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Typical mobile robots can be modeled as parallel mechanisms by employing an interfacing variable between the ground and the wheels. Based on this conception, this work employs the screw theory as an alternative approach to model such parallel-natured mobile robots. The screw approach not only facilitates the geometric interpretation in the process of inverse and forward kinematics by employing the concept of reciprocal screws, but also provides a meaningful closed-form solution. Specifically, in this work the screw-based kinematic modeling and geometric analysis are carried out for the popular differential-driven mobile robot with a caster wheel. This work shows that the screw-based kinematic approach not only facilitates kinematic modeling for different generalized inputs, but also provides a useful tool to model the redundant actuation case. The proposed approach can also be applied to kinematic modeling and analysis of general type of mobile robots.