A linear actuator member applies a vertical force to a vessel or to a holding apparatus in which a vessel is contained. A linear to angular motion constraining member such as a cage structure having a helical track translates linearly directed force and motion applied by the linear actuator member into a combined linear and rotational motion of the vessel. The combined vertical and rotational motion of the vessel in response to the vertical force is repeatable according to a predefined agitation pattern for mixing components in the vessel.