An Effective Identification Method of Branches, Circuits and Full Rotatability of Stephenson Six-Bar Mechanisms Without Closed-Form Position Solutions

An Effective Identification Method of Branches, Circuits and Full Rotatability of Stephenson Six-Bar Mechanisms Without Closed-Form Position Solutions

There is no simple formula for predicting the full rotatability of the synthesized Stephenson six-bar mechanisms without closed-form position solutions. Therefore, in this work we propose a method for identification of full rotatability for the synthesized Stephenson six-bar mechanisms to validate whether or not a simple motor is sufficient or an additional controller is needed. Several methods have been proposed in the literature for the identification of the branches, circuits and full rotatability of the Stephenson six-bar mechanisms. However, most of these methods depend upon the coupler curves or I / O curve of the four-bar loop of the six-bar mechanism. Moreover, some extra mathematical tools are needed to find singularities, including the Sturm function or discriminant corresponding to the inputoutput equation. In this work, techniques for the identification of singularities, branches, circuits and full rotatability are integrated into an effective numerical method in which the input-output position equation is directly solved using a bisection method and the numbers coded for assembly modes for the prescribed input angles. All the identifications can be completed using the real I / O position curves and results table. An example is illustrated to show the effectiveness of the proposed method. Three synthesized Stephenson-II six-bar mechanisms discussed in the literature are examined and it is found that two of them do not have full rotatability.