pantograph binding reactions

[s.melotto]

Hello everyone, I am doing a study of the binding reactions of a pantograph and I have some doubts about the trend of the "rb" reaction as an attached scheme. I created an excel file to calculate it in the various positions, both of opening the pantograph and of position of the load on the platform. I don't understand how to load all the weight to right the reaction is negative . I also attach excel files to understand if in the various formulas there is some error.
Thank you.

 

[meccanicamg]

Have you tried to look at the various posts about it?
rb will always be mono verse until you stand on the platform. If you go out to the left... rebound and change your mark.

 

[meccanicamg]

If you want to have global static data, draw structure with ftool or lesm and get global reactions.
rb is simply calculated considering all rigid pantograph as a cube, two ground reactions and strength on the platform ranging from dx to sx. Everything like a monolithic beam.

 

[Marco F inox]

Maybe you meant "low reaction load."
in any static position you put the platform, you have a tied to the ground to the left, which subdues a rigid arm that reaches the p2.
the other rigid arm on the ground in b that reaches point p1, is a lightning lever in c.
It is obvious that a certain load, if too much to left, raises b.
and that is why in the platforms, it is always necessary to bind on the ground both the point to that point b, the latter with a reversed guide, which embraces the wheels.

 

[s.melotto]

Maybe you meant "low reaction load."
in any static position you put the platform, you have a tied to the ground to the left, which subdues a rigid arm that reaches the p2.
the other rigid arm on the ground in b that reaches point p1, is a lightning lever in c.
It is obvious that a certain load, if too much to left, raises b.
and that is why in the platforms, it is always necessary to bind on the ground both the point to that point b, the latter with a reversed guide, which embraces the wheels.

thanks for the answer, it is a semotive pantograph, I wanted to understand in what position the load tends to change of sign "rb" by pressing the bearing of the cart towards the high part of the guide. all because I had a problem with a cart that deformed the guide where it flows "rb" at the top, so it means that "rb" pushed upwards.
Thank you.

 

[davidex]

see formula to calculate b should be =m23*cos(pi()/2-r23)
the other geometric formulas are ok, but you could check them with cad too.

I don't know if I just interpret your scheme (p+rb = rav + f*sin(β+γ)), but it seems to me that there is no real static balance of forces in the excel, so there's definitely something else that doesn't...

 

[Marco F inox]

considering balanced and symmetrical the structure and brought to a certain opening, it is necessary to do the equality between the two moments (force x arm), of the weight force for his arm, (variable in the shift to the left), given from his distance from the vertical passing by c, and from the rb force (variable both in intensity and direction) for his arm that is always the same, (its distance from the vertical passing by c not varied).
from this balance it is seen that with the concentrated load in p2, on the point b will act the same strength, down( the reaction is given by the floor), as the arms are equal.
shifting the load to the left, it decreases its arm and therefore its moment, also decreases the force acting in b, as its arm remained equal.
when the load is half, ie on the perpendicular passing by c,. his moment is worth zero,
the reaction in b.
in this condition of balance, the cart b does not exert any force, neither upward, nor downward.
moving the load still to the left, the two moments do not contrast anymore, but go in the same direction rotational, so you have the contact of the b wheels with the upper part of the rail.
the load in point p1, will generate the same strength of the wheels b upwards.
this calculation is independent from the opening of the platform, it is valid at any time and excludes a priori any consideration on the relative corners.