The mechanism such as a motor or a pump comprises a cam (10) and a cylinder block (12) which has a plurality of cylinders (14A, 14B, 14) connected to communication orifices (34A, 35A; 34B, 35B) disposed in a communication face (18). The mechanism further comprises a fluid distributor (20) having a distribution face (22) which is provided with distribution orifices (31A-31F, 32A-32F) suitable for being connected to the feed or to the discharge. The communication orifices and the distribution orifices communicate with one another as the cylinder block and the distributor rotate relative to each other. At least certain cylinders (14A, 14B) are connected to at least two communication orifices (34A, 35A; 34B; 35B) spaced apart angularly (.alpha.) so that they communicate simultaneously with respective distribution orifices connected to the feed or to the discharge.