Mobile robots are increasingly used for service-like applications in which the service points are known and the mobile robot starts from a starting location, visits all the service points requested and returns to the starting location. The tour construction problem in these applications can be treated as a Travelling Salesman Problem (TSP). Classical tour construction algorithms that are proposed for the TSP find tours do not consider robot kinematic constraints. These tours may have sharp turns at some service points. When a mobile robot follows such a tour, it stops, turns and speeds up again. Therefore, the robots waste a considerable amount of power and time. In these cases, tour smoothing can be used to overcome this problem. However, smoothing an existing tour may result in unnecessarily long tours. In this study, a Smooth Tour Construction (STC) approach is proposed for mobile robots with kinematic constraints. The STC approach considers tour construction and tour smoothing concurrently. The logic behind the tour construction part of the approach is based on the Savings Algorithm (SA). The tour smoothing is based on Dubins' arc-line approach. Experiments are conducted for P3-DX robots in a laboratory environment. Comparisons are also drawn with various tour smoothing algorithms in simulation environments to demonstrate the effectiveness of the proposed STC approach.