Compared with rigid robots, flexible robots have soft and extensible bodies enforcing their abilities to absorb shock and vibration, hence reducing the impact of probable collisions. Due to their high adaptability and minimally invasive features, soft robots are used in various fields. The McKibben hydraulic artificial muscles are the most popular soft actuator because of the controllability of hydraulic actuator and high force to weight ratio. When its deformation reaches a certain level, the actuators can be stopped automatically without any other braking mechanism. The research of McKibben hydraulic artificial muscles is beneficial to the theoretical analysis of soft actuators in the mechanical system. The design of soft actuators with different deformations promotes the development of soft robots. In this paper, a static modeling of the McKibben hydraulic artificial muscles is established, and its correctness is verified by theoretical analysis and experiment. In this model, the deformation mechanism of the artificial muscle and the law of output force is put forward. The relationship between muscle pressure, load, deformation, and muscle design parameters is presented through the mechanical analysis of the braid, elastic tube, and sealed-end. The law of the muscle deformation with high pressure is predicted. The reason for the muscle’s tiny elongation with extremely high pressure is found through the analysis of the relationship between the angle of the braid, the length of single braided thread, and the pressure. With the increase of pressure, the angle of the braid tends to a fixed value. As the stress of braided thread increases, so does its length. The length changes obviously when the stress is extremely enormous. The angle of the braid and the length of the braided thread control the deformation of artificial muscles, resulting in a slight lengthening with extreme high pressure. Under normal pressure, the length of the braided wire is negligible, so that the entire muscle becomes shorter. According to the modeling and theoretical analysis, a new McKibben hydraulic artificial muscle that can elongate under normal rising pressure is designed. This artificial muscle can grow longer with pressure increases, eventually reaching its maximum length. During this time, its diameter barely changes. Its access pressure is higher than that of conventional elongated artificial muscles. Through experiments, the relationship between the muscle deformation, pressure, and load still conform to this theoretical model. This model can be used for the control of soft actuators and the design of new soft robots. This extensional McKibben hydraulic artificial muscles and the conventional McKibben hydraulic artificial muscles can be used in the bilateral control of soft robots.

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