Apportionment 101

You have a total allowable error d_tot. You have N axes. You need to decide how much error each axis gets, and within each axis, how much each component (bearings, structure, actuator, sensor, cables) gets.

Error-type factors

The first split is by type of error: geometric, thermal, load-induced, process. Each gets a factor — typically 1.0 for geometric and load-induced (the big contributors), 0.25 for thermal and process (if they're managed well). The factors scale how much of the budget that error type gets relative to the others.

Linear vs RSS

Now: how do the four error types sum into d_tot?

• Linear sum — worst-case. Every error adds with the same sign. Conservative. d_tot = Σ f_i · d_base ⇒ d_base = d_tot / Σ f_i.
• RSS — statistical. Errors are uncorrelated random variables. d_tot² = Σ (f_i · d_base)² ⇒ d_base = d_tot / √(Σ f_i²). Much less conservative; allows larger per-component budgets.
• Averaged — the mean of the two. A pragmatic "expected case" compromise.

Within-axis split

Given a per-axis allocation, split across components using axis sensitivity factors. The same linear-vs-RSS choice applies inside each axis too.

Try it

Open the apportionment tool and change N axes, d_tot, and factors. See the three tables update live.