ME 4590 Dynamics of Machinery
Principle of Virtual Work
Principle of Virtual Work
If a mechanical system whose configuration is defined by a set of independent
generalized coordinates qk (k  1,..., n) is in static equilibrium, then the
generalized force associated with each of the qk (k  1,..., n) must be zero. That is,
Fqk  0
(k  1,
, n) .
Recall that if a system has "n" degrees of freedom, then "n" independent
generalized coordinates are required to completely define its configuration. Hence,
for an "n" degree of freedom system in static equilibrium, we can write "n"
independent equilibrium equations.
Example
For the simple pendulum shown, we can calculate
the torque M required to hold the bar at some angle
 by using the principle of virtual work as
follows:
M
v  
 

F   W  G    M  B   0
  
 


 mg j   C i  S j    Mk    k 
L
2


or
M  mg L2 S
Note: The contribution of the weight force could also have been calculated using
the potential energy function for weight. That is,
 F W  
 
L
L

 mg C   mg S .
 
2
2

Kamman – ME4590: page 1/1