Page 867 - Mechanical Engineers' Handbook (Volume 2)

858 Mechatronics

Gauge
R 1
R 2
V excitation i 1 i 2
+ –
A V AB B
i 1 i 2
R 3
R 4 = potentiometer
Figure 48 Strain gauge circuit.

the change in voltage will be small and (2) the voltage will be centered about a larger
unchanged voltage.
For these reasons a Wheatstone bridge is used. It is shown in the analysis below that
the change in voltage (V ) resulting from the change in the gauge is centered about 0 V
AB
and can then be amplified using a differential amplifier (described earlier in this chapter).
• used to measure small changes in resistance (Fig. 48).
Turn potentiometer until
V V (74)
A B
Kirchhoff’s voltage law gives

V iR iR 0 (75)
AB 12 21
V iR iR 0 (76)
AB 13 24
and
V iR iR 0 (77)
ex 12 13
V ex i (R R ) 0 (78)
1
3
2
where
V
i ex (79)
1
R R 3
2
and
iR iR 0 (80)
V ex 21 24
V ex i (R R ) 0 (81)
2
1
4
where
i V ex (82)
2
R R 4
1
Substituting (79) and (82) into (75) yields
V V ex (R ) V ex

1
AB
R R 3 2 R R 4 R 0 (83)
2
1
Substituting (79) and (82) into (76) gives