Determining the number of degrees of freedom

[Amaelle]

Good day
I have issue to understand why in the second case we still have 1 degree of freedom, because according to my understanding ( the circles for me represent the trajectory of the rotation of the two segment, and according to it the two segments can't rotate simultaneously. but according to the book , in the second case the vertical displacement of point B is a allowed?
any hints would be highly appreciated thanks!

 

[BvU]

Are the sections allowed to bend and stretch ?

 

[Amaelle]

Are the sections allowed to bend and stretch ?

I thought it was a mechanical engineering section, so any question regarding this topics should be accepted

 

[BvU]

The context eludes me. Both pictures have h = v - n = (2+2+2) - (3+3) = 0 as 'explaining' text !?
I also don't follow what the circles represent.

I thought it was a mechanical engineering section

If you don't know (and don't give more context), who does ?

so any question regarding this topics should be accepted

Ah, you mean the ME forum ? Yes, all and any question is Ok. But you can influence your chances to get sensible assistance by helping the helpers

 

[Amaelle]

the circles represent rotational motion of the two segments around the hinges on points A and C, I have uploaded another picture to illustrate the point

 

[Amaelle]

n represents the degree of freedom , v the number of constraint, and h is the degree of static determinacy,

 

[BvU]

the circles represent rotational motion

Ah, but in this second picture the axis of rotation is at the support points -- much more sensible

n represents the degree of freedom , v the number of constraint, and h is the degree of static determinacy

Confusion again. Probably n represents the number of degrees of freedom ? Of what ? Where does the 3+3 come from ?
v is the number of constraints. Fine. Of what ? Of points A, B and C ? Where does the 2+2+2 come from ?
I can guess, but you might clarify things first ...

I suppose a circle means a hinge -- what about the cups at A and C ?

 

[Amaelle]

Thanks Bvu for your prompt reply and sorry for all that troubles!
let me better explain: n explain the degree of freedoms, we have two bodies assembled via an internal hinge, so degree of freedom of the system is 3+3 =6
v is the number of constraints : we have two hinges and one internal hinges so the number of constraints is 2+2+2=6

As you might know the hinges only prevent horizontal and vertical displacement not rotation and the the rotation shown on the pic are the rotations around the hinges A and C,
Thanks!

 

[BvU]

I suppose a circle means a hinge -- what about the cups at A and C ?

 

[Amaelle]

the cups means the possible sens of rotation

 

[BvU]

How do you deduct a possible sense of rotation ? Both cups at A

and C

look the same to me

this being the one at C

( Maybe I gave them a wrong name ? half-circles ? )In both figures in post #1 they use the same n (3+3) and conclude the same h (0) in the captions.

Is there more to this than we assume so far ? Would the left figure upside down also conclude 'no rigid body motions' ?

In that case, where does the transition take place from 'no rigid body motions' to 'vertical displacement of point B is allowed!' ? only when ab and bc are prefectly aligned ? or in a region around that ? What can cause such a discontinuity ?