基于机械系统动力学方程的增广法建立考虑球面副间隙的4-SPS/CU并联机构动力学模型。为了简化该并联机构的动力学模型，通过质量矩的方法视驱动支链为一个整体。根据含间隙球面副元素的接触方式建立该间隙运动副的运动学模型，求出含间隙球面副元素之间的接触变形量与相对接触速度。考虑到接触体之间接触刚度与机械系统动力学模型之间的耦合性，以非线性刚度系数代替Flores接触模型中的常数刚度系数而提出一种改进的接触力模型，并基于该接触力模型利用接触变形量与相对法向接触速度建立间隙运动副元素之间的法向接触力模型，为了保证数值运算的稳定性，采用具有动态修正系数的Coulomb摩擦模型，建立接触体之间的切向接触力模型。进一步把间隙运动副元素之间的接触力转换到该间隙运动副所连接的驱动支链和上平台的质心上，并把该接触力集成到4-SPS/CU并联机构动力学模型的广义力中，从而成功引入了关节间隙效应，采用Baumgarte稳定约束法避免了积分过程中的约束违约问题。通过数值分析预测球面副间隙对4-SPS/CU并联机构动力学性能的影响。

Dynamics model of 4-SPS/CU parallel mechanism with spherical joint clearance is formulated based on augmented method in the equations of motion for mechanism systems. The driven chain in this parallel mechanism is regarded as a unit via the method of mass moment in order to simplify the dynamics modeling. The kinematic model of spherical joint with clearance is established on the ground of contact type between elements in the clearance joint. The contact deformation and relative contact velocity are presented on account of the above research. A new contact force model is presented, which replaces the constant stiffness coefficient of the Flores contact model with nonlinear stiffness coefficient considering to the coupling between the contact stiffness of contact elements and dynamics model of mechanism system. The normal contact force between the contact elements is evaluated based on the new contact model, and the tangential contact force is derived according to the Coulomb friction model with dynamic correction coefficient to ensure the stability of numerical computation. The contact forces between the socket and ball are converted to the mass center of driven chain and upper platform interconnected by this clearance joint, and the converted contact force is integrated to the generalized force in equations of motion of 4-SPS/CU parallel mechanism to introduce the effect of spherical joint clearance. The Baumgarte stabilization method is used for solving dynamics equations in order to stabilize the constraints violation. The influence of spherical joint with clearance on the dynamics performance of this parallel mechanism is predicted by numerical analysis