中文摘要：

基于矩阵QR分解，提出一种具有通用性的少自由度并联机构运动学建模方法，建立少自由度机构正、逆一二阶影响系数矩阵，同时得到了少自由度并联机构操作端的速度、加速度的约束方程及一二阶约束矩阵。基于虚功原理，建立少自由度机构的柔度模型，并在此基础上推导出少自由度并联机构在各维方向刚度表达式。分析3RPs机构的运动学输出的耦合性，建立其柔度模型及方向刚度模型，并验证了此机构的结构约束对运动学的影响。通过机构在移动方向刚度及转动方向刚度的球面坐标分布，直观地描述少自由度并联机构的结构约束对其刚度性能的影响。

英文摘要：

A method to build the kinematic of lower-mobility parallel mechanism is mentioned based on the matrix QR decomposition. The forward and inverse kinematic model is built based on the first and second order influence matrix. The velocity and acceleration constraint matrix are also built. Based on the principle of virtual work, the flexibility matrix and directional stiffness are built. The coupling kinematic of the 3RPS mechanism is analyzed. The directional stiffness of 3RPS is analyzed to verify the structural constraint, and the directional stiffness is visually describes by the distribution of spherical coordinates.