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A vacuum-driven inclined hexagonal prism soft-rigid hybrid contraction actuator inspired by Kresling origami pattern and with low driving pressure, high contraction ratio, and fast response was proposed. The advantages of soft-rigid hybrid vacuum contraction actuators over conventional positive-type oscillators were investigated. Under 30 kPa vacuum pressure, the actuator can realize a torsional angle of 87°, contraction ratio of 59%, contracting response time of 0.2 s, and restoring response time of 0.42 s. The design and fabrication of the proposed actuator were discussed. A mathematical model treating all creases as a combination of linear and torsion springs, which is firstly considered compared with previously proposed models of Kresling origami-based actuators, was established to predict the output performance. The excellent output force prediction performance of the proposed method was validated experimentally. To investigate the application potential of the proposed modular actuator, six actuators were assembled on a pipe-crawling robot that can crawl in horizontal, vertical, elbow rigid pipes as well as flexible pipes with inner diameters ranging from 55 to 71 mm. The robot achieved a maximum crawling velocity of 34.8 mm/s (0.226 body lengths per second) and maximum load of 1000 g (12.5 times its own weight) in tests. Thus, the excellent application potential of the proposed actuator was validated.