A reverse static force analysis of a special planar three-spring system

This paper studies the closed-form solution of equilibrium situations of a special planar three-spring system exerted by given static forces (a constant static force exerts on an end of the platform, and a constant couple exerts on the platform). A 54th degree polynomial in one unknown is obtained finally. So this system has, at most, 54 solutions of static equilibrium situations theoretically. By verifying numerically, there are only 16 groups of real solutions in 54 groups of solutions in the example.