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

This paper presents a graphical technique to 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 needs to be located with the proposed technique; the remaining instant centers can be located from the Aronhold-Kennedy theorem. An important 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 connected to 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. A key concept is to instantaneously freeze the aforementioned binary links and regard each six-bar linkage as a four-bar linkage. The paper shows how these ideas can be related to locate the absolute instant centers for the two coupler links of this eight-bar linkage.