I have constructed a 3 DOF robot arm. I want it to follow a trajectory on a 2D plane (XY). Tha shapes I want to follow are lines, cycles and splines. I now the math behind these 3 shaped (how they are defined). I have the kinematics, the inverse kinematics the jacobian and the whole control system (with the PID controller). The system receives as inputs, Xd(position), Xd'(velocity) and Xd''(acceleration) over time.
So here is were I am stuck. How do I translate the shape to the position, velocity and acceleration that each joint needs to make so the end effector moves in the Cartesian space according to that shape?