Page 55 - Handbook of Biomechatronics

Actuator Technologies 49

and substantially increase weight (transmissions often weigh twice as much as
the motor). In addition, they have a disproportionate effect on reflected
inertia: whereas the force is scaled up by N:1 and the speed is scaled down
2
by N:1, the inertia of the motor is scaled up by N :1. Thus, a motor with a
relatively insignificant inertia can end up having a substantial inertia if
coupled to a transmission with a 1000:1 ratio, which is not uncommon.
1
Finally, many transmissions introduce hard nonlinearities that are percep-
tible to humans and difficult to control, including static friction and backlash.
It is important to choose a transmission that achieves the desired goals while
introducing a minimum of these undesirable attributes.
As an aside, designers typically focus on the maximum force a transmis-
sion can produce. However, many transmissions have a maximum speed as
well (typically necessitated by the bearings in the design), and this limit
should not be overlooked.

3.2.1 Linear Transmissions
Linear transmissions convert the rotation of the motor to a linear output.
This linear output may either be used to produce linear motion, or coupled
to a linkage to produce a rotary motion. Linear transmissions typically have
lower output inertia than rotary counterparts with comparable specifica-
tions, and can often withstand higher loads. However, they often take up
a considerable amount of space, and they typically introduce soft nonline-
arities into the transmission ratio across the range of motion. Many
biomechatronic designs use linear transmissions, particularly in powered
prostheses and orthoses.
The simplest form of a linear transmission is a lead screw, which is com-
posed of a threaded rod and a nut (Fig. 10A). The input of the transmission
(coupled to the motor) is the threaded rod. The output of the transmission is
the nut. The nut is prevented from rotating by guiding rods or other struc-
tural components, such that when the threaded rod is rotated, the nut moves
along the threaded rod. Compared with a standard screw, a lead screw’s
tooth profile is engineered to be more efficient and withstand greater loads.
Most lead screws have noticeable static friction, and are inherently non-
backdrivable, which is often undesirable in biomechatronic applications,
but can be useful for things like powered upper limb prostheses. Ball screws

1
A hard nonlinearity has undefined derivatives. Examples include backlash and static friction. In con-
trast, soft nonlinearities have defined derivatives. Examples include quadratic viscous drag, or the sinu-
soidal effects of gravity on linkages.