Four position Synthesis of Spherical 4R Mechanism Based on Solution Region

According to the given parameters of four positions, the four-position synthesis of the spherical 4R mechanism was completed by constructing the solution region of the mechanism. Based on the parameters of the given position, solving the Burmester circle points curve and classifying and arranging the Burmester circle points, the map of mechanism type solution region and feasible region can be established, then different geometric regions were used to represent different mechanism type solutions and whether the mechanism solutions have motion defect. Finally, the solution that satisfies the requirements is selected from the feasible region to complete the four-position synthesis of the spherical 4R mechanism, then obtain the mechanism solution that satisfies the requirements and has no motion defect. This method makes the design process more efficient. Finally, an example is given to illustrate and verify the synthesis method.