Planar motion of wheeled moving platforms, on which a camera is installed to capture videos, is common in real-world scenarios. For a general planar motion, Scaramuzza et al. proposed a linear one-point model to recover motions from a video under a potential assumption that the camera needs to be placed somewhere between the rear wheels of a moving platform. However, the assumption is too restricted for researchers and manufacturers, because the camera is generally fixed either on the front top of vehicles for a broad view or near the left/right mirrors because of the requirement of mechanical design. In this paper, we focus on motion modeling of wheeled moving platforms without the restriction of cameras' location on a vehicle, and propose a quadratic motion model to circumvent the limitation. Newton's iterative method and bounded quadratic least squares are used to solve the quadratic optimization problem. We test our model on both the synthetic data and the real data, and conclude that the tradeoff between model error and computational error and that between performance and computational cost are the main concerns in the practice of visual odometry. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.