[joeavaerage]

Hi,
OK, I would guess your estimate of the weight of the X and Y axis combo of 300kg is about right. That in turn suggests that your servo could hold it aloft without reduction. That would leave little or no torque, without
dipping into the overload capacity, for accelerating the load. That in turn suggests you need some reduction, but I would suggest 2:1 would be fine. That would mean that 2.4Nm is to accommodate the weight of the axis
and another 2.4Nm to accelerate the axis. You may think that does not sound adequate but I can assure you it is, and can show you the calculations that govern the acceleration.

As you say you need a belt drive in order to make everything fit, so a belt reduction of 2:1 or thereabouts would be perfect.

I use a belt drive on my fifth axis platter with a 750W Delta B2 servo of 2.4Nm (rated). The gear reducer is 6.75:1 so in truth I'm really only using a small fraction of the servos available torque mostly whereas you will be using
the lions share of the servos torque continuously. My belt is only 15mm wide and is perfectly adequate. In your situation I would think that 20mm or 25mm width would be appropriate as you can expect that continuous load.
Wider is not required.

What you don't quite seem to grasp is that a 5mm pitch ballscrew offers a great GREAT deal of force multiplication and that only a modest servo will in fact cause the knee assembly to move very comfortably indeed. Don't sweat the
belt, as I have proven even a 15mm belt is more than sufficient to transit 1 hp (750W).

One thing you do need to consider is the diameter of the pulley. It is very tempting to reduce the size of the servo pulley, but there is a distinct limit. The belt is likely to have a tooth pitch of 5mm, or maybe 8mm in the wider
belt sizes. Thus with a small pulley very few teeth are engaged, increasing the strain on each tooth with consequent accelerated wear. As you can see from my pic the pulleys I chose are 47mm diameter and therefore there are
15 teeth engaged (5mm pitch). This I have found to be perfectly adequate but for continuous service at moderate loads I would not go lower, but would in fact prefer more engagement.

I would suggest with an 8mm pitch belt that the min diameter of the servo pulley be 76mm or thereabouts. If you adopt a 2:1 reduction then the ballscrew pulley will be 152mm or thereabouts.

If you want to do the acceleration calculation I need the diameter, pitch and length of the ballscrew, your best estimate of the mass of the knee assembly, and the rotational inertia of servo from the spec sheet.
What may surprise you is that the acceleration is limited NOT by the mass of the knee assembly, but rather the rotational inertia of the ballscrew. My guess is that you'll find that counter-intuitive but is none-the-less
correct.

As an example my machine has a servo very similar to yours. It is direct coupled to a 32mm diameter 5mm pitch ballcsrew 750mm long. The assumed axis mass is 150kg. My servo will accelerate the axis
at 2.7m/s² or 0.27g using rated torque only. The momentum is 80% in the ballscrew, 12.5% in the servo and only 7.5% the linear accelerating mass. Yes that is correct, despite the axis weighing 150kg
the ballscrew has ten times the momentum!!!

I have done this same calculation for many others on the forum, and that basic idea that the ballscrew either dominates or at least is a large contributor to the total momentum occurs again and again, to the surprise of many.

Craig