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Decoupled parallel mechanisms (DPMs) have the characteristics of compact structure and simple control with wide applications. This paper presents a new method of type synthesis for DPMs by virtue of Lie groups and screw theory. The method consists of synthesis at limb level and configuration level. At limb level, Lie group is used to synthesize the limbs with required DOFs. At configuration level, screw theory is adopted to determine configuration with synthesized limbs that satisfy the type synthesis criteria of DPMs. The type synthesis criteria including limb decoupling and selection of the driving pairs are presented. Upon the formulation, the procedure of type synthesis of DPMs is developed. Type synthesis is conducted with the proposed method, which leads to new spatial and planar fully decoupled 2T1R mechanisms.

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This paper presents a novel ankle rehabilitation (2-CRS+PU)&R hybrid mechanism, which can meet the size requirements of different adult lower limbs based on the three-movement model of the ankle. This model is related to three types of movement modes of the ankle movement, without axis offset, which can cover the ankle joint movements. The inverse and forward position/kinematics results analysis of the mechanism is established based on the closed-loop vector method and using the optimization of particle groups algorithm. Four groups of position solutions of the mechanism are obtained. The kinematics simulation is analyzed using ADAMS software. The variations of the velocity and acceleration of all limbs are stable, without any sudden changes, which can effectively ensure the safety and comfort of the ankle model end-user. The dexterity of the mechanism is analyzed based on the transport function, and the results indicate that the mechanism has an excellent transfer performance in yielding the structure parameters. Finally, the rehabilitation evaluation is conducted according to the three types of movement modes of the ankle joint. The results show that this ankle rehabilitation mechanism can provide a superior rehabilitation function.