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Optimize delta kinematics

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Co-Authored-By: ejtagle <ejtagle@hotmail.com>
This commit is contained in:
Scott Lahteine 2018-07-04 22:28:34 -05:00
parent 1367df2875
commit 2992112da0
2 changed files with 21 additions and 21 deletions
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34
Marlin/src/module/delta.cpp
View File

@ -155,38 +155,38 @@ float delta_safe_distance_from_top() {
*
* The result is stored in the cartes[] array.
*/
void forward_kinematics_DELTA(float z1, float z2, float z3) {
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
float p12[3] = { delta_tower[B_AXIS][X_AXIS] - delta_tower[A_AXIS][X_AXIS], delta_tower[B_AXIS][Y_AXIS] - delta_tower[A_AXIS][Y_AXIS], z2 - z1 };
const float p12[3] = { delta_tower[B_AXIS][X_AXIS] - delta_tower[A_AXIS][X_AXIS], delta_tower[B_AXIS][Y_AXIS] - delta_tower[A_AXIS][Y_AXIS], z2 - z1 };
// Get the Magnitude of vector.
float d = SQRT( sq(p12[0]) + sq(p12[1]) + sq(p12[2]) );
// Get the reciprocal of Magnitude of vector.
const float d2 = sq(p12[0]) + sq(p12[1]) + sq(p12[2]), inv_d = RSQRT(d2);
// Create unit vector by dividing by magnitude.
float ex[3] = { p12[0] / d, p12[1] / d, p12[2] / d };
// Create unit vector by multiplying by the inverse of the magnitude.
const float 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.
float p13[3] = { delta_tower[C_AXIS][X_AXIS] - delta_tower[A_AXIS][X_AXIS], delta_tower[C_AXIS][Y_AXIS] - delta_tower[A_AXIS][Y_AXIS], z3 - z1 };
const float p13[3] = { delta_tower[C_AXIS][X_AXIS] - delta_tower[A_AXIS][X_AXIS], delta_tower[C_AXIS][Y_AXIS] - delta_tower[A_AXIS][Y_AXIS], z3 - z1 };
// Use the dot product to find the component of this vector on the X axis.
float i = ex[0] * p13[0] + ex[1] * p13[1] + ex[2] * p13[2];
const float 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.
float iex[3] = { ex[0] * i, ex[1] * i, ex[2] * i };
const float 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 of Y component
float j = SQRT( sq(ey[0]) + sq(ey[1]) + sq(ey[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] /= j; ey[1] /= j; ey[2] /= j;
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);
float ez[3] = {
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]
@ -194,16 +194,16 @@ void forward_kinematics_DELTA(float z1, float z2, float z3) {
// 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
float Xnew = (delta_diagonal_rod_2_tower[A_AXIS] - delta_diagonal_rod_2_tower[B_AXIS] + sq(d)) / (d * 2),
Ynew = ((delta_diagonal_rod_2_tower[A_AXIS] - delta_diagonal_rod_2_tower[C_AXIS] + HYPOT2(i, j)) / 2 - i * Xnew) / j,
Znew = SQRT(delta_diagonal_rod_2_tower[A_AXIS] - HYPOT2(Xnew, Ynew));
const float Xnew = (delta_diagonal_rod_2_tower[A_AXIS] - delta_diagonal_rod_2_tower[B_AXIS] + d2) * inv_d * 0.5,
Ynew = ((delta_diagonal_rod_2_tower[A_AXIS] - delta_diagonal_rod_2_tower[C_AXIS] + sq(i) + j2) * 0.5 - i * Xnew) * inv_j,
Znew = SQRT(delta_diagonal_rod_2_tower[A_AXIS] - 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[X_AXIS] = delta_tower[A_AXIS][X_AXIS] + ex[0] * Xnew + ey[0] * Ynew - ez[0] * Znew;
cartes[Y_AXIS] = delta_tower[A_AXIS][Y_AXIS] + ex[1] * Xnew + ey[1] * Ynew - ez[1] * Znew;
cartes[Z_AXIS] = z1 + ex[2] * Xnew + ey[2] * Ynew - ez[2] * Znew;
cartes[Z_AXIS] = z1 + ex[2] * Xnew + ey[2] * Ynew - ez[2] * Znew;
}
#if ENABLED(SENSORLESS_HOMING)

8
Marlin/src/module/delta.h
View File

@ -65,14 +65,14 @@ void recalc_delta_settings();
*/
// Macro to obtain the Z position of an individual tower
#define DELTA_Z(V,T) V[Z_AXIS] + SQRT( \
#define DELTA_Z(V,T) V[Z_AXIS] + SQRT( \
delta_diagonal_rod_2_tower[T] - HYPOT2( \
delta_tower[T][X_AXIS] - V[X_AXIS], \
delta_tower[T][Y_AXIS] - V[Y_AXIS] \
) \
)
#define DELTA_IK(V) do { \
#define DELTA_IK(V) do { \
delta[A_AXIS] = DELTA_Z(V, A_AXIS); \
delta[B_AXIS] = DELTA_Z(V, B_AXIS); \
delta[C_AXIS] = DELTA_Z(V, C_AXIS); \
@ -111,9 +111,9 @@ float delta_safe_distance_from_top();
*
* The result is stored in the cartes[] array.
*/
void forward_kinematics_DELTA(float z1, float z2, float z3);
void forward_kinematics_DELTA(const float &z1, const float &z2, const float &z3);
FORCE_INLINE void forward_kinematics_DELTA(float point[ABC]) {
FORCE_INLINE void forward_kinematics_DELTA(const float (&point)[ABC]) {
forward_kinematics_DELTA(point[A_AXIS], point[B_AXIS], point[C_AXIS]);
}