中文摘要：

提出了一种新型的三支链六自由度并联机构3-U^rPS。以3-U^rPS上平台三个顶点之间的长度为约束条件，中间变量即移动副的位移为未知量而建立约束方程，研究了该并联机构正解的封闭解形式，得到一元八次方程。利用十自由度球面机构本身的几何特征，得出了反解的封闭解形式，然后利用反解对正解进行了数值验证，其中一个实数解与反解求得的结果相对应，证明该正反解分析过程是正确的。

英文摘要：

A 6-degree-of-freedom （6-DOF） parallel mechanism with 3 limbs 3-U^rPS was presented here. The composition joint Ur is a spatial five-bar mechanism, P is a prismatic joint and S is a spherical joint. A study of the forward position problem of the 3-U^rPS mechanism was put forward and the closedform solution was obtained, the resultant equation was an 8th order polynomial. The closed-form solution of the inverse position problem was also achieved, and then a numerical example is brought forward to verify the correctness of the forward and inverse position analysis, in all of the results one of the forward solutions is corresponding to the inverse solution. The mechanism can be applied to the force feedback device of the virtual reality system.