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In-pipe robots provide inspection and maintenance services to various pipelines. This article proposes an algorithm to calculate the required radial variations for in-pipe robots to pass through pipeline elbows smoothly. It first gives a full overview of a robot passing through a U-shaped elbow and identifies the problem location where the radial dimension changes the most. It then presents a detailed analysis on the focused stage and deduces the algorithm. Based on the obtained algorithm, a realizing Matlab program is written to calculate all possible lengths of front and rear legs at every moment during the process. Finally, the calculation results are presented to precisely describe the track of movement, the length deformations during the whole process, and different contributions of structural variables. This article provides the design and the control of an in-pipe robot with an algorithm to calculate the lengths of its legs at every moment and to what extent the deformations of elastic legs are required. [ABSTRACT FROM AUTHOR]