ME 5550 Intermediate Dynamics Principle of Virtual Work 

```ME 5550 Intermediate Dynamics
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 &quot;n&quot; degrees of freedom, then &quot;n&quot; independent generalized
coordinates are required to completely define its configuration. Hence, for an &quot;n&quot; degree of
freedom system in static equilibrium, we can write &quot;n&quot; 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:
F   F W   F M  0


 R vG 
 RB 
 W 
  M 

 
 




L


  mg j  cos( ) i  sin ( ) j     Mk    k 
2


or
L
M  mg sin ( )
2
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
cos(

)


mg
sin( ) .


 
2
2

Kamman – ME 5550 – page: 1/1
```