The proposed study provides a solution of the inverse and forward kinematic problems and workspace analysis for a five-degree-of-freedom parallel–serial manipulator, in which the parallel kinematic chain is made in the form of a tripod and the serial kinematic chain is made in the form of two carriages displaced in perpendicular directions. The proposed manipulator allows to realize five independent movements—three translations and two rotations motion pattern (3T2R). Analytical relationships between the coordinates of the end-effector and five controlled movements provided by manipulator’s drives (generalized coordinates) were determined. The approach of reachable workspace calculation was defined with respect to available design constraints of the manipulator based on the obtained algorithms of the inverse and forward kinematics. Case studies are considered based on the obtained algorithms of inverse and forward kinematics. For the inverse kinematic problem, the solution is obtained in accordance with the given laws of position and orientation change of the end-effector, corresponding to the motion along a spiral-helical trajectory. For the forward kinematic problem, various assemblies of the manipulator are obtained at the same given values of the generalized coordinates. An example of reachable workspace designing finalizes the proposed study. Dimensions and extreme values of the end-effector orientation angles are calculated.

拟议的研究为五自由度并联-串行机械手提供了逆向和正向运动学问题的解决方案以及工作空间分析，其中并联运动学链以三脚架的形式制成，而串行运动学链为以在垂直方向上移位的两个滑架的形式制成。提出的操纵器允许实现五个独立的运动-三个平移和两个旋转运动模式（3T2R）。确定了末端执行器的坐标与机械手的驱动器提供的五个受控运动（通用坐标）之间的解析关系。根据获得的逆向和正向运动学算法，针对机械手的可用设计约束条件定义了可到达的工作空间计算方法。基于获得的逆向和正向运动学算法来考虑案例研究。对于逆运动学问题，根据给定的末端执行器的位置和方向变化定律来获得解，该定律对应于沿着螺旋-螺旋轨迹的运动。对于正向运动学问题，在广义坐标的相同给定值下获得了机械手的各种组件。可达性工作空间设计的一个示例完成了拟议的研究。计算末端执行器定向角的尺寸和极值。对应于沿着螺旋螺旋轨迹的运动。对于正向运动学问题，在广义坐标的相同给定值下获得了机械手的各种组件。可达性工作空间设计的一个示例完成了拟议的研究。计算末端执行器定向角的尺寸和极值。对应于沿着螺旋螺旋轨迹的运动。对于正向运动学问题，在广义坐标的相同给定值下获得了机械手的各种组件。可达性工作空间设计的一个示例完成了拟议的研究。计算末端执行器定向角的尺寸和极值。