Page 222 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 7.1 Generalized Coordinates 209

For the potential energy, the reference can be chosen at the level of the
support point:

U = -m i(/i cos 6) - rri2{l\ cos 6^ + I2 cos O2)
The potential energy is then seen to be a function only of the generalized
coordinates:
U =U{q„q^, .. .) (7.1-3)
Example 7.1-1
Consider the plane mechanism shown in Fig. 7.1-3, where the members are assumed
to be rigid. Describe all possible motions in terms of generalized coordinates.

Solution: As shown in Fig. 7.1-3, the displacements can be obtained by the superposition
of two displacements and Qj. Because and ^2 independent, they are
generalized coordinates, and the system has 2 DOF.

Example 7.1-2
The plane frame shown in Fig. 7.1-4 has flexible members. Determine a set of
generalized coordinates of the system. Assume that the corners remain at 90°.

7i,

' 74 ^--------
n
75

T7T ~7~y

Figure 7.1-4.