Page 869 - Mechanical Engineers' Handbook (Volume 2)

860 Mechatronics
Electrical model Mechanical model

Motor inertia
Effective
i in L R rotary
+ spring
+
Arm inertia
V in
V emf Gears

–
–
Motor
Figure 50 Model of mechatronic system.

1. No friction
2. Motor rotor and arm are the only significant masses
3. Small motions
Now the constitutive relationships for the motor and gears can be written and Kirchhoff’s
voltage law can be applied to the electrical circuit. Then, free-body diagrams can be created
for each mechanical element; see Fig. 51:
• Motor relations:
Ki torque of the motor (torque constant)(input current) (89)
t in
where K is the torque constant.
t
˙
V emf K K (90)
e motor
e
where K is the electromotive force (emf) constant.
e

I motor
1
I arm
1
2

spring
⋅⋅
I motor m
2 = N
1
2
⋅⋅

in ⋅ ⋅ I a a
spring
a = 1 m
m N

a

spring = K effective a
Figure 51 Free-body diagrams.