There is a surge of research interest in the field of tensegrity robotics. Robots developed under this paradigm provide many advantages and have distinguishing features in terms of structural compliance, dexterity, safety, and weight reduction. This paper proposes a new robotic mechanism based on tensegrity ('tension-integrity') robots and reconfigurable modular robots. The specific actuation schemes for this tensegrity robot with multiple degrees of freedom are presented. This article describes an easy-to-assemble 350 mm tensegrity based robot prototype by stacking a series of rigid struts linked with tensegrity joints that have no direct rigid contact with each other. The functionality of the proposed robot is validated by the experimental results by integrating the polyhedral parallel structure as its skeleton and series of tensegrity joints. The proposed manipulator is capable of reaching bending angles up to 76 degrees. An adaptive cable driven underactuated robotic gripper is designed and attached to the tensegrity manipulator for grasping objects in different shapes, weights, and sizes.