中文摘要：

3-PRRU并联机构具有2个转动和1个移动自由度,是少自由度并联机构中的一个重要分支,具有较大的应用潜力。运用几何代数对3-PRRU并联机构进行自由度分析。首先用几何代数表示了分支和动平台的运动空间;然后通过对分支运动空间求交得到动平台的运动空间,该运动空间的基给出了3-PRRU并联机构自由度的符号表达式。使用几何代数方法所得结果具有几何直观性,且不需要对机构进行约束分析,运算更为简捷。

英文摘要：

The 3-DOF parallel mechanism（PM）with one translational and two rotational（1T2R）DOFs is an important category of the lower-mobility PM.Mobility is a basic property of a mechanism.This paper analyzes the mobility of a 3-PRRU PM based on geometric algebra（GA）.Firstly,the twist space of the limb and moving platform are represented by geometric algebra.Then,the twist space of the moving platform is obtained by taking the intersection of the twist space of all the limbs.Finally,the symbolic expression of mobility of a 3-PRRU PM is given by the basis of the twist space on the moving platform.Using GA-based method,geometric intuition is the advantage of this method.Without resorting constraint equation,the calculation is more convenient and fast.