# Equilibrium of rigid bodies

I wanted to evaluate the safety of a walking aid device (walker). For example, if the way it is constructed and whenever I handle it, there are no risk of rotation, around its center of mass, turning over, i.e imbalance/instability.

For example, a walker with 4 wheels. A person performs around 20% of its body weight for holding the handles of the walker. When the person pushes the walker, will it be a possibility for the walker to turn over, is it unstable?

So, there is a theoretically way to calculate that? And virtually? Can I use ANSYS to check that?

Thanks!

• This is a very complex question. Many particular situations can be calculated. That's the problem. There are many ways a person can fall. There is no such thing as "no risk" so abandon that possibility altogether. – Inquisitive Aug 7 '16 at 23:01
• I think what you're looking for is static load analysis - the sum of the vector weight of the walker applied at center of mass combined with the vector of input force applied to the handles. I believe you're looking for the equivalent resulting vector to fall within the footprint of the walker. But, if the walker has four wheels, then how could you flip it over by pushing it? Wouldn't it just roll forward? – Chuck Aug 8 '16 at 12:45
• @Chuck yes I believe that's it. If the forces applied are equal then yes, the walker will just roll forward if that happens. But a person with some disabilities could apply a greater force in only one handle, then the walker could flip it over. So, by the static load analysis is there a way to know the limit of the force applied at each handle so the walker will not rotate (total torque equals zero)? – user3717679 Aug 8 '16 at 13:41
• @user3717679 - Yes, instead of setting up the equations with a known input force and trying to calculate the output torque/force, you need to start with a known output (zero) and solve for the input. This will be difficult, though, because the input is a vector - a force with a direction. It's still not clear to me what you mean by flip - I imagine a front over back motion, causing the person to pitch forward/backward, but again, I would think the wheels would prevent that in basically all cases. Do you mean roll (side-side)? Can you provide a diagram? – Chuck Aug 8 '16 at 14:00
• @Chuck here is a representation of the device. It is only the base but you can see where the forces are applied (red arrows). So can we assure the device has static equilibrium? link of the diagram – user3717679 Aug 10 '16 at 11:55

Your question is stability. Will the design turn over? You don't need any software for this, not even algebra. Only a ruler (ok, you could do this in CAD). What you need to do, is make a Free Body Diagram (FBD).

The FBD has:

• a center of gravity,
• several pivot points,
• a human messing with your design.

The center of gravity is where the weight of your design applies (red). The pivot points is the point around which your design would turn over, I think these would be the wheels of your design (pawns). The human is the force trying to turn over your design (blue). The blue and red force cross at a certain point. That's where you can add them up. If you draw a triangle to the pivots from that point, and the resulting force stays within the triangle, it's stable.

Add up forces by putting them head-to-tail, starting from the crossing point. As you can see, here it's just unstable. But that's enough.

Now to make this work for you, you have to draw both the dimensions and forces scale. It doesn't matter how big the forces are in relation to the dimensions, just draw them in a practical size.

You can do this for slightly more complicated designs too! Here is an example of mine: a lifting crane with several weights, loads, working under an angle, and fully parametric. 