The structure of a 3-PRS parallel mechanism, including two rotation degrees of freedoms （DOFs） and one prismatic DOF, is analyzed. The kinematic equation of a motion platform is given by a closed vector method and a simplified coordinate transfer matrix, and then the kinematic forward solution of this parallel mechanism is optimized by making use of a genetic algorithm object function, which is substituted into the kinematic equation and the length of a linked rod is solved. This approach has a small error and high precision compared with the known connecting rod, and provides a foundation for their control strategies. This method does not select the initial iteration value and does not need a complicated mathematical deduction. The results are satisfactory and the implement is easy. Thusly, it is also suitable for other similar parallel mechanisms.%根据3-PRS并联机构具有2个转动自由度和1个移动自由度的结构特点，利用封闭矢量方法和简化坐标转换矩阵，得到该机构运动平台中心的运动方程，然后运用遗传算法并结合其运动方程给出并联机构运动学位置正解适应度函数和目标函数，将计算结果代入运动方程求出杆长，其误差小、精度高，为3-PRS并联机构的控制策略奠定了基础．该解法既不需要选取迭代初值，也不需要复杂的数学推导，容易实现而且通用性强．
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