A Note on the Waldron Construction for Transmission Angle Rectification

[+] Author and Article Information
Thomas R. Chase

Mechanical Engineering Department, University of Minnesota, 111 Church St. SE, Minneapolis, MN 55455trchase@me.umn.edu

Interestingly, Filemon does not actually show this construction in her paper.

Note that γ32 is not used in determining the angle of the limiting lines. This is because it does not reference the first position.

An equivalent construction is originally proposed by Sun and Waldron (9).

Moving pivot A1 may need be placed at or near a limiting line to meet other constraints.

The non-Grashof mechanism has only one circuit.

This is a limitation of all “branch” rectification procedures which monitor only the angle between the coupler and follower links.

These observations are based on results of quizzing junior-level students on the proposed procedure.

J. Mech. Des 128(2), 509-512 (May 24, 2005) (4 pages) doi:10.1115/1.2168471 History: Received December 31, 2004; Revised May 24, 2005

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.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Synthesis of a four-bar linkage to carry the scoop of a front loader. The follower link, OB−B, has been synthesized using steps 1–4 of Table 1. The angles required for steps 5b and 5d are also shown.

Grahic Jump Location
Figure 2

Definition of terms for a four-bar linkage

Grahic Jump Location
Figure 3

Defining the legal region for moving pivot A1 with γmin set to 35deg

Grahic Jump Location
Figure 4

Final solution, showing transmission angles at each precision position



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