A multi-link engine has a piston (10) that moves inside a cylinder. A piston pin (21) connects the piston to an upper link (11), which is connected to a lower link (12). A crank pin of a crankshaft (33) supports the lower link thereon. The lower link is pivotally connected to one end of a control link (13), which is connected at another end to the engine block body by a control shaft (24). The control shaft (24) is lower than a crank journal of the crankshaft, and disposed on a first side of a plane that is parallel to a cylinder center axis and that contains a center rotational axis of the crank journal. The cylinder center axis is located on a second (i.e., opposite the first side) plane. The control link (13) has a center axis that is parallel to the cylinder center axis when the piston is near top and bottom dead centers.