@Nakcam thank you for clearification.
Robot kinematics is based on a chain of the actuators: axes with position and orientation and arms between them. The endpoint is just an additional arm without axis. So you can add axes at the beginning and end, but inverse kinematics must be able to calculate it. Your rotating base is included in the 4 axis parallel robot type. Your linear axis at the beginning is something additional. The robot type sometimes has an additional actuator at the endpoint, for rotation of the end plate or for a gripper.
I proceed tomorrow to develop, because I feel that I have understood it now. I will develop with the blue line being curved optionally. (not a straight line between the three hinges of the blue line).