A Graphical Method to Find the Secondary Instantaneous Centers of Zero Velocity for the Double Butterfly Linkage

The Aronhold-Kennedy theorem cannot locate all of the instantaneous centers of zero velocity for a planar, single-degree-of-freedom, indeterminate linkage. This paper presents a graphical technique that will locate the secondary instantaneous centers of zero velocity for a well-known indeterminate linkage; namely, the double butterfly linkage. Only one of the secondary instant centers of this eight-bar linkage needs to be located with the proposed technique; the remaining instant centers can then be located using the Aronhold-Kennedy theorem. The first step in the graphical method is to regard the double butterfly linkage as two six-bar linkages. This is accomplished by replacing the ternary link pinned to the ground by two binary links, removing the pin which connects the two coupler links, and attaching a slider to each coupler link at the coupler pin. The second step is to reduce two of the five-bar loops of the double butterfly linkage to four-bar loops by instantaneously freezing the aforementioned binary links. The paper shows how these two important steps are used to locate the absolute instant centers for the two coupler links of this indeterminate eight-bar linkage.