Abstract

The mobility problem of multi-loop linkages is difficult due to its complexity and nonlinearity. This paper proposes a simple treatment to determine the rotatability between any two links, adjoined or not, in planar multi-loop linkages. The rotation angle of the floating link with respect to (w.r.t.) the reference link is established so that there is no ambiguity in analyzing the rotation range of the floating link. Based on the joint rotation space (JRS) method, not only the branch formation but also the rotatability between any two links on each of the branches can be identified. It is a visualized method that reveals the rotation characteristic of multi-loop linkages. The paper demonstrates the rotation range of the floating link w.r.t. reference link on six-bar Stephenson linkages, 2-D.O.F. 7-bar linkages and the 3-D.O.F. 8-bar parallel manipulators. This might be the first paper to deal with the rotatability of 3-D.O.F. planar multi-loop linkages. At last, the paper applies the method to predict the clearance-induced angle uncertainty of the eight-bar parallel manipulators, which determines the worst orientation error of the end-effector and fills up the void of the clearance uncertainty model proposed by Ting [1]. The approach extends single loop N-bar rotatability laws to deal with the rotatability between any two links in multi-loop linkages.

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