What Calculations Are Needed to Achieve Equilibrium in These Statics Problems?

[Aaron]

Hi, I have a couple of questions from a statics assignment that I'm in need of help on. Here's what I have so far:

http://216.170.11.226/pub/6131.jpg

Two rods are connected by a slider block as shown. Neglecting the effect of friction, determine the couple Ma required to hold the system in equilibrium.

And this is what I believe the forces are:

http://216.170.11.226/pub/6131-2.jpg

It would seem to me that the external forces are irrelevant to this problem, but I'm guessing not. What I came up with for this problem is:

Sum of moments about B=0 => -25+Nd*271.89=0 => Nd=0.0919
Sum of moments about A=0 => -.0919*150+Ma=0 => Ma=13.79 N*m

I know the answer is Ma=15.22 N*m. I'm guessing that I also need to consider external forces or something.


The next problem is

http://216.170.11.226/pub/6129.jpg

The double toggle mechanism shown is used in a punching machine. Knowing that the links AB and BC are each of length 150 mm, determine the couple M required to hold the system in equilibrium when Phi=20 (degrees).

Once again, my analysis of the problem is:

http://216.170.11.226/pub/6129-2.jpg

Obvious things are:
Dy+Ey+Ay+800=0
Dx+Ex+Ax=0

sum of moments about B of AB=0 => M+By*150*cos(30)+Bx*150*sin(30)=0

Since AB is a two-force body, Bx=B*cos(30), By=B*sin(30) and A=-B.

B'x=-Bx
B'y=-By
Cx=C*cos(30)
Cy=C*sin(30)
sum of moments about C of BC=0 => -B'x*150*sin(30)+By*150*cos(30)=0
sum of moments about B of BC=0 => -Cy*150*cos(30)+Cx*150*sin(30)=0

And so on and so forth. If I continue in this manner I figure I'll end up with something around 24 equations, there has got to be a simplier method. Any idea what that might be?

Any hints or help would greatly be appreciated.

Thanks
-Aaron

 

[Aaron]

Ok, the first problem is easy, I just forgot to get a perpendicular distance to the force, so it works fine now.

As for the second problem, I was thinking about just balancing the Fx, Fy, Ma, Md, and Me, but that doesn't seem to work either. Any suggestions would be appreciated.

 

[NateTG]

Is $$N_D$$ supposed to be an applied force in that drawing?

Can you list the terms you have for the net forces, and net torques, and which point they are about?

 

[Aaron]

Sorry, $$N_D$$ was an internal force from the collar. Thanks anyway, but I managed to figure this one out.