A Note on the Waldron Construction for Transmission Angle Rectification

Graphical methods for synthesizing planar four-bar linkage motion generators to pass through two or three precision positions are well known. However, the practicality of these methods is limited by a high probability that the resulting linkages will suffer from kinematic defects. These may include change of circuit, change of branch or poor transmission angle. This technical brief distills earlier work of Waldron and associates (Chaung, J. C, Strong, R. T., and Waldron, K. J., 1981, J. Mech. Des., 103(3), pp. 657–664, Sun, J. W. H., and Waldron, K. J., 1981, Mech. Mach. Theory, 16(4), pp. 385–397, and Waldron, K. J., 1976, ASME J. Eng. Ind., 98(1), pp. 176–182) to an approachable procedure for controlling the transmission angle of four-bar linkages during synthesis. The procedure simultaneously eliminates the branch defect. It eliminates the circuit defect for some Grashof types but not others. The procedure is integrated with the established graphical synthesis methods by the addition of a few easily implemented substeps. The procedure is simple enough to be performed manually by undergraduates. Nevertheless, it is powerful enough to substantially improve the likelihood that the synthesized linkages will perform well when constructed. The procedure is explained in reference to an application.