空间三簧系统的静力逆分析初探

The Initial Investigation of Reverse Force Analysis of a Spatial Three-Spring System

对空间三簧系统进行了封闭解型静力逆分析。该系统是由三根弹簧组成，每根弹簧的一端与地基铰接，另一端铰接在同一点上。一已知力下作用于公共铰接点上，目的是求它可能的平衡位置。将方程组进行三角化，解此方程组，剔除增根后，得到２２组满足初始约束方程的真根，也就是说，空间三簧系统的静平衡位置，多个数例判明，其最大数为２２．但一般实际构形数远小于此，这个结果为进一步寻求无增根的解析解指明了方向。

A closed-form reverse force analysis is performed on a spatial three-spring sys-tem. The system consists of three springs,they are grounded to ball joints at one end and at-tached to a common one at the other.Aknown force is exerted to the common ball joint ofthe system,The goal is to find out the possible static equilibrium positions. The system of e-quations are triangulated and solved.After discarding the extraneous roots,22 sets of rootswhich satisfy the initial constraint equations are obtained,that is to say,the largest numberof possible static equilibrium positions is 22.But the number of practical configurations isgenerally less than it.This result may be helpful in finding out the closed form solutionwithout extraneous roots.