This invention can be profitably employed in the fields of medicine and sports in the machines used to strengthen the muscles of the knee and in knee tutors. In its simplest version, the articulated joint is formed by two plates (1, 2) which can move freely on one another; alternatively, one plate (1) or the other (2) can be fastened to a fixed structure by means of a fastener. One of the plates features two openings (2.2, 2.3), where the first (2.2) is located at the center of a plate and is shaped like a rectangle. The second opening (2.3) has a specific shape: at first it is a circumference whose radius is equal to "I"; subsequently, it is a spiral which returns towards the center of the plate (2). The other plate features two pins (1.2 and 1.3), located at a distance "I"; the first pin (1.2) is located in the central position and is inserted into opening the (2.2); the second pin (1.3) is in a peripheral position and is located in the second opening (2.3). Alternatively the plate (2) can be replaced by several overlapping plates (3, 4, 5, 6, 7); the semi-plates are arranged in overlapping couples (4, 7 and 5, 6). The semi-plates (4, 7) are fastened to the plate (3) by means of a pin (4.1) placed in an ideal point of rotation (11) and are therefore free to rotate onto the semi-plates (5, 6).