Page 45 - Handbook of Biomechatronics

Actuator Technologies 39

(e.g., only when not moving, or at one-half maximum speed/torque). There
is, however, an easily accessible metric that incorporates the ability of an
actuator to achieve any combination of torque, position, speed, and accel-
eration, in a compact normalizable metric. That metric is the speed ratio—the
reciprocal of the mechanical time constant (a metric that is often reported in
actuator specification sheets and is equal to the amount of time for an
unloaded motor to rise to 63.2% of its final velocity after application of a
command voltage). The speed ratio can be expressed in various forms, as
shown in the equation below. Although not well understood and rarely
used, the speed ratio incorporates each of those four parameters
(Sensinger, 2010a), and can be used to streamline the design of
biomechatronic actuators.

K 2 K 2 1
SR ¼ t ¼ m ¼
J m R J m τ m
where K t is the torque constant, K m is the motor constant, J m is the inertia of
the motor, R is the resistance of the motor windings, and τ m is the mechan-
ical time constant.

2.2.5 Efficiency
Efficiency is another useful metric. Efficiency is defined as the amount of
output power (typically, mechanical) divided by the amount of input power
(typically, electrical). Peak efficiency for electrical motors does not occur in
the same region as peak mechanical power—it occurs at higher speeds
(Alciatore and Histand, 2003). Although efficiency is a useful metric, its
use as a biomechatronic design metric is often eclipsed by total weight.

2.2.6 Total Weight
The total weight of biomechatronic actuators is often an afterthought, but it
is actually a powerful metric, if used properly (Sensinger, 2010a). Imagine
that you are trying to compare a series of actuators for a given application,
and that you have the ability to generate envelope visualizations or access to
torque and speed densities. The mechanical properties of the task can be used
to calculate the weight of the actuator needed to perform the task (e.g., if the
task requires 10Nm of torque, and a particular actuator design has a torque
density of 10Nm/kg, then your actuator weight is 1kg). The electrical
requirements of the task can also be calculated. This energy draw can be
multiplied by the energy density of the supply (e.g., a battery), and added