The robot arm is composed of two parallel branches (2, 3) formed from a reduced number of segments (5, 6, 7) and connected to each other by a wrist (5) through a wrist holder (8), the directions of which are kept approximately constant by transmissions (12 to 16). The working space of this control arm is large and it is free of any kinetic singularities except at the end positions, and good decoupling of translation and rotation movements is achieved.