Introduction to Robotics, H. Harry Asada
1
Chapter 2
Actuators and Drive Systems
Actuators are one of the key components contained in a robotic system. A robot has many
degrees of freedom, each of which is a servoed joint generating desired motion. We begin with
basic actuator characteristics and drive amplifiers to understand behavior of servoed joints.
Most of today’s robotic systems are powered by electric servomotors. Therefore, we
focus on electromechanical actuators.
2.1 DC Motors
Figure 21 illustrates the construction of a DC servomotor, consisting of a stator, a rotor,
and a commutation mechanism. The stator consists of permanent magnets, creating a magnetic
field in the air gap between the rotor and the stator. The rotor has several windings arranged
symmetrically around the motor shaft. An electric current applied to the motor is delivered to
individual windings through the brushcommutation mechanism, as shown in the figure. As the
rotor rotates the polarity of the current flowing to the individual windings is altered. This allows
the rotor to rotate continually.
Figure 2.1.1
Construction of DC motor
Let
m
τ
be the torque created at the air gap, and
i
the current flowing to the rotor
windings. The torque is in general proportional to the current, and is given by
i
K
t
m
⋅
=
(
2
.
1
.
1
)
where the proportionality constant
is called the
torque constant
,
one of the key parameters
describing the characteristics of a DC motor. The torque constant is determined by the strength of
the magnetic field, the number of turns of the windings, the effective area of the air gap, the
radius of the rotor, and other parameters associated with materials properties.
t
K
In an attempt to derive other characteristics of a DC motor, let us first consider an
idealized energy transducer having no power loss in converting electric power into mechanical
Department of Mechanical Engineering
Massachusetts Institute of Technology
Angle
θ
Stator Winding
Bearings
Shaft
Brush
i
a
N
Commutator
S
Inertia
Load
Figure by MIT OCW.
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2
power. Let
E
be the voltage applied to the idealized transducer. The electric power is then given
by
, which must be equivalent to the mechanical power:
i
E
⋅
m
m
in
i
E
P
ω
τ
⋅
=
⋅
=
(
2
.
1
.
2
)
where
m
is the angular velocity of the motor rotor. Substituting eq.(1) into eq.(2) and dividing
both sides by
i
yield the second fundamental relationship of a DC motor:
m
t
K
E
=
(
2
.
1
.
3
)
The above expression dictates that the voltage across the idealized power transducer is
proportional to the angular velocity and that the proportionality constant is the same as the torque
constant given by eq.(1). This voltage
E
is called the back emf (electromotive force) generated at
the air gap, and the proportionality constant is often called the back emf constant.
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 Fall '05
 HarryAsada

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