Robots with transformable tracked mechanisms are widely used in complex terrains because of their high adaptability, and many studies on novel locomotion mechanisms have been conducted to make them able to climb higher obstacles. Developing underactuated transformable mechanisms for tracked robots could decrease the number of actuators used while maintaining the flexibility and obstacle-crossing capability of these robots, and increasing their cost performance. Therefore, the underactuated tracked robots have appreciable research potential. In this paper, a novel tracked robot with a newly proposed underactuated revolute‒revolute‒prismatic (RRP) transformable mechanism, which is inspired by the sit-up actions of humans, was developed. The newly proposed tracked robot has only two actuators installed on the track pulleys for moving and does not need extra actuators for transformations. Instead, it could concentrate the track belt’s tension toward one side, and the unbalanced tension would drive the linkage mechanisms to change its configuration. Through this method, the proposed underactuated design could change its external shape to create support points with the terrain and move its center of mass actively at the same time while climbing obstacles or crossing other kinds of terrains, thus greatly improving the climbing capability of the robot. The geometry and kinematic relationships of the robot and the crossing strategies for three kinds of typical obstacles are discussed. On the basis of such crossing motions, the parameters of links in the robot are designed to make sure the robot has sufficient stability while climbing obstacles. Terrain-crossing dynamic simulations were run and analyzed to prove the feasibility of the robot. A prototype was built and tested. Experiments show that the proposed robot could climb platforms with heights up to 33.3% of the robot’s length or cross gaps with widths up to 43.5% of the robot’s length.