By providing a single housing and shackle assembly constructed for enabling the shackle to be opened and/or closed using either a rotatable dial combination construction or a key activating tumbler construction, with the movement of the shackle being controlled by a trigger member, an effective, easily produced, padlock is achieved which incorporates two separate and independent locking systems formed in a single padlock. In addition, the trigger member and shackle each incorporate uniquely constructed, cooperating surfaces, each of which comprise a grooved zone or concave curved zone which is positioned directly adjacent a cooperating convexly curved zone. By employing these two curved surfaces on both the shackle and trigger member, the controlled pivotal movement of the shackle is realized.