Hi,
Thank you all for your contribution. I apologise for not giving enough information here so let me correct that by sharing this video of the mechanism in motion.
Secondly, Timo you are absolutely correct about the pros and cons you listed. The cost is lower than a harmonic drive, the torque is greater due to the huge ratio. In this example over the range of travel, the average ratio of the stepper motor rotation to the b-axis is 85.2 and at a speed of 500RPM it takes 2.55s to do a full 90-degree sweep which is fine for me. If I need it to be faster I can change the ration by changes the ballscrew lead.
The thing I wanted to mention here is that the relationship between the ballscrew travel and the angle of the b-axis can be defined by a function rather than a mapping in order to get an exact and accurate relationship. It is similar to the relationship between the travel of a piston and the angle of the crankshaft, as explained in the video below.
Is there anyway I can insert this function into LinuxCNC?