc_target[E_AXIS] = position[E_AXIS];
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for (i = 1; i<segments; i++) { // Increment (segments-1)
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if (count < N_ARC_CORRECTION) {
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// Apply vector rotation matrix
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r_axisi = r_axis0*sin_T + r_axis1*cos_T;
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r_axis0 = r_axis0*cos_T - r_axis1*sin_T;
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r_axis1 = r_axisi;
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count++;
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} else {
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// Arc correction to radius vector. Computed only every N_ARC_CORRECTION increments.
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// Compute exact location by applying transformation matrix from initial radius vector(=-offset).
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cos_Ti = cos(i*theta_per_segment);
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sin_Ti = sin(i*theta_per_segment);
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r_axis0 = -offset[axis_0]*cos_Ti + offset[axis_1]*sin_Ti;
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r_axis1 = -offset[axis_0]*sin_Ti - offset[axis_1]*cos_Ti;
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count = 0;
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}
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// Update arc_target location
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arc_target[axis_0] = center_axis0 + r_axis0;
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arc_target[axis_1] = center_axis1 + r_axis1;
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arc_target[axis_linear] += linear_per_segment;
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arc_target[E_AXIS] += extruder_per_segment;
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clamp_to_software_endstops(arc_target);
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plan_buffer_line(arc_target[X_AXIS], arc_target[Y_AXIS], arc_target[Z_AXIS], arc_target[E_AXIS], feed_rate, extruder);
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}
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// Ensure last segment arrives at target location.
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plan_buffer_line(target[X_AXIS], target[Y_AXIS], target[Z_AXIS], target[E_AXIS], feed_rate, extruder);
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// plan_set_acceleration_manager_enabled(acceleration_manager_was_enabled);
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}
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