Design and Analysis of Kinematic Couplings for Modular Machine ...

1yhxrβα2 3Figure 2.7: Arrangement of three-pin interface.The three-pin interface is realized by fashioning an upper interface plate with a triangular arrangementof shouldered or dowel pins, and manufacturing a bottom interface with a triangular arrangement of oversizedcutouts with flat or curved contact surfaces with which the pins make contact. When the top interfaceplate is engaged with the bottom interface plate, the pins are seated against the contact surfaces by introducingan in-plane preload force (F p ) at the first pin, offset by the angle θ from the local x-axis. A disturbanceload D o = [D x,o , D y,o , D z,o , DM x,o , DM y,o , DM z,o ] is resolved into an effective six-tuple D = [D x , D y ,D z , DM x , DM y , DM z ] applied at the local origin, and normal preload forces F z1 , F z2 , and F z3 are appliedusing bolts through the centers of pins 1, 2, and 3, respectively. Assuming normal reaction forces at each ofthe engagement locations between the pins and bottom plate, the in-plane reaction forces and the requirednormal preloads to maintain dynamic stability are the solution of the static system:31