in many types of torque converters i e not only in those shown in the drawing and described in the specification of the present application furthermore the torque converter 1 can employ several torsional vibration dampers for example the damper 18 and a second damper between the turbine 14 and the hub 15 the rivets 30 connect the piston 19 of the bypass clutch 17 with the arms 36 radially outwardly of the plate like central portion or body 24 a of the input 24 the arms 36 can be pivoted relative to the body 24 a i e the rivets 30 can move within limits relative to the body 24 a in the axial direction of the housing 13 fig2 shows that the surfaces bounding each recess 27 can be disposed at least substantially at right angles to each other each arm 36 of the input 24 shown in fig2 has a trapezoidal shape and tapers radially inwardly toward the center of the input body 24 a this ensures that the rigidity of each arm 36 decreases radially inwardly toward the junction with the body 24 a in other words the flexibility of each arm 36 decreases in a direction toward the axis x u2014 x such arrangement is desirable because it reduces the likelihood of breakage of the arms in the regions of the rivets 30 especially due to fatigue in response to axial and or other stressing during repeated engagement and disengagement of the bypass clutch 17 as well as while the bypass clutch is at least partly engaged still further such configurations of the arms 36 exert a positive influence upon the piston 19 of.