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This paper studies a geometric-based method for smooth path generation for nonholonomic mobile robots, which are subject to dynamic and curvature constraints. It first studies polar polynomial curve and its properties for it to be used in curvature-smooth transition. In the design of such a path, it is examinable whether the robot constraints and curvature requirement are satisfied. Then, connection using such a curve is extended to the case that the robot is performing rotation at its start position. Next, a computationally efficient way is proposed for collision test of the curve in order to achieve realtime path planning. Finally, extensive simulation experiments are carried out to verify the proposed method.