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.
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March 2002
Technical Papers
A Polynomial Equation for a Coupler Curve of the Double Butterfly Linkage
Gordon R. Pennock, Associate Professor,,
Gordon R. Pennock, Associate Professor,
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-1288
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Atif Hasan, Test Engineer,
Atif Hasan, Test Engineer,
Valeo Motors and Actuators, Auburn Hills, MI 48326-2356
Search for other works by this author on:
Gordon R. Pennock, Associate Professor,
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-1288
Atif Hasan, Test Engineer,
Valeo Motors and Actuators, Auburn Hills, MI 48326-2356
Contributed by the Mechanisms Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received Apr. 2000. Associate Editor: K. Farhang.
J. Mech. Des. Mar 2002, 124(1): 39-46 (8 pages)
Published Online: April 1, 2000
Article history
Received:
April 1, 2000
Citation
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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