The RMS torque is a thermal equivalent to be compared with a motor continuous thermal limit.

For simplicity, the above example does not include jerk.  In actuality, the acceleration and deceleration torque ramps are each subdivided into many samples, allowing a more precise RMS torque calculation for S-curved and CAM profiles.
 

Torque profile for each move segment

Inertia mismatch (IM) is the ratio of system load Inertia to motor rotor inertia

Option 1: Brake is part of the load inertia
Option 2: Brake is part of the motor inertia
Gear Motor: Brake and gearbox are part of the motor inertia

Basic Concepts

Rules of thumb for speed vs stability:

   1. Move time minimization is primary objective
         a. As a general rule, IM < 10
         b. Typically, 3 < IM < 7

   2. Stability and precision is primary objective
       a. As a general rule IM < 3
         b. IM = 1 is ideal

As the inertia mismatch decreases, the motor rotor inertia becomes a larger portion of the system load.  A lower inertia mismatch offers improved stability, but comes at a cost.  Holding the load inertia and motion profiles constant, a motor with increased rotor inertia, increases the system inertia.  Hence, for the same motion profile, additional torque and power is required to accelerate and decelerate the increased system inertia.  The increased torque and power requirements may lead to upsizing system components including the inverter, bleeder, infeed module, etc.