Normally, one link of the four-bar linkage is fixed to the frame; another supplies the input; the motion of the third one with respect to the base is the output. A novel application of the four-bar linkage is proposed that a parallelogram mechanism is applied to be a rolling robot for which there is neither a constant base nor a constant output. Four sides take turns to be the support link and an adjacent link of the support one is regarded as the output in turn. The rolling motion is actuated by an internal angle change which is supplied by the rocker oscillation of a crank-rocker mechanism, not a motor directly. The unidirectional rotation of the motor simplifies the control system. A planar 4R parallelogram is suggested to roll straight under the driving of a planar 4R crank-rocker mechanism. For turning, a spatial RSRS quadrilateral is presented to roll and turn driven by a spatial RSUS crank-rocker mechanism. The principle of tipping and rolling are explained. Simulations testify the parameter design of the driving rank-rocker mechanism. An experimental prototype is fabricated to verify the feasibility of the concept.

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