2-UPR-SPR并联机构转轴分析

两转一移(2R1T)并联机构转动自由度的轴线包括瞬时转轴和连续转轴。转轴的性质和在空间的分布对2R1T并联机构的轨迹规划和运动学标定等具有重要意义，尤其是在对末端姿态能力要求高的应用如五轴数控加工中更为重要。五自由度Exechon混联加工中心被广泛应用于高端制造业，其由属于2R1T并联机构的2-UPR-SPR并联机构和RR串联机构组成。运用螺旋理论，建立2-UPR-SPR并联机构在初始位形、动平台发生单自由度连续转动后的位形、动平台发生两自由度连续转动后位形下的各分支运动螺旋系和约束螺旋系。根据刚体转轴与约束力作用的关系，确定了动平台的两条连续转轴，这两条转轴的方向与机构位形相关，且分别过参考坐标系原点和球铰中心点。

Analysis of Rotational Axes of 2-UPR-SPR Parallel Mechanism

2R1T Parallel mechanism (PM) can undergo one translational degree of freedom (DOF) and two rotational DOFs. It contains two kinds of rotational axes: continuous rotational axis and instantaneous rotational axis. The property and geometrical distribution of rotational axes in space are important to trajectory planning and kinematic calibration of parallel mechanisms in which high orientation ability is required, such as five axes parallel kinematic machine (PKM). The 5-DOF Exechon hybrid machining center has been widely used in the advanced manufacturing. It consists of a 2-UPR-SPR PM which belongs to 2R1T PM and a RR serial mechanism. Using screw theory, limb twist system and limb constraint system were established when the 2-UPR-SPR PM is at the initial configuration and configurations after continuous rotation of 1 DOF and 2 DOFs. Based on the relation of rotation axis and constraint force of rigid body, two continuous rotational axes of the moving platform have been identified. These two continuous rotational axes is dependent on the configuration of the 2-UPR-SPR PM and pass through the origin of the reference frame and the center of the spherical joint.