The kinematics has attracted continuous interests in the field of robotics. Terminal position and orientation coupling phenomenon is the key problem and the first consideration in the kinematics of lower mobility robots. However, this property was usually neglected or has not been well solved. This paper discusses the terminal position and orientation coupling issues in lower mobility robots, especially for the lower mobility hybrid robots. First, this paper reveals the terminal position and orientation coupling in serial and parallel robots. Then, based on elimination theory, an approach for establishing the terminal position and orientation coupling equations for hybrid robots is proposed, which is illustrated in detail by the (3-RPS) + (RR) and (3-RPS) + (3-RCR) hybrid robots. The results show that the hybrid robots have highly nonlinear terminal position and orientation coupling relations, which are more complicated than serial and parallel robots. The research of this paper is valuable in kinematics modeling of robots.

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