This paper presents a closed-form polynomial equation for the path of a point fixed in the coupler links of the single degree-of-freedom eight-bar linkage commonly referred to as the double butterfly linkage. The revolute joint that connects the two coupler links of this planar linkage is a special point on the two links and is chosen to be the coupler point. A systematic approach is presented to obtain the coupler curve equation, which expresses the Cartesian coordinates of the coupler point as a function of the link dimensions only; i.e., the equation is independent of the angular joint displacements of the linkage. From this systematic approach, the polynomial equation describing the coupler curve is shown to be, at most, forty-eighth order. This equation is believed to be an original contribution to the literature on coupler curves of a planar eight-bar linkage. The authors hope that this work will result in the eight-bar linkage playing a more prominent role in modern machinery.
A Polynomial Equation for a Coupler Curve of the Double Butterfly Linkage
Contributed by the Mechanisms Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received Apr. 2000. Associate Editor: K. Farhang.
Pennock, G. R., and Hasan, A. (April 1, 2000). "A Polynomial Equation for a Coupler Curve of the Double Butterfly Linkage ." ASME. J. Mech. Des. March 2002; 124(1): 39–46. https://doi.org/10.1115/1.1436087
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