Abstract: Agitation mechanisms for homogenization devices for processing sample materials in tubes that are secured by tube holders to the agitation mechanisms. Each agitation mechanism includes a first rotary member having a first fixed rotational axis, a second rotary member having a second fixed rotational axis, and a connecting member that extends between them, is rotationally mounted to them at third and fourth non-fixed rotational axes, and to which the tube holder is mounted, with the first and third rotational axes defining a first offset, and with the second and fourth rotational axes defining a second offset. When the first rotary member is driven through rotation, the sample in the tube in the tube holder on the connecting member is driven through a nonlinearly reciprocating motion profile to produce a grinding shear action to better homogenize the samples. Other disclosed embodiments produce linearly reciprocating motion profiles.