To materialize smooth valve opening and closure even if lift amount changes in a camshaft, to manufacture a hard precise three-dimensional cam without dispersion between cylinders in a method for manufacturing the cam shaft, and to improve engine performance by advancing valve timing as lift becomes smaller in a valve system for an engine.

The three-dimensional cam includes a lift part, a base circle part and a ramp part. A lift area of a large lift part of the lift part is formed to keep longer lift time than a small lift part. The base circle part is provided with a perfect circle cylindrical shape in a view from an axial direction. Cross section passing a large and a small lift starting points and a center of one end part is formed in an elliptical shape. The ramp part is formed with a constant width. The three-dimensional cam is ground by a grinding wheel provided with an elliptical rotating body. The variable valve timing device advances valve timing as lift becomes smaller.