Dynamics of a 3-DOF (degree of freedom) rotational platform was analyzed. This rotational platform, which consists of a 2-DOF spherical parallel mechanism and a rotational degree connecting in series to the platform of the 2-DOF mechanism, has only 3 rotation freedoms. System's input-and-output velocity functions were established according to rotational platform's geometry and motion characteristics, and then the velocity Jacobian metrics and energy functions were obtained. System's dynamics model was established by Lagrange method and virtual work principle, and then the drive torque was solved when given the external load, velocities and accelerations. The

examples of dynamics simulation were given. The drive torques' changing curves of the 2-DOF spherical mechanism was discussed under the situation of uniform speed and acceleration. Finally, according to the dynamics functions, a third degree's kinematics equation was obtained respecting to its torque and output angle. 

对三自由度旋转台进行了动力学分析。该旋转台只有3个方向的转动自由度, 由二自由度球面并联机构和串联在其上的旋转电机构成。根据旋转台的几何和运动特性建立了系统的输入输出速度方程, 得出了速度Jacobian矩阵和动能方程。利用拉格朗日法和虚功原理, 建立了系统的动力学模型, 解决了特定外载荷和速度、加速度条件下如何求解驱动力矩的问题。给出了动力学的仿真运算实例, 讨论了在匀速和匀加速情况下, 二自由度球面并联机构驱动力矩的变化。最后根据动力学方程, 得出了串联在二自由度球面并联机构上的第三个自由度的力矩与输出转角的运动学方程。

串并联机构, 旋转台, 动力学, 拉格朗日法, 虚功原理