Parallel robots (PRs) are closed-chain manipulators with diverse applications due to their accuracy and high payload. However, there are configurations within the workspace named Type II singularities where the PRs lose control of the end-effector movements. Type II singularities are a problem for applications where complete control of the end-effector is essential. Trajectory planning produces accurate movements of a PR by avoiding Type II singularities. Generally, singularity avoidance is achieved by optimising a geometrical path with a velocity profile considering singular configurations as obstacles. This research presents an algorithm that avoids Type II singularities by modifying the trajectory of a subset of the actuators. The subset of actuators represents the limbs responsible for a Type II singularity, and they are identified by the angle between two Output Twist Screws. The proposed avoidance algorithm does not require optimisation procedures, which reduces the computational cost for offline trajectory planning and makes it suitable for online trajectory planning. The avoidance algorithm is implemented in offline trajectory planning for a pick and place planar PR and a spatial knee rehabilitation PR

翻译：并联机器人（PRs）作为闭环链式操作机构，凭借其高精度与高负载能力在多个领域得到应用。然而，工作空间内存在称为II型奇异性的位形，此时并联机器人将失去对末端执行器运动的控制能力。对于需要完全控制末端执行器的应用场景，II型奇异性是亟待解决的问题。轨迹规划通过规避II型奇异性实现并联机器人的精确运动，通常采用将奇异位形视为障碍物，结合速度廓线优化几何路径的方式完成奇异性规避。本研究提出一种通过调整部分驱动关节轨迹来规避II型奇异性的算法。该驱动子集对应引发II型奇异性的支链，可通过两条输出旋量之间的夹角进行识别。该规避算法无需优化过程，不仅降低了离线轨迹规划的计算成本，更使其适用于在线轨迹规划场景。该算法已在平面拾放并联机器人及空间膝关节康复并联机器人的离线轨迹规划中完成实现验证。