A robot arm (500) for positioning a tool (44) with controlled orientation. The robot arm (500) comprises an inner-arm linkage (15, 18, 29; 15, 18, 77); an outer-arm linkage (23; 81; 173; 228; 632; 384) and a first actuator (1; 249) configured to rotate the inner-arm linkage about a first axis of rotation (180). The inner-arm linkage includes a first inner link (15) that at an inner end is arranged to rotate around a fourth axis of rotation (185), and a second inner link (18) that at an inner end is arranged to rotate around a different, third axis of rotation (182, 185), wherein the axes of rotation (182, 185) are perpendicular to the first axis of rotation (180), and the rotations result in a geometric reconfiguration of the inner-arm linkage. The inner-arm linkage also includes a connection shaft (29; 77) mounted at an outer end of the first inner link and at an outer end of the second inner link by means of joints of at least one degree of freedom, is connected to the outer-arm linkage via the connection shaft, is connected to the tool and forms a first kinematic chain that gives a first degree of freedom for positioning the tool. A second actuator (2; 254) is configured to rotate the outer-arm linkage around the second axis of rotation, thereby forming a second kinematic chain giving a second degree of freedom for positioning the tool. A third actuator (3) is configured to move the outer-arm linkage by actuating the geometrically reconfigurable inner-arm linkage, resulting in a movement of the second axis of rotation around which the outer-arm linkage is arranged to rotate, thereby forming a third kinematic chain giving a third degree of freedom for positioning the tool. The robot arm also comprises one or more transmission mechanisms that in combination with the outer-arm linkage are arranged to accomplish the controlled orientation of the tool.