Through firstorder linear mapping, a spacetime Π was mapped out from the configuration space of a system with a holonomic rheonomic constraint. The geometric properties (metric and connection) of the spacetime Π were induced, and the equations of motion of the constrained system in the spacetime Π were obtained. When the first order linear mapping is not integrable, the spacetime Π is a RiemannCartan space.When the first order linear mapping is integrable, the spacetime Π degenerates into a Riemann space. In the latter case, the equations of motion of the holonomic rheonomic system in the spacetime Π is equivalent to the Lagrange equations described with generalized coordinates.