I am trying to compute the optimal (a non-optimal solution would also work) size of carts that can move along guiding rails. Each cart is connected to the rails at two points. Each cart is also connected to the cart in front of it and the one behind it. It is a closed system. The carts can be connected directly as in picture (a) or there can be some arbitrary but constant size connector between them. In the first step I am just looking for a solution that works mechanically. It would also be great to know what is the best arrangement that allows the least force.
In picture (a) I can find many solutions. However, my guiding rails have to have a shape as in (c). I can change the rails a little bit but they will have to have inside angles (red) and outside angles (yellow) as depicted.
I tried experimentally to find a working solution through simulation, but is there an analytic way to compute which size of carts could move along these rails?
I don't have a kinematics background and don't know what it is that I am looking for. Any pointer towards keywords/ papers where I can start my research would be very much appreciated. So far I am stuck at "Polygon Effect".