基于方位特征集设计理论和方法,设计了一种全由转动副组成的、动平台能实现空间三平移一转动的无过约束并联机器人机构,对其进行了拓扑结构特性分析;导出了机构位置逆解方程和雅可比矩阵,通过算例和Pro/E的仿真结果,验证了模型的正确性;并进一步对该并联机构作业空间的几何性质、转动灵活性及奇异轨迹进行了分析。分析表明,该机构具有几何形状规则的作业空间及较好的运动灵活性,但在工作空间内具有发生位形奇异的可能,因此,在运动过程中应当避开特殊运动位置以避免奇异位形的发生。
A new non-overstrained four-DOF parallel kinematic mechanism (PKM) for realizing three-dimensional translations and rotation is presented, which is composed only with revolute joints. The topological structure characteristics, such as the POC set of moving platform, mobility and the mechanism coupling degree, are first obtained based on the design theory of position and orientation characteristic (POC) set. By means of the D - H matrix, the kinematic inverse equations of the PKM are established and Jacobian matrix, singularity are subsequently derived and analyzed. The virtual mechanism is modeled and the kinematics is simulated by using Pro/E software. By comparing the theoretical calculation analysis of examples with the results derived from simulation, the inverse positional solutions are proved to be correct. Based on the kinematic inverse equations, the 3D boundary search method is used to describe the geometrical feature and cross section of constant orientation workspace. Furthermore, the distribution of singularity position is presented and the rotational capacity among the workspace is evaluated. The results show that the workspace has regular geometrical shape and the rotational capacity is satisfactory, but the singular may appear in the workspace. Hence, it is necessary to obtain the singularity-free workspace of the PKM, which can guarantee the mechanism to avoid singularities. The study has guiding significance and reference value to the design and control of this kind of PKM.