Universal Robots Forum

Circle move math


i’m currently trying to write a interpolate_pose for circle moves but i’m struggling with the calculation of the Center of the Circle which is defined by 3 Poses:
Start : {x0,y0,z0}
ViaP: {x1,y1,z1}
End: {x2,y2,z2}

searching the Center M = {a,b,c}

and given these 3 Points i have 3 equations of a Sphere with 4 unknowns:

which i can’t solve for a,b,c and r. What am i missing? i think it has somethink to do that all 3 Pose Points lie on the equator of the sphere points :face_with_monocle:

this helped a lot. Implementing Answer 6 got me the right Center of Circle Point :slight_smile: