This paper addresses the synthesis problem of Watt-I and Stephenson-IIIa six-bar linkages motion generation for four specified task positions. Both of them have one thing in common — theirs floating links which used as end-effectors are connected to a coupler plane of a four-bar linkage. Once the task positions of end-effector are given, we can calculate the corresponding positions of the coupler plane. Then our focus is on the synthesis of a four bar-linkage and the way that a RR chain can be attached to constrain the links of this four-bar linkage. This synthesis problem of four-bar linkage motion generation can be settled by a solution region method. And then we can present an equation of pivot curve that each point on this curve can generate a satisfactory RR chain. A new local solution region that is more practicable is presented by the last numerical example.

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