Cinemática para brazo robot Delta

 // robot geometry

 //(look at pics above for explanation)

 const float e = 115.0;     // Longitud del lado del triángulo equilátero pequeño (el que se moverá).

 const float f = 457.3;     // Longitud del lado del triángulo equilátero grande  (el que estará estático).

 const float re = 232.0;    // Longitud del brazo que va unido al triángulo pequeño y a 'rf'.

 const float rf = 112.0;    // Longitud del pequeño brazo que está unido al eje del servo y a 're'.

 // trigonometric constants

 const float sqrt3 = sqrt(3.0);

 const float pi = 3.141592653;    // Pi

 const float sin120 = sqrt3/2.0;   

 const float cos120 = -0.5;        

 const float tan60 = sqrt3;

 const float sin30 = 0.5;

 const float tan30 = 1/sqrt3;

 // forward kinematics: (theta1, theta2, theta3) -> (x0, y0, z0)

 // returned status: 0=OK, -1=non-existing position

 int delta_calcForward(float theta1, float theta2, float theta3, float &x0, float &y0, float &z0) {

     float t = (f-e)*tan30/2;

     float dtr = pi/(float)180.0;

     theta1 *= dtr;

     theta2 *= dtr;

     theta3 *= dtr;

     float y1 = -(t + rf*cos(theta1));

     float z1 = -rf*sin(theta1);

     float y2 = (t + rf*cos(theta2))*sin30;

     float x2 = y2*tan60;

     float z2 = -rf*sin(theta2);

     float y3 = (t + rf*cos(theta3))*sin30;

     float x3 = -y3*tan60;

     float z3 = -rf*sin(theta3);

     float dnm = (y2-y1)*x3-(y3-y1)*x2;

     float w1 = y1*y1 + z1*z1;

     float w2 = x2*x2 + y2*y2 + z2*z2;

     float w3 = x3*x3 + y3*y3 + z3*z3;

     // x = (a1*z + b1)/dnm

     float a1 = (z2-z1)*(y3-y1)-(z3-z1)*(y2-y1);

     float b1 = -((w2-w1)*(y3-y1)-(w3-w1)*(y2-y1))/2.0;

     // y = (a2*z + b2)/dnm;

     float a2 = -(z2-z1)*x3+(z3-z1)*x2;

     float b2 = ((w2-w1)*x3 - (w3-w1)*x2)/2.0;

     // a*z^2 + b*z + c = 0

     float a = a1*a1 + a2*a2 + dnm*dnm;

     float b = 2*(a1*b1 + a2*(b2-y1*dnm) - z1*dnm*dnm);

     float c = (b2-y1*dnm)*(b2-y1*dnm) + b1*b1 + dnm*dnm*(z1*z1 - re*re);

     // discriminant

     float d = b*b - (float)4.0*a*c;

     if (d < 0) return -1; // non-existing point

     z0 = -(float)0.5*(b+sqrt(d))/a;

     x0 = (a1*z0 + b1)/dnm;

     y0 = (a2*z0 + b2)/dnm;

     return 0;

 }

 // inverse kinematics

 // helper functions, calculates angle theta1 (for YZ-pane)

 int delta_calcAngleYZ(float x0, float y0, float z0, float &theta) {

     float y1 = -0.5 * 0.57735 * f; // f/2 * tg 30

     y0 -= 0.5 * 0.57735    * e;    // shift center to edge

     // z = a + b*y

     float a = (x0*x0 + y0*y0 + z0*z0 +rf*rf - re*re - y1*y1)/(2*z0);

     float b = (y1-y0)/z0;

     // discriminant

     float d = -(a+b*y1)*(a+b*y1)+rf*(b*b*rf+rf); 

     if (d < 0) return -1; // non-existing point

     float yj = (y1 - a*b - sqrt(d))/(b*b + 1); // choosing outer point

     float zj = a + b*yj;

     theta = 180.0*atan(-zj/(y1 - yj))/pi + ((yj>y1)?180.0:0.0); // Si se cumple que yj>y1 entonces suma "180.0", de lo contrario no suma nada "0.0".

     return 0;

 }

 // inverse kinematics: (x0, y0, z0) -> (theta1, theta2, theta3)

 // returned status: 0=OK, -1=non-existing position

 int delta_calcInverse(float x0, float y0, float z0, float &theta1, float &theta2, float &theta3) {

     theta1 = theta2 = theta3 = 0;

     int status = delta_calcAngleYZ(x0, y0, z0, theta1);

     if (status == 0) status = delta_calcAngleYZ(x0*cos120 + y0*sin120, y0*cos120-x0*sin120, z0, theta2);  // rotate coords to +120 deg

     if (status == 0) status = delta_calcAngleYZ(x0*cos120 - y0*sin120, y0*cos120+x0*sin120, z0, theta3);  // rotate coords to -120 deg

     return status;

 }