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# How to determine the kinematic constrains?

## How to determine the kinematic constrains?

(OP)
Hello Community,
i need help in defining the connection between x3 and x1 (kinematic constraints). My Professor can´t explain it well, im confused. Is there a scheme on how to determine the kinematic constrains?

A homogeneous cylindrical pulley (mass m1, radius r1) has a rope S1, which is connected to the surrounding area via a spring (stiffness c)

The disk rolls on the horizontal
plane. The center point of the cylinder is connected to block 3 (mass m3)via a second, rigid rope S2

The rope S2 is guided via a massless deflection pulley 2
(radius r2), on whose bearing the constant frictional torque
MR acts on the bearing

In the sketch, the spring is relaxed and the
system is released from rest

Determine the speed v3 of the block 3 as a function of its deflection x3 from its rest position.

Given: m1, m3, g, r1, r2, c, MR.

### RE: How to determine the kinematic constrains?

As a starting (finishing?) point I'd start with the final static position ... everything stationary. I think the tension in S2 is the weight of m3. I'm not sure about the load in spring S1 ... for moment equilibrium it should be S2/2, but the Fx force equilibrium it should be equal to S2 (but then the moments don't balance).

Look at the dynamics of each part, in isolation ... m3 is only moving up/down, with some dynamic acceleration. The spring, S1, can only extend. The wheel, 1, translates and rotates.

What simpler problems have you solved ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

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