A device for supporting and adjusting the position of a patient's head during surgeries, comprising: - a supporting structure for resting the device on an application, said supporting structure defining a first axis (e x,W), a second axis (e y,W), and a third axis (e z,W) that are mutually orthogonal, - a mobile platform defining a platform centre (O m) and being constrained to the supporting structure by an adjusting mechanism suitable to position the platform in relation to the supporting structure in a neutral position and to adjust the position of the platform in relation to the supporting structure. - a gripping device connected to the platform and having locking means suitable to lock the head to the gripping device, characterized in that the adjusting mechanism comprises: - a first arm having a first saddle (P 1) slidably connected to the supporting structure along a first trajectory (u 1,1) and positionable along the first trajectory (u 1,1) by a first actuator, as well as a first rod (L 1,1) having a first end rotatably connected to the first saddle (P 1) and a second end rotatably connected to the platform, - a second arm having a second saddle (P 2) slidably connected to the supporting structure along a second trajectory (u 2,1) and positionable along the second trajectory (u 2,1) by a second actuator, as well as a second rod (L 2,1) having a first end rotatably connected to the second saddle (P 2) and a second end rotatably connected to the platform, - a third arm having a third saddle (P 3) slidably connected to the supporting structure along a third trajectory (u 3,1) and positionable along the third trajectory (u 3,1) by a third actuator, as well as a third rod having a first end rotatably connected to the third saddle (P 3) and a second end rotatably connected to the platform, - a fourth arm having a fourth saddle (P 4) slidably connected to the supporting structure along a fourth trajectory (u 4,1) and positionable along the fourth trajectory (u 4,1) by a fourth actuator, as well as a fourth rod (L 4) having a first end rotatably connected to the fourth saddle (P 4) and a second end rotatably connected to the platform, - a fifth arm having a fifth saddle (P 5) slidably connected to the supporting structure along a fifth trajectory (u 5,1) and positionable along the fifth trajectory (u 5,1) by a fifth actuator, as well as a fifth rod (L 5,1) having a first end rotatably connected to the fifth saddle (P 5) and a second end rotatably connected to the platform, - wherein the platform and the first, second, third, fourth, and fifth arms form together an articulated frame displaceable by the first, second, third, fourth, and fifth actuators so that the platform can translate in the direction of the first axis (e x,W), the second axis (e y,W), and the third axis (e z,W) and rotate around the second axis (e y,W) and the third axis ( z,W). - a supporting structure for resting the device on an application, said supporting structure defining a first axis (e x,W), a second axis (e y,W), and a third axis (e z,W) that are mutually orthogonal, - a mobile platform defining a platform centre (O m) and being constrained to the supporting structure by an adjusting mechanism suitable to position the platform in relation to the supporting structure in a neutral position and to adjust the position of the platform in relation to the supporting structure. - a gripping device connected to the platform and having locking means suitable to lock the head to the gripping device, - a first arm having a first saddle (P 1) slidably connected to the supporting structure along a first trajectory (u 1,1) and positionable along the first trajectory (u 1,1) by a first actuator, as well as a first rod (L 1,1) having a first end rotatably connected to the first saddle (P 1) and a second end rotatably connected to the platform, - a second arm having a second saddle (P 2) slidably connected to the supporting structure along a second trajectory (u 2,1) and positionable along the second trajectory (u 2,1) by a second actuator, as well as a second rod (L 2,1) having a first end rotatably connected to the second saddle (P 2) and a second end rotatably connected to the platform, - a third arm having a third saddle (P 3) slidably connected to the supporting structure along a third trajectory (u 3,1) and positionable along the third trajectory (u 3,1) by a third actuator, as well as a third rod having a first end rotatably connected to the third saddle (P 3) and a second end rotatably connected to the platform, - a fourth arm having a fourth saddle (P 4) slidably connected to the supporting structure along a fourth trajectory (u 4,1) and positionable along the fourth trajectory (u 4,1) by a fourth actuator, as well as a fourth rod (L 4) having a first end rotatably connected to the fourth saddle (P 4) and a second end rotatably connected to the platform, - a fifth arm having a fifth saddle (P 5) slidably connected to the supporting structure along a fifth trajectory (u 5,1) and positionable along the fifth trajectory (u 5,1) by a fifth actuator, as well as a fifth rod (L 5,1) having a first end rotatably connected to the fifth saddle (P 5) and a second end rotatably connected to the platform, - wherein the platform and the first, second, third, fourth, and fifth arms form together an articulated frame displaceable by the first, second, third, fourth, and fifth actuators so that the platform can translate in the direction of the first axis (e x,W), the second axis (e y,W), and the third axis (e z,W) and rotate around the second axis (e y,W) and the third axis ( z,W).