Is this 5-axis machine possible with LinuxCNC?

I've designed a router for a specific job requirement for my company. 

Requirement : Engraving letters on a curved surface (Tire Mold Side Walls).

X, Z, C, B axis must work simultaniously.

I want this machine to operate on LinuxCNC but there is no kinematics available.

C and B axis are different than examples in the 5-Axis Kinematics pdf provided by Linuxcnc. 

Is this machine possible?

 

There is a XYZBC kinematics module but the example shows the B axis tilting the C axis
Is the maths any different if the B rotates around the head? I'm not sure that it is.

I just named them from my head, I am not sure if I named the axis corrently.

Thank you so much Andy!

I currently have 4 axis EspritCAM and planning to buy 5 Axis module for CAM. Re-seller provide G-code support. I think I can figure that out this way. What do you think?

I directed your question to my reseller and they anwered ''Esprit requires machine kinematics to work with.'' I will be sending them the cad files that I have for the machine and they will bring that into the program. They also said that you can active RTCP for simultanious 5-axis machining but I don't understand how it is connected to the TCP.

I think I should start simple and work my way up. I am an experienced cnc programmer and an operator but I am inexperieced when it comes to building one. I built a 4-axis router on Mach3 before but it is much simpler than what I am trying to achieve with this machine.

I am planning to follow tutorials shared in the forum and Youtube.I am open to any advice. You are very helpful, thank you.