Abstract This paper aims to develop an approach for the reconfiguration of a parallel kinematic manipulator (PKM) with four degrees of freedom (DoF) designed to tackle tasks of diagnosis and rehabilitation in an injured knee. The original layout of the 4-DoF manipulator presents Type-II singular configurations within its workspace. Thus, we proposed to reconfigure the manipulator for avoiding such singularities (owing to the Forward Jacobian of the PKM) during typical rehabilitation trajectories. We achieve the reconfiguration of the PKM through a minimization problem where the design variables correspond to the anchoring points of the robot limbs on fixed and mobile platforms. The objective function relies on the minimization of the forces exert by the actuators for a specific trajectory. The minimization problem considers constraints equations to avoid Type-II singularities, which guarantee the feasibility of the active generalized coordinates for a particular path. To evaluate the proposed conceptual strategy, we build a prototype where reconfiguration occurs by moving the position of the anchoring points to holes bored in the fixed and mobile platforms. Simulations and experiments of several study cases enable testing the strategy performance. The results show that the reconfiguration strategy allows obtaining trajectories having minimum actuation forces without Type-II singularities.

中文翻译：

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重新配置具有 2T2R 运动的平行运动机械手，通过最小化执行器力来避免奇异点

摘要 本文旨在开发一种重新配置具有四自由度 (DoF) 的平行运动机械手 (PKM) 的方法，旨在解决受伤膝关节的诊断和康复任务。4-DoF 机械手的原始布局在其工作空间内呈现 II 型奇异配置。因此，我们建议重新配置操纵器以避免在典型的康复轨迹期间出现这种奇点（由于 PKM 的前向雅可比矩阵）。我们通过最小化问题实现 PKM 的重新配置，其中设计变量对应于固定和移动平台上机器人肢体的锚定点。目标函数依赖于致动器对特定轨迹施加的力的最小化。最小化问题考虑约束方程以避免类型 II 奇点，这保证了特定路径的活动广义坐标的可行性。为了评估所提出的概念策略，我们构建了一个原型，通过将锚点的位置移动到固定和移动平台上的钻孔来进行重新配置。几个研究案例的模拟和实验可以测试策略性能。结果表明，重新配置策略允许获得具有最小驱动力的轨迹，而没有 II 型奇异点。我们构建了一个原型，通过将锚点的位置移动到固定和移动平台上的钻孔来进行重新配置。几个研究案例的模拟和实验可以测试策略性能。结果表明，重新配置策略允许获得具有最小驱动力的轨迹，而没有 II 型奇异点。我们构建了一个原型，通过将锚点的位置移动到固定和移动平台上的钻孔来进行重新配置。几个研究案例的模拟和实验可以测试策略性能。结果表明，重新配置策略允许获得具有最小驱动力的轨迹，而没有 II 型奇异点。