In this paper, we study the kinematics of a legged robot with half-circular leg morphology. In particular, our focus is on the RHex hexapod platform. A new kinematic model for RHex is developed considering the leg shape and its consequences, which was over simplified in the previous models seen in literature. The formulation is an accurate kinematic representation of the robot in the sagittal plane that is based on a four-link mechanism analogy. When only pure rolling motion of the legs are considered, it is found that when front and rear pairs of legs are in contact with the ground, the robot becomes a one degree-offreedom mechanism and position of the middle pair of legs are redundant. The problem is solved in two steps; the first one being the determination of the initial configuration of the leg angular positions which defines the initial value of the variable distance of the front and rear leg and ground contact ponts. After the initial configuration of the system is set, pitch angle of the robot body can be manipulated by controlling one of the leg angular positions and the results are presented on an example case; positioning a body fixed unactuated sensor by controlling robot body pitch angle through the actuation of one of the legs. The results are a good display of the multi-functional aspect of the legs in addition to their use for locomotion.
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