I've been busy for a few days, so have not had a chance to reply.

Regarding the cutting forces, I'm not sure if tangent was the correct term (it's been a few years since I've had to use such terms!), but imagine you have a bit round bar mounted on the 4th axis, and you want to machine a flat across the top of the bar using a vertical cutter. At the point where the cutter is directly over the centreline and at maximum cutting depth, is where you're going to get maximum torque working against the 4th axis.

You can calculate things to a reasonable accuracy, if you know the angles involved, and how the cutter torque will be getting applied to the workpiece/4th axis.


Regarding brakes, they're generally used for where you need to lock an axis in use (i.e. where you need to move to a set position and lock solidly), or when powered off (i.e. to stop a vertical axis dropping when the system is powered off).
You could potentially use one on a 4th axis, but you would have to generate code that continually unlocks, moves, then locks the motor in between machining. Otherwise you still need sufficient torque from the motor to hold things steady against the cutting forces.


Now Steppers and servos.
What you have to bear in mind, is a stepper is essentially a form of brushless servo motor. Using a suitable encoder and servo driver, you can run a stepper motor as a servo motor.
The big draw back though, is due to the internal design of a stepper motor, you get magnetic detents as the slotted rotor aligns with the permanent magnets, which affects performance compared with a properly designed brushless servo motor, which will have hardly noticeable detents.

Steppers don't lock solid. There is an air gap between the rotor and coil, so you're relying on a magnetic field to hold the rotor, which means there is a bit 'spring' to even the full step position.
As Hanermo has mentioned, microstepping reduces holding torque. The worst point is at the halfstep point, as you have two coils 50% energised, which theoretically puts the rotor exactly between the motors natural detent point, meaning the motor itself is trying to push/pull the rotor to the nearest detent point.

Where servos have the advantage, is the lack of magnetic detent improves performance, and you have an encoder. Servos are rarely perfectly held on position. They will normally always be dithering at least an encoder count or two, especially if they're subjected to any kind of varying load. Under normal use, even with perfect tuning, they will always be out a few counts, however compared with a stepper motor, servos should produce near continuous torque at any point in their rotation, and produce near constant torque over their entire rated speed range.

However, you don't really need to know any of this. If you design the system around rated torques (in the case of steppers, look at the torque/speed graph, to get the torque at the maximum speed you think you'll be machining), then you shouldn't have any problems.

Don't rely on servo peak torques, as they're more to allow for rapid acceleration. If you exceed the rated torque, depending on the motor/driver, the driver will shut down after a set time (my drivers calculate how much energy has been put in the motor, and use an algorithm to calculate if the motor has overheated), the motor may have a thermal switch to shut things down, or worst case scenario with no overheat detection system, you end up with a very hot paperweight.