  Multi-speed transmissions can enhance the performance and reduce the overall
cost of an electric vehicle, but they also introduce a challenge: avoiding
gearshift jerk, which may sometimes prove to be impossible in the presence of
motor and clutch saturation. In this article, we introduce three theorems that
explicitly define the fundamental limitations to no-jerk gearshifts resulting
from motor or actuator saturation. We compare gearshifts that consist of
transferring transmission torque from one friction clutch to another, to the
case in which one of the clutches is a one-way clutch. We show that systems
with a one-way clutch are more prone to motor saturation, causing gearshift
jerk to be more often inevitable. We also study the influence of planetary
gearsets on the gearshift dynamical trajectories, and expose the impact on the
no-jerk limitations. This work offers tools to compare transmission
architectures during the conceptual design phase of a new electric vehicle.
