Scara Arm forward kinematic equation simulator

Source code :

App made using processing version 3 for windows.

float l1 = 12;  //length of l1
float l2 = 9.7; //length of l2

float l1_scaled = 0;
float l2_scaled = 0;

float l_total;

int width = 650;
int height = 650;

int centerX = width/2;
int centerY = height/2;

int circle_diameter = (width - 75);

float angle;

void setup() {
  l_total = l1+l2;
  l1_scaled = (circle_diameter/2)*(l1/l_total);
  l2_scaled = (circle_diameter/2)*(l2/l_total);

void draw() {
  ellipse(centerX, centerY,circle_diameter,circle_diameter);
  line((width/2), 0, (width/2), height); 
  line(0, (height/2), width, (height/2));
  float s_ang, a_ang;
  float ret_vals[] = new float[2];
  float x1y1_vals[] = new float[2];
  ret_vals = mouseXY_2_unitXY();
  s_ang = calc_shoulder_ang(ret_vals[0], ret_vals[1]);
  x1y1_vals = draw_shoulder(s_ang, l1_scaled);
  a_ang = calc_arm_ang(ret_vals[0], ret_vals[1]);
  draw_arm(x1y1_vals[0], x1y1_vals[1], a_ang, l2_scaled, s_ang); 
  text("END EFFECTOR XY", 35,85);
  text("X = " + ret_vals[0], 50,100);
  text("Y = " + ret_vals[1], 50,120);
  text("S = " + s_ang + "degrees",50,(height-50) );
  text("E = " + a_ang + "degrees",50,(height-30) );

float calc_shoulder_ang (float x, float y){
  float shoulder_angle, yx_div, q_ang;
  yx_div = (float)y/x;
  q_ang = acos( (x*x + y*y + (l1_scaled*l1_scaled) - (l2_scaled*l2_scaled)) / ((2*l1_scaled)*sqrt(x*x + y*y)) );
  shoulder_angle = degrees(atan(yx_div) -q_ang);
  return shoulder_angle;

float[] draw_shoulder(float ang, float l1_scaled){
  float angle = radians(ang);
  float[] xy_vals= new float[2];
  float x,y;
  x = cos(angle) * l2_scaled;
  y = sin(angle) * l2_scaled;
  line(centerX, centerY, (centerX + x), (centerY -y) ); //-y due to x-y co-ord system
  xy_vals[0] = centerX + x  ;
  xy_vals[1] = centerY -y;
  return xy_vals;

float calc_arm_ang (float x, float y) {
  float arm_angle;
  arm_angle = degrees( acos( (x*x + y*y -(l1_scaled*l1_scaled) -(l2_scaled*l2_scaled)) / (2*l1_scaled*l2_scaled) ) );
  return arm_angle;

float draw_arm(float xpos, float ypos, float a_ang, float l, float shoulder_ang){
  float arm_angle = radians(shoulder_ang + a_ang);
  float x,y;
  x = cos(arm_angle) * l2_scaled;
  y = sin(arm_angle) * l2_scaled;
  line(xpos, ypos, (xpos +x), (ypos - y)); //-y due to x-y co-ord system
  return angle;

void draw_line(float xpos, float ypos, float ang, float l){
  float angle = radians(ang);
  float x,y;
  x = cos(angle) * 100;
  y = sin(angle) * 100;
  line(xpos, ypos, (xpos +x), (ypos - y)); //-y due to x-y co-ord system

void draw_all(int effector_x, int effector_y) {

float[] mouseXY_2_unitXY(){
  float[] coords= new float[2];
  coords[0] = mouseX - (width/2);
  coords[1] = (height/2) - mouseY;
  return coords;

Look at this diagram to get an idea of what the S and E angles are:

Forward Kinematic Equations:

Forward kinematic equations
Forward kinematic equations

Diagram and equations source :

3 thoughts on “Scara Arm forward kinematic equation simulator

  1. This is cool! If my Robotics module runs next year, I’ll have to remember to show the students this. I’ve come across processing before, but I’ve never written anything in it – I’m impressed by how short your code is.

    I’m getting strange results when x < 0. The end effector remains in the right half plane when I move the mouse to the left of the x axis. I think the problem is with the atan function on line 73:

    shoulder_angle = degrees(atan(yx_div) -q_ang);

    Does processing provide a function called "atan2"? In most languages, the list of trig functions includes this additional inverse tan function which takes x and y as separate float arguments, rather than y/x as a single float argument. This means that it can output a different angle when x and/or y is negative. The atan function gives the same answer for (-x,-y) as for (x,y), but atan2 gives you two different answers.


    1. I always thought that the left hand plane was out of bounds or something because of the way the equations work – the x and y values are squared in some places so I thought it was something to do with that. I’ve been doing some mad work arounds when using servo scara arms like if I had a negative x and y val I’d put them into the equations as positive and then try and rotate the angles to the right quadrant – literally hours wasted away thinking it was really complicated to do, D’oh! – boom stick in atan2 – took 2 seconds and it’s working perfectly. so uh…Thanks! I’ve updated this post btw so it should be working now 🙂 processing is handy it’s kinda like the arduino ide but for graphics.

  2. in
    float[] draw_shoulder(float ang, float l1_scaled){
    float angle = radians(ang);
    float[] xy_vals= new float[2];
    float x,y;

    x = cos(angle) * l2_scaled;
    y = sin(angle) * l2_scaled; …

    l2_scaled should be replaced with l1_scaled as parameter entering to function not as value from setup()

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