In this paper, we offer a new design for a spherical mobile robot with much ability in maneuvering, which can be used for discovery and patrolling applications. Our proposed design consists of two essential parts: the inside drive unit which is called IDU and the outer spherical shell that can be made of glass, plastics or any other similar material. The IDU of our presented model is mounted inside the spherical shell and has four motors (two servo and two linear motors). The servo motors, which connect pendulums and outer shell, generate the driving torque. Linear motors are used to displace the center of mass that causes the robot to tilt. Therefore, the motion of the robot can be on a curve. Firstly, the dynamic model of a simplified version of this kind of spherical robots is obtained. Having dynamic modeling, we can obtain proper moment of two servo motors and proper displacement of two linear motors to drive robot along straight and circular trajectories. By using a dynamic simulation in MSC.ADAMS package, we can verify the accuracy of the obtained dynamic model to track a circular trajectory.