At present, the research of motion/force characteristics is concentrated on the single-platform parallel mechanisms (PMs). On the contrary, relatively little attention has been paid to the double-platform PMs, and there is also no unified index. What actually causes this? One of the reasons is that the complex and inaccessible wrench system of this manipulator with the double platforms. Especially the transmission wrench screws (TWSs) are no longer like its traditional concept, i.e., linear forces along the symmetric axis of the passive arms. Essentially, the TWSs in the double-platform PMs should be applied to the end effector but not to the sub-platforms from active arms. With this new idea, the concept equivalent transmission wrench screw (ETWS) of PMs with double platforms is firstly proposed and its identification process is also provided. Then, the motion/force transmission index which considers the input transmission index (ITI) and output transmission index (OTI) is extended to the area of kinematic performance evaluation of the double-platform PMs. Finally, the validity of the proposed extension is verified by the transmission index (TI) based on the concept of pressure angle. In this paper, the typical Par4 mechanism is investigated as an example. This extended approach with a new definition of the ETWS which covers the concept of the TWS in traditional mechanism actually provides a uniform kinematic performance index of both single- and double-platforms PMs.

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