I have a probem which involves an object sliding along a rail supported by a number of hangers.
I have got a fair way through this problem to the point where I have the total force and the total couple required to keep all the hangers in contact with the rail.
Thus I end up with two equations:
Ft = SUM(Fh) : Total Force = sum of the individual hanger forces
Mt = SUM(Fh x Ph) : Total Moment = sum of the cross product of the forces and the hanger positions.
I Know Ft, Mt and all the values of Ph. I want to find sensible values for Fh
This can be solved as a simple simultaneous equation for two hangers.
For 3 hangers this can be viewed as two planes and the line of intersection gives the range of possible solutions.
Choosing the point on this line closest to the origin (all forces zero point) minimises the maximum force acting on any of the hangers.
I want to do an equivalent minimisation of the maximum force for any number of hangers.
Unfortunately I seem to have reached the edge of my maths ability, can you help?