Soft crawling robots exhibit efficient locomotion across various terrains and demonstrate robustness to diverse environmental conditions. Here, we propose a valveless soft-legged robot that integrates a pair of rotary bellows-enclosed soft transmission systems (R-BESTS). The proposed R-BESTS can directly transmit the servo rotation into leg swing motion. A timing belt controls the pair of R-BESTS to maintain synchronous rotation in opposite phases, realizing alternating tripod gaits of walking and turning. We explored several designs to understand the role of a reinforcement skeleton in twisting the R-BESTS' input bellows units. The bending sequences of the robot legs are controlled through structural design for the output bellows units. Finally, we demonstrate untethered locomotion with the soft robotic decapod. Experimental results show that our robot can walk at 1.75 centimeters per second (0.07 body length per second) for 90 min, turn with a 15-centimeter (0.6 BL) radius, carry a payload of 200 g, and adapt to different terrains.