Hybrid robots consist of both serial and parallel mechanisms, which have advantages in stiffness and workspace compared with serial/parallel robots when machining composite material. However, the forward and inverse kinematics of hybrid robots generally do not have analytic solutions. This paper deals with the analytic forward and inverse kinematics solutions of a 5-degree-of-freedom (DOF) hybrid robot which consists with a 3-DOF 2UPU/SP parallel mechanism (PM) and a 2-DOF rotating head. In the forward kinematic problem, a method is proposed to transfer the high order kinematic equation to a 4th-order polynomial based on the Sylvester's dialytic elimination, and the analytic solutions can be further obtained by Ferrari's method. In the inverse problem, the redundant Euler angles expressed by four rotations are firstly proposed for decoupling different motions, then, the closed-form solution of inverse kinematics can be found. Finally, a simulation trajectory is given, and the result shows that the accuracy of the solutions’ calculation reaches femtometer grade and the efficiency reaches microsecond grade; furthermore, an experiment is performed on the prototype to validate the effectiveness of the proposed forward and inverse kinematics.

混合机器人由串联和并联机构组成，与在加工复合材料时的串联/并联机器人相比，在刚性和工作空间方面具有优势。但是，混合机器人的正向运动学和逆向运动学通常没有解析解。本文研究了具有3自由度2UPU / SP并联机构（PM）和2自由度旋转头的5自由度（DOF）混合机器人的正向和逆向运动学解析解。在正向运动学问题中，提出了一种基于西尔维斯特渗析消除法将高阶运动学方程式转化为四阶多项式的方法，并可以通过法拉利方法进一步获得解析解。在反问题中 首先提出了由四转角表示的多余的欧拉角来解耦不同的运动，然后求出逆运动学的闭式解。最后给出了仿真轨迹，结果表明，解的计算精度达到飞米级，效率达到了微秒级。此外，对原型进行了实验，以验证所提出的正向和反向运动学的有效性。