74 lines
2.8 KiB
C
74 lines
2.8 KiB
C
// Rotary delta kinematics stepper pulse time generation
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//
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// Copyright (C) 2019 Kevin O'Connor <kevin@koconnor.net>
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//
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// This file may be distributed under the terms of the GNU GPLv3 license.
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#include <math.h> // sqrt
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#include <stddef.h> // offsetof
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#include <stdlib.h> // malloc
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#include <string.h> // memset
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#include "compiler.h" // __visible
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#include "itersolve.h" // struct stepper_kinematics
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#include "trapq.h" // move_get_coord
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// The arm angle calculation is based on the following two formulas:
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// elbow_x**2 + elbow_y**2 = upper_arm**2
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// (effector_x - elbow_x)**2 + (effector_y - elbow_y)**2 = lower_arm**2
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// Calculate upper arm angle given xy position of effector joint
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// (relative to shoulder joint), upper arm length, and lower arm length.
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static inline double
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rotary_two_arm_calc(double dx, double dy, double upper_arm2, double lower_arm2)
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{
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// Determine constants such that: elbow_y = c1 - c2*elbow_x
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double inv_dy = 1. / dy;
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double c1 = .5 * inv_dy * (dx*dx + dy*dy + upper_arm2 - lower_arm2);
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double c2 = dx * inv_dy;
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// Calculate scaled elbow coordinates via quadratic equation.
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double scale = c2*c2 + 1.0;
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double scaled_elbow_x = c1*c2 + sqrt(scale*upper_arm2 - c1*c1);
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double scaled_elbow_y = c1*scale - c2*scaled_elbow_x;
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// Calculate angle in radians
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return atan2(scaled_elbow_y, scaled_elbow_x);
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}
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struct rotary_stepper {
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struct stepper_kinematics sk;
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double cos, sin, shoulder_radius, shoulder_height;
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double upper_arm2, lower_arm2;
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};
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static double
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rotary_stepper_calc_position(struct stepper_kinematics *sk, struct move *m
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, double move_time)
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{
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struct rotary_stepper *rs = container_of(sk, struct rotary_stepper, sk);
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struct coord c = move_get_coord(m, move_time);
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// Rotate and shift axes to an origin at shoulder joint with upper
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// arm constrained to xy plane and x aligned to shoulder platform.
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double sjz = c.y * rs->cos - c.x * rs->sin;
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double sjx = c.x * rs->cos + c.y * rs->sin - rs->shoulder_radius;
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double sjy = c.z - rs->shoulder_height;
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// Calculate angle in radians
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return rotary_two_arm_calc(sjx, sjy, rs->upper_arm2
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, rs->lower_arm2 - sjz*sjz);
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}
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struct stepper_kinematics * __visible
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rotary_delta_stepper_alloc(double shoulder_radius, double shoulder_height
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, double angle, double upper_arm, double lower_arm)
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{
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struct rotary_stepper *rs = malloc(sizeof(*rs));
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memset(rs, 0, sizeof(*rs));
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rs->cos = cos(angle);
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rs->sin = sin(angle);
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rs->shoulder_radius = shoulder_radius;
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rs->shoulder_height = shoulder_height;
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rs->upper_arm2 = upper_arm * upper_arm;
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rs->lower_arm2 = lower_arm * lower_arm;
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rs->sk.calc_position_cb = rotary_stepper_calc_position;
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rs->sk.active_flags = AF_X | AF_Y | AF_Z;
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return &rs->sk;
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}
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