An Example of Kinematic Constraint Instability

Consider the model shown in Fig. 4.20 which is similar to Fig. 4.19. Here, a rod of length I with mass m and moment of inertia I is pivoted at point O at one end and slides against a moving surface at another. Initially, the rod makes an angle 0q with 

Considering the degrees of freedom, y and 6 (with respect to the point O as shown in Fig. 4.20), the equations of motion for this system can be written as (assuming bilateral contact between the end of the rod and the conveyor) 

Py is the vertical reaction force of the vertical linear spring and damper coimected to the point O and is calculated as 

T is the torque reaction of the rotational spring and damper at point O and it is calculated as 

The bilateral contact between the rod and the moving surface, introduces the constraint  

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