The Optimal Kinematic Synthesis of Planar, Full Cycle, Constant-Velocity, Straight-Line Mechanisms


This thesis addresses the optimal kinematic synthesis of planar, full cycle, constant velocity, straight-line mechanisms. Exact and approximate straight line generating mechansisms in the literature were analyzed for their constatnt-velocity characteristcs. Some exact straight-line mechanisms depending on special link length ratios or on the principle of inversion, are shown to not have constant-velocity charactertists, wtih uniform input velocity. Mechanisms that were found to have constant-velocity characteristics include: the Chebychev cognate four bar (Spragg and Tesar, 1972), the Watt 7R six-bar (klein-Breteler, 1979, 1985), the 5R2P Stephenson six-bar (Burke and Bagci, 1984; Johnson, 1985 and Hodges and Pisano, 1992), the drag-link driven slider (Schoen, 1965), the Whitworth riven slider (Aquirre, 1987), the gear-link mechanisms (Lee and Freudenstein, 1976) and the symmetric double rocker 8-bar (Wunderlich, 1968).

An optimal design method utilizing planar kinematic elements, the ADS (Vanderplaats, 1988) optimization package, and PostScript graphic output was developed. In addition to finding optimal designs for mechanisms in the literature, elliptical gear sets were utilized to modify the constant input velocity and impart varying amounts of constant-velocity characteristics to some of the straight-line mechanisms.

Cost functions proposed and studied included a two-term formulation involving the scan fraction and the velocity error and a formulation using the area between the velocity profile and the line defining the lower bound on the acceptable velocity deviation.  The area cost function was found to be simple to implement and was used to find the majority of the optimal designs in this study. Inclusion of assembly constraints assured full cycle mobility.

scan fractions as high as 40 to 50 percent, with typical velocity errors as low as 2 percent were found for several mechanisms with unconstrained transmission angles. Constraining transmission angles to the interval 30 through 150 degrees resulted in scan fractions being reduced to an upper limit of 25 to 40 percent with corresponding velocity errors still limited to 2 percent. For several mechanisms, displacements perpendicular to the straight-line motion were found to be appreciable in magnitude.

Peter Hall Hodges
Publication date: 
December 31, 1991
Publication type: 
Ph.D. Dissertation
Hodges, P. H. (1991). The Optimal Kinematic Synthesis of Planar, Full Cycle, Constant-velocity, Straight-line Mechanisms. United States: University of California, Berkeley.

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