‘Kinematics’ is a term often used in orthopaedics, unfortunately not always in the correct sense of the word. The term ‘kinematics’ is derived from mechanical engineering and refers to the relative motion of rigid bodies. In mechanical engineering the description has to be mathematically exact and correct. Tibiofemoral kinematics of the knee is hard to describe unequivocally and mathematically correct. The reason for this is twofold:

As explained, the term kinematics refers to the relative motion of the femur and the tibia. In other words, it describes how the normal knee is moving. This understanding precedes all discussions on pathophysiology, diagnosis and treatment and forms the basis of our clinical work. Also, understanding normal kinematics is mandatory for improving our surgical techniques. A simplified example can make this very clear. Imagine a door with three hinges (Fig. 3.1). One of the hinges is broken (marked with a red star). It is clear that the door has a single axis of rotation, allowing us to open and close it. If we replace the broken hinge with a new hinge, but we put the new hinge outside of the axis of rotation, it is intuitively clear that the door will either not open anymore or, alternatively, the hinge will break. In orthopaedic terms one can translate this, respectively, into a stiff joint or a failed procedure. This example applies equally to ligament and joint replacement surgery.

The study of how the femur moves on the tibia has a long history. The first known description dates back to 1836 when Weber and Weber [1] described the movement on the medial side to be ‘like a cradle’. Since that first description, based upon direct visual observation of a cadaveric specimen, several methods have been used to examine the kinematics of the human knee.

The first radiological study was performed by Zuppinger [2], who stated that the femur rolled back across the tibia during flexion as a result of the so-called rigid four-bar link mechanism provided by the two cruciate ligaments. In 1971, Frankel [3] introduced the concept of the instant centre of rotation to the orthopaedic community. He emphasized that as one link (rigid body) rotates around the other, there is at any given moment in time a point with zero velocity. That point is called the instant centre of rotation (Fig. 3.2).

He concluded that ‘due to the shapes of the bones and the restraints on motion imposed by the ligaments, capsule, and muscles, the instantaneous centres for successive positions of the links of the knee move’.

The initial work by Frankel was carried out by taking ‘true lateral’ X-rays of the knee in patients lying on the side, at discrete intervals of 10–20° in the range of full extension to 90° of flexion. The knee was treated as if it were a ‘planar mechanism’. In other words, the movement of the knee was reduced to a two-dimensional projection of a three-dimensional reality (Fig. 3.3). Menschik introduced in 1974 the concept of the four-bar linkage, representing the cruciate ligaments in two dimensions as two rigid bars and the lines connecting their insertion points on the femur and tibia as the two other rigid bars [4]. The instant centre of rotation is located at the point of intersection of the cruciate ligaments. This ‘rigid four-bar linkage’ was later widely popularized by Müller.

In the years following, the limitations of this methodology became clear, with the major flaw being the inability to ascertain the location of the axes of rotation before performing kinematic analyses [5]. In 1983, Grood and Suntay presented a joint coordinate system providing a geometric description of the three-dimensional rotational and translational motion between two rigid bodies, applied to the knee joint. The main step forward was the definition of a ‘floating axis’. With this model, the described joint displacements became independent of the order in which the component rotations and translations occur [6].

The new mathematical insights led to the concept of the helical axis and opened the door for a correct scientific description of the kinematics of the knee [7]. However, as the mathematical accuracy improved, the complexity increased and the model appeared to be impractical and difficult to apply to the clinical setting: the clinicians failed to understand the engineers.

Hollister, and later Churchill, tried to bridge the gap [8, 9]. Hollister’s model essentially described knee motion as pure rotations occurring around two axes: the so-called flexion-extension axis and the so-called longitudinal rotation axis, with the understanding of the flexion-extension axis not being exactly located in the coronal plane and the longitudinal axis not being exactly located in the sagittal plane [8]. As a consequence, these mathematical ‘simple rotations’ meant in reality flexion-extension, varus-valgus and internal-external rotation of the knee joint, once again confusing the clinician trying to apply this knowledge to the practical setting. Churchill addressed this problem by allowing a mathematical error in the kinematic description, based on a loaded rig experiment with an ankle load of 100 N and a combined hamstrings load of 30 N [9]. They used an optimization technique to identify the locations of the so-called ‘optimal flexion’ and ‘longitudinal rotation’ axes. Knee motion was then described with the following formula: